BrainWave-ML/RL1 · Datasets at Hugging Face

prompt list	ground_truth string
[ { "content": "On segment $AC$, point $B$ is such that $AB = 14$ and $BC = 28$. Semicircles are constructed on segments $AB$, $BC$, and $AC$ as diameters in the same half-plane relative to line $AB$. Determine the radius of the circle that is tangent to all three semicircles.", "role": "user" } ]	6
[ { "content": "Find the limit of the sequence \\(x_n\\) defined by \\(x_1=1\\) and \\(x_{n+1}=2+\\frac{3}{x_n}+\\frac{1}{n}\\).", "role": "user" } ]	3
[ { "content": "Suppose $f$ and $g$ are entire functions and $g(z) \\neq 0$ for all $z \\in \\mathbb{C}$. If $\|f(z)\| \\leq \|g(z)\|$, which of the following must be true about $f$? (a) $f(z) \\neq 0$ for all $z \\in \\mathbb{C}$ (b) $f$ is a constant function (c) $f(0) = 0$ (d) For some $c \\in \\mathbb{C}$, $f(z) = c g(z)$", "role": "user" } ]	D
[ { "content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> reasoning process here </think> <answer> answer here </answer>.", "role": "system" }, { "content": "How do you derive first order half life?", "role": "user" } ]	t_(1/2) = ln2/k
[ { "content": "Determine the number of zeros of the function \\( f(z) = z^2 + \\cosh(iz) \\) within the region \\( \|z\| < \\frac{1}{2} \\).", "role": "user" } ]	0
[ { "content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> reasoning process here </think> <answer> answer here </answer>.", "role": "system" }, { "content": "Suppose ABCD's stock price is currently $60. In the next six months it will either fall to $30 or rise to $80. What is the current value of a six-month call option with an exercise price of $70 using the delta hedging method? The six-month risk-free interest tale is 4% (periodic rate).", "role": "user" } ]	6.23
[ { "content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> reasoning process here </think> <answer> answer here </answer>.", "role": "system" }, { "content": "An average dairy cow produces 10,896 grams of methane gas, {eq}CH_4\n\n{/eq}, each year. What volume of {eq}CH_4\n\n{/eq} is produced at 25 degrees Celsius and 740 mmHg? (Hint: Convert grams to moles of {eq}CH_4\n\n{/eq}.)", "role": "user" } ]	17059 L
[ { "content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> reasoning process here </think> <answer> answer here </answer>.", "role": "system" }, { "content": "A student notice that the molar absorptivity was 504 mL/(mgm). What is the molar absorptivity in units of L/(molcm)? The molar mass of the compound is 210g/mol.", "role": "user" } ]	1050 L/(mol*cm)
[ { "content": "Show that the order of the automorphism group of \\(Z_3 \\times Z_3\\) is 48.", "role": "user" } ]	48
[ { "content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> reasoning process here </think> <answer> answer here </answer>.", "role": "system" }, { "content": "For the reaction {eq}N_2(g)+3H_2(g)<-->2NH_3(g) Kp = 4.20\\times10-3\n\n{/eq} at 339 C . What is K for the reaction at this temperature? Enter your answer numerically.", "role": "user" } ]	1.05e+1
[ { "content": "Consider the function \\(f(x)=\\int_x^{2x}\\frac{\\sin t}{t}dt\\). Determine the value of \\(x\\) on the interval \\((0,\\frac{3\\pi}{2})\\) at which this function attains a local maximum.", "role": "user" } ]	\dfrac{\pi}{3}
[ { "content": "Let $(n_k)$ be an increasing sequence of positive integers. Define $E$ as the set of all $x$ such that the sequence $\\sin(n_k x)$ converges. Prove that the Lebesgue measure of $E$, $\\mu(E)$, is zero.", "role": "user" } ]	0
[ { "content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> reasoning process here </think> <answer> answer here </answer>.", "role": "system" }, { "content": "Charlotte, a 65 kg scuba diver, shoots a 2 kg spear from her speargun with a speed of 15 m/s at a fish who darts quickly away without getting hit.\n\nWhat is Charlotte's recoil velocity?", "role": "user" } ]	0.46 m/s
[ { "content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> reasoning process here </think> <answer> answer here </answer>.", "role": "system" }, { "content": "A roller coaster (358 kg) moves from A (1.19 m above the ground) to B (26.2 m above the ground). Two non-conservative forces are present: friction does {eq}-2.12 \\times 10^4\\ J\n\n{/eq} of work on the car, and a chain mechanism does {eq}+5.09 \\times 10^4\\ J\n\n{/eq} of work to help the car up a long climb. What is the change in the car's kinetic energy {eq}KE_f - KE_i\n\n{/eq} from A to B?", "role": "user" } ]	-5.81e4 J
[ { "content": "Is there a Hausdorff compactification of the irrational numbers with its usual topology such that the remainder is a discrete space?", "role": "user" } ]	No
[ { "content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> reasoning process here </think> <answer> answer here </answer>.", "role": "system" }, { "content": "How to calculate momentum after a collision?", "role": "user" } ]	The total momentum after a collision is equal to the total momentum before the collision. For two objects in an elastic collision: p_{1i} + p_{2i} = p_{1f} + p_{2f}. For an inelastic collision: p_{1i} + p_{2i} = p_f, where p_f is the momentum of the combined object.
[ { "content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> reasoning process here </think> <answer> answer here </answer>.", "role": "system" }, { "content": "The Mundell-Fleming model takes the world interest rate r* as an exogenous variable. Briefly explain the two factors that can cause the world interest rate to change.", "role": "user" } ]	Changes in the policies of large open economies and changes in current account balances or terms of trade can cause changes in the world interest rate.
[ { "content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> reasoning process here </think> <answer> answer here </answer>.", "role": "system" }, { "content": "The objects listed below are placed at the top of a ramp, and roll down to the bottom without slipping. Assuming that there in no air resistance, rank them in order from fastest average rolling speed to slowest. bowling\n\nball\n\nhollow\n\nglobe\n\npenny\n\nwedding\n\nring", "role": "user" } ]	bowling ball > penny > hollow globe > wedding ring
[ { "content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> reasoning process here </think> <answer> answer here </answer>.", "role": "system" }, { "content": "An investment offers a 15.5 percent total return over the coming year. Bill Bernanke thinks the total real return on this investment will be only 6.5 percent. What does Bill believe the inflation rate will be over the next year?\n\na. 10.99%\n\nb. 8.45%\n\nc. 9.72%\n\nd. -7.79%\n\ne. 5.92%", "role": "user" } ]	8.45%
[ { "content": "Let $X \\subset \\mathbb{R}^n$ be a bounded and connected set, and let $f: X \\to \\mathbb{R}$ be a polynomial function. Consider a point $x \\in X$ and the nearest global maximum $m \\in X$ to $x$. Suppose that in every neighborhood of $x$, there exists a point $y$ and a path $p_t$ such that $p_0 = y$, $p_1 = m$, and for every $t < t'$, $f(p_t) < f(p_{t'})$ and $d(x, p_t) < d(x, p_{t'})$. Does this imply that $x$ is not a local maximum of $f$?", "role": "user" } ]	Yes
[ { "content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> reasoning process here </think> <answer> answer here </answer>.", "role": "system" }, { "content": "Your energy bill is expected to be $250 next month (month 1) and is expected to grow at 0.64% per month for the foreseeable future (aka forever), after your utility provider ran into financial trouble. You read recently that installing solar panels on your roof will reduce your energy bill by 20% (so month 1 would be $200) and decrease the growth of the bill to 0.23% per month for the foreseeable future. Assuming this is true, that you plan to stay in the house for the foreseeable future, and that the applicable discount rate is 11% per year, from a pure financial perspective what is the most you d be willing to pay today to have solar panels installed immediately? Assume the panels could be installed quickly and the cost savings would start in month 1.", "role": "user" } ]	$61,235.23
[ { "content": "Let $n$ be an odd integer with exactly 11 positive divisors. Find the number of positive divisors of $8n^3$.", "role": "user" } ]	124
[ { "content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> reasoning process here </think> <answer> answer here </answer>.", "role": "system" }, { "content": "The rate constant for this first-order reaction is 0.0770 s{eq}^{-1}\n\n{/eq} at 400 degrees Celsius.\n\n{eq}A \\to \\text{products}\n\n{/eq}\n\nAfter how many seconds will 19.3% of the reactant remain?", "role": "user" } ]	21.4 seconds
[ { "content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> reasoning process here </think> <answer> answer here </answer>.", "role": "system" }, { "content": "A conical water tank, vertex down, is filled with water. If the tank has a radius of 8 feet and height 10 feet, find the work required to pump the water {eq}(p = 62.4~lb/ft^3)\n\n{/eq} to top of the tank.", "role": "user" } ]	313656.6105
[ { "content": "Suppose $f(x, y)$ is defined on some neighbourhood of $(0, 0)$. If $u(x, y) = \\sin f(x, y)$ is continuous at $(0, 0)$, does it imply that $f(x, y)$ is continuous at $(0, 0)$? Provide a justification for your answer.", "role": "user" } ]	No
[ { "content": "Determine whether the set \\(I_3 = \\{[a,b) \\times [c,d) \\times [e,f) \\mid a,b,c,d,e,f\\in\\Bbb{R}\\}\\) forms a semiring over \\(\\Bbb{R}^3\\).", "role": "user" } ]	Yes
[ { "content": "Given the quadratic equations \\(x^2 - 10ax - 11b = 0\\) with roots \\(c\\) and \\(d\\), and \\(x^2 - 10cx - 11d = 0\\) with roots \\(a\\) and \\(b\\), find the value of \\(a + b + c + d\\).", "role": "user" } ]	1210
[ { "content": "Determine the value of $r$ that maximizes the expression: $$\\sum_{k=0}^{r} \\binom{20}{r-k} \\binom{20}{k}.$$", "role": "user" } ]	20
[ { "content": "Christine must buy at least $45$ fluid ounces of milk at the store. The store only sells milk in $200$ milliliter bottles. If there are $33.8$ fluid ounces in $1$ liter, then what is the smallest number of bottles that Christine could buy? (You may use a calculator on this problem.)", "role": "user" } ]	7
[ { "content": "Consider 9 distinct apples and 7 distinct bananas to be placed into 6 identical bins. Determine the number of ways to configure the bins such that exactly one bin contains 5 apples, exactly one bin contains 3 bananas, and the remaining 4 bins each contain 1 apple and 1 banana. Provide your answer as a single number.", "role": "user" } ]	105840
[ { "content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> reasoning process here </think> <answer> answer here </answer>.", "role": "system" }, { "content": "Calculate the mass (in mg) of solid chromium(III) nitrate needed to make 250 mL of an aqueous solution with a pH of 4.00. The {eq}K_a\n\n{/eq} of {eq}Cr(H_2O)_6^{3+}\n\n{/eq} is {eq}1.0 \\times 10^{-4}\n\n{/eq}.", "role": "user" } ]	12 mg
[ { "content": "Let \\( S = \\{ x \\in \\mathbb{R} : 2x^2 \\cos\\frac{1}{x} = 1 \\} \\) and \\( T = \\{ x \\in \\mathbb{R} : 2x^2 \\cos\\frac{1}{x} \\leq 1 \\} \\cup \\{0\\} \\). Under the usual metric on \\( \\mathbb{R} \\), which of the sets \\( S \\) or \\( T \\) is complete?", "role": "user" } ]	T
[ { "content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> reasoning process here </think> <answer> answer here </answer>.", "role": "system" }, { "content": "A stock is trading for 43, and just paid a dividend of 1.0 which is expected to grow at a fraction 0.18 per year. If Goldman Sacs charges a fraction 0.18 as a flotation cost, what is the required rate of return on the new stock issued?", "role": "user" } ]	21.34%
[ { "content": "If $\\sin x + \\sin y = \\frac{96}{65}$ and $\\cos x + \\cos y = \\frac{72}{65}$, then what is the value of $\\tan x + \\tan y$?", "role": "user" } ]	\frac{507}{112}
[ { "content": "Calculate the limit \\( \\lim_{n \\to \\infty}\\frac{\\sqrt[n]{(2n)!}}{2n} \\) using Stirling's approximation.", "role": "user" } ]	\infty
[ { "content": "Evaluate the contour integral \\( \\oint_{C_3 (0)} \\frac{z+7}{z^4 + z^3 - 2 z^2}\\,dz \\) using the Residue Theorem, where \\(C_3(0)\\) is the circle of radius 3 centered at the origin, oriented counter-clockwise.", "role": "user" } ]	0
[ { "content": "What is the largest $4$ digit integer congruent to $15 \\pmod{22}?$", "role": "user" } ]	9981
[ { "content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> reasoning process here </think> <answer> answer here </answer>.", "role": "system" }, { "content": "Nike, Inc. reported the following plant assets and intangible assets for the year ended May 31, 2007 (in millions):\n\nother plant assets: $767.2\n\nland $193.8; patents and trademarks (at cost): $115.5\n\nmachinery and equipment: $1,817.2\n\nbuildings: $840.9\n\ngoodwill (at cost): $130.8\n\naccumulated amortization: $47.1\n\naccumulated depreciation: $1,940.8\n\nPrepare a partial balance sheet for Nike for these items.", "role": "user" } ]	Partial Balance Sheet Intangible Assets: Patents and Trademarks (at cost) $115.5 Goodwill (at cost) $130.8 Less: Accumulated Amortization $47.1 Total Intangible Assets $199.2 Plant Assets: Other Plant Assets $767.2 Land $193.8 Machinery and Equipment $1,817.2 Buildings $840.9 Less: Accumulated Depreciation $1,940.8 Total Plant Assets $678.3 Total Plant and Intangible Assets $1,877.5
[ { "content": "Evaluate the limit: $$\\lim_{u\\to 0}\\frac{(u+1)^2\\sin(3u-3)}{\\cos(u^3+u-1)\\sin^2(u^2-u)}.$$", "role": "user" } ]	-\infty
[ { "content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> reasoning process here </think> <answer> answer here </answer>.", "role": "system" }, { "content": "At STP a gas occupies a 69.5 kiloliter balloon. How many mol of the gas must be in the balloon?", "role": "user" } ]	3102.67 mole
[ { "content": "Let \\( a_{n} \\) be the coefficient of the \\( x \\) term in the expansion of \\( (3-\\sqrt{x})^{n} \\) for \\( n=2,3,4, \\cdots \\). Find \\( \\lim _{n \\rightarrow \\infty}\\left(\\frac{3^{2}}{a_{2}}+\\frac{3^{3}}{a_{3}}+\\cdots+\\frac{3^{n}}{a_{n}}\\right) \\).", "role": "user" } ]	18
[ { "content": "Suppose $A \\subset \\mathbb{R}^2$ is an open subset such that there exist infinitely many homeomorphisms that, when restricted to $A$, give self-maps that are also homeomorphisms. Does it follow that $A$ is an open disc?", "role": "user" } ]	No
[ { "content": "Given a matrix where the value at each index is determined by the XOR operation between the column and row indices, and a fixed amount is subtracted from each element (ensuring non-negative results), calculate the sum of all elements in the matrix. For example, consider a matrix with 5 rows and 8 columns:\n\n\\[\n\\begin{bmatrix}\n0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 \\\\\n1 & 0 & 3 & 2 & 5 & 4 & 7 & 6 \\\\\n2 & 3 & 0 & 1 & 6 & 7 & 4 & 5 \\\\\n3 & 2 & 1 & 0 & 7 & 6 & 5 & 4 \\\\\n4 & 5 & 6 & 7 & 0 & 1 & 2 & 3 \\\\\n\\end{bmatrix}\n\\]\n\nAfter subtracting a fixed amount from each element (ensuring non-negative results), the matrix becomes:\n\n\\[\n\\begin{bmatrix}\n0 & 0 & 1 & 2 & 3 & 4 & 5 & 6 \\\\\n0 & 0 & 2 & 1 & 4 & 3 & 6 & 5 \\\\\n1 & 2 & 0 & 0 & 5 & 6 & 3 & 4 \\\\\n2 & 1 & 0 & 0 & 6 & 5 & 4 & 3 \\\\\n3 & 4 & 5 & 6 & 0 & 0 & 1 & 2 \\\\\n\\end{bmatrix}\n\\]\n\nFind the sum of all elements in the modified matrix.", "role": "user" } ]	105
[ { "content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> reasoning process here </think> <answer> answer here </answer>.", "role": "system" }, { "content": "Dewitt Industries has adopted the following production budget for the first 4 months of 2017.\n\n \n \n \n Month \n Units \n \n \n \n \n January \n 10,240 \n \n \n February \n 8,340 \n \n \n March \n 5,150 \n \n \n April \n 4,130 \n \n \n\n\nEach unit requires 3 pounds of raw materials costing {eq}\\$2\n\n{/eq} per pound. On December 31, 2016, the ending raw materials inventory was 6,144 pounds. Management wants to have a raw materials inventory at the end of the month equal to {eq}20\\%\n\n{/eq} of next month's production requirements.\n\nPrepare a direct materials purchases budget by month for the first quarter.", "role": "user" } ]	$135,048
[ { "content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> reasoning process here </think> <answer> answer here </answer>.", "role": "system" }, { "content": "Physical Phitness, Inc., operates three divisions, Weak, Average, and Strong. As it turns out, the Weak division has the lowest operating income, and the president wants to close it. \"Survival of the fittest, I say!\" was his response when the Weak division's manager insisted that his division earned money for the company. Following is the most recent financial analysis for each division:\n\n \n \n \n \n Weak \n Average \n Strong \n \n \n Sales \n $125,600 \n $349,200 \n $543,800 \n \n \n Variable expenses \n 52,500 \n 198,700 \n 309,600 \n \n \n Contribution margin \n 73,100 \n 150,500 \n 234,200 \n \n \n Direct expenses \n 37,400 \n 75,100 \n 117,000 \n \n \n Allocated expenses \n 52,100 \n 52,100 \n 52,100 \n \n \n Operating income \n $(16,400) \n $23,300 \n $65,100 \n \n \n\n\nBy how much would total income change if the Weak division were dropped?", "role": "user" } ]	$35,700
[ { "content": "In an equilateral triangle \\(\\triangle ABC\\) with side length 4, point \\(D\\) is located on side \\(BC\\) such that \\(BD = 1\\). Let \\(r\\) and \\(s\\) be the radii of the inscribed circles of triangles \\(\\triangle ADB\\) and \\(\\triangle ADC\\), respectively. Calculate the product \\(rs\\).", "role": "user" } ]	4 - \sqrt{13}
[ { "content": "Given the polynomial \\(x^4 + px^3 + qx^2 + rx + s = 0\\) with rational coefficients and four complex roots, two of the roots add up to \\(3 + 4i\\) and the other two have a product of \\(13-i\\). Compute the value of \\(q\\).", "role": "user" } ]	51
[ { "content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> reasoning process here </think> <answer> answer here </answer>.", "role": "system" }, { "content": "A horizontal vinyl record of radius 0.13 m rotates about a vertical axis through its center with an angular speed of 4.7 rad/s. The rotational inertia of the record about its axis of rotation is {eq}5.0 \\times 10^{-4} \\ {\\rm kgm^2}\n\n{/eq}. A wad of putty of mass 0.020 kg drops vertically onto the record from above and sticks to the edge of the record. What is the angular speed of the record immediately after the putty sticks to it?", "role": "user" } ]	2.80 kgm^2/s
[ { "content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> reasoning process here </think> <answer> answer here </answer>.", "role": "system" }, { "content": "The following information pertains to the Moline Facility for the month of May (all materials are added at the beginning of the process):\n\n \n \n \n \n Units \n Material Costs \n \n \n Beginning work in process \n 70,000 \n $30,000 \n \n \n Started in May \n 250,000 \n 103,400 \n \n \n Units completed \n 235,000 \n \n \n \n Ending work in process \n 85,000 \n \n \n \n\n\nCompute the cost per equivalent unit for materials using the FIFO method.", "role": "user" } ]	$0.42
[ { "content": "Determine the values of $p \\geq 0$ for which the integral \\( \\int_0^{\\infty} \\frac{dx}{x^{p}+x^{-p}} \\) converges.", "role": "user" } ]	p > 1
[ { "content": "Find the maximum volume of a rectangular solid in the first octant ($x \\geq 0$, $y \\geq 0$, $z \\geq 0$) with one vertex at the origin and the opposite vertex lying on the plane $x + y + z = 1$. Use the method of Lagrange multipliers to derive the system of equations needed to solve for the maximum volume.", "role": "user" } ]	\dfrac{1}{27}
[ { "content": "Find the orthogonal complement of the subset \\( C = \\{ u \\in L^2(0,2) : \\int_0^2 u(t) \\, dt = 1 \\} \\) in the space \\( L^2(0,2) \\).", "role": "user" } ]	\{0\}
[ { "content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> reasoning process here </think> <answer> answer here </answer>.", "role": "system" }, { "content": "Carotenoids, present in all organisms capable of photosynthesis, extend the range of light absorbed by the organism. They exhibit the maximal capacity for absorption of light in the range of 440-470 nm. Calculate the energy in kilojoules represented by absorption of an Avogadro's number of photons of wavelength 460 nm.", "role": "user" } ]	2.60e+05 J
[ { "content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> reasoning process here </think> <answer> answer here </answer>.", "role": "system" }, { "content": "A solution of aqueous nitric acid contains 5.00% nitric acid by mass. Calculate the molarity of the solution. The molar mass of nitric acid is 61.01 g/mol.", "role": "user" } ]	0.820 mol/L
[ { "content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> reasoning process here </think> <answer> answer here </answer>.", "role": "system" }, { "content": "Where are critical biodiversity hotspots located?", "role": "user" } ]	Critical biodiversity hotspots are located across the globe, spanning Africa, Asia-Pacific, Europe and Central Asia, North and Central America, and South America. Examples include the Cape Floristic Region, Madagascar and the Indian Ocean Islands, Japan, the forests of Eastern Australia, the Mediterranean Basin, Madrean pine-oak woodlands, the Atlantic forest, and the tropical Andes.
[ { "content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> reasoning process here </think> <answer> answer here </answer>.", "role": "system" }, { "content": "A student kept her 60-watt, 120-volt study lamp turned on from {eq}2:00 \\, \\mathrm{PM}\n\n{/eq} until {eq}6:00 \\, \\mathrm{PM}\n\n{/eq}. How many coulombs of charge went through it?", "role": "user" } ]	7200 C
[ { "content": "Find the Fourier series representation of the function \\(W(t)\\) given by:\n\\[\nW(t) = \\begin{cases} 2, & \\text{for } -2 \\leq t < 4 \\\\ 0, & \\text{otherwise} \\end{cases}\n\\]\nUse the formulas for \\(a_n\\) and \\(b_n\\) extended for an interval of length \\(2l\\).", "role": "user" } ]	2
[ { "content": "Solve the inequality $$-13(r+5) + 25 > 4(r-10)$$for $r$. Express your answer in interval notation.", "role": "user" } ]	(-\infty,0)
[ { "content": "Determine whether there exists a Lebesgue measurable set $D \\supset [0,1]$ such that $D \\neq [0,1]$ and $\\lambda^{*}(D) = 1$. Provide a justification for your answer.", "role": "user" } ]	Yes
[ { "content": "Determine the spectrum of the $C^*$-algebra formed by the direct sum $C(K) \\oplus C(K')$, where $K$ and $K'$ are compact Hausdorff spaces.", "role": "user" } ]	K \sqcup K'
[ { "content": "Let $X$ be a metric space and let $U, V \\subset X$ be open and bounded subsets. Is the Hausdorff metric \\( h(U,V) = \\max(\\sup_{x\\in U}\\inf_{y\\in V}d(x,y),\\sup_{x\\in V}\\inf_{y\\in U}d(x,y)) \\) defined for all possible choices of $U$ and $V$?", "role": "user" } ]	Yes
[ { "content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> reasoning process here </think> <answer> answer here </answer>.", "role": "system" }, { "content": "A motorist drives south at 20m/s for 3 mins, then turns west and travels at 25m/s for 2 mins, and finally travels northeast at 30m/s for 1min. For this 6 min trip, find the total vector displacement.", "role": "user" } ]	2898 m from origin at an angle 233.4 degrees from the positive x-axis
[ { "content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> reasoning process here </think> <answer> answer here </answer>.", "role": "system" }, { "content": "How does an infinite geometric series apply to being pushed on a swing?", "role": "user" } ]	21 m
[ { "content": "Find \\(\\lim\\limits_{x\\to +\\infty} \\frac{x^{2}e^{-x}}{x^{2}+1}\\sin(xe^{x^{2}})\\).", "role": "user" } ]	0
[ { "content": "Does the uniform convergence of a sequence of Lipschitz continuous functions imply that the limit function is also Lipschitz continuous?", "role": "user" } ]	No
[ { "content": "Suppose we have \\(n\\) independent variables from \\(U[0,1+\\theta]\\) and let \\(\\lambda=1+\\theta\\). The estimator of \\(\\theta\\) is given by \\(\\bar{\\theta}=2 \\bar{X} - 1\\). Find the bias of \\(\\bar{\\theta}\\) given that the distribution of \\(\\bar{X}\\) for \\(n\\) variables from \\(U[0,1]\\) is the Bates distribution.", "role": "user" } ]	0
[ { "content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> reasoning process here </think> <answer> answer here </answer>.", "role": "system" }, { "content": "Mitchell Company had the following budgeted sales for the first half of next year:\n\n \n \n \n \n Cash Sales \n Credit Sales \n \n \n January \n $90,000 \n $190,000 \n \n \n February \n $95,000 \n $210,000 \n \n \n March \n $52,000 \n $170,000 \n \n \n April \n $57,000 \n $152,000 \n \n \n May \n $67,000 \n $240,000 \n \n \n June \n $120,000 \n $420,000 \n \n \n\n\nThe company is in the process of preparing a cash budget and must determine the expected cash collections by month. To this end, the following information has been assembled.\n\n \n \n \n Collections on credit sales: \n \n \n 50% in month of sales \n \n \n 25% in month of following sales \n \n \n 25.0% in second month following sales \n \n \n\n\nAssume that the accounts receivable balance on January 1 was $68,000. Of this amount, $46,000 represented uncollected December sales and $22,000 represented uncollected November sales. Given these data the total cash collected during January would be:", "role": "user" } ]	$230,000
[ { "content": "Simplify the expression: \\[ \\frac{\\left(a^{2} b \\sqrt{b}-6 a^{5 / 3} b^{5 / 4}+12 a b \\sqrt[3]{a}-8 a b^{3 / 4}\\right)^{2 / 3}}{a b \\sqrt[3]{a}-4 a b^{3 / 4}+4 a^{2 / 3} \\sqrt{b}} \\]", "role": "user" } ]	1
[ { "content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> reasoning process here </think> <answer> answer here </answer>.", "role": "system" }, { "content": "A light meter reports that a camera setting of 1/500 s at f/1.0 will give a correct exposure. But the photographer wishes to use f/22 to increase the depth of the field. what should the shutter speed be?", "role": "user" } ]	0.968 s
[ { "content": "Find the Shnirelman density of the set \\( A = \\{ \\lfloor n \\ln (n) \\rfloor : n = 1,2,3,... \\} \\).", "role": "user" } ]	0
[ { "content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> reasoning process here </think> <answer> answer here </answer>.", "role": "system" }, { "content": "Apple Inc has a beta of 1.35. The tax rate is 40%, and Apple is financed with 30% debt. What is Apple's unlevered beta?", "role": "user" } ]	1.073
[ { "content": "Calculate the circulation of the vector field \\( \\vec{F}(x, y, z) = \\langle \\sin(x^2+z)-2yz, 2xz + \\sin(y^2+z), \\sin(x^2+y^2)\\rangle \\) along the circle parameterized by \\( \\vec{r}(t)=\\langle\\cos(t), \\sin(t), 1\\rangle \\) for \\( t \\in [0, 2\\pi] \\). Use Stoke's Theorem to evaluate the integral.", "role": "user" } ]	4\pi
[ { "content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> reasoning process here </think> <answer> answer here </answer>.", "role": "system" }, { "content": "Determine what is the increase in volume (in {eq}cm^3\n\n{/eq}) of an Aluminum sphere with a radius of 11.1 cm when it is heated from {eq}0^oC{/eq} to {eq}80^oC{/eq}?", "role": "user" } ]	34 cm^3
[ { "content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> reasoning process here </think> <answer> answer here </answer>.", "role": "system" }, { "content": "A vertical right circular cylindrical tank measures 28 ft high and 8 ft in diameter. It is full of liquid weighing {eq}62.4 1b / ft^3\n\n{/eq}. How much work does it take to pump the liquid to the level of the top of the tank?\n\nThe amount of work required is ft-1b.", "role": "user" } ]	1229534 ft-lb
[ { "content": "If $\\frac{1}{x} + \\frac{1}{y} = 3$ and $\\frac{1}{x} - \\frac{1}{y} = -7$ what is the value of $x + y$? Express your answer as a common fraction.", "role": "user" } ]	-\frac{3}{10}
[ { "content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> reasoning process here </think> <answer> answer here </answer>.", "role": "system" }, { "content": "A 60.0 gram lead bullet hits a steel plate, both initially at 28 degrees C. The bullet melts and splatters on impact. Assuming that the bullet receives 82% of its kinetic energy as heat energy, at what minimum speed must it be traveling to melt on impact? (The melting temperature of Lead is 327 degrees C)", "role": "user" } ]	385.635 m/s
[ { "content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> reasoning process here </think> <answer> answer here </answer>.", "role": "system" }, { "content": "A car is moving at 53 miles per hour. The kinetic energy of that car is 5 {eq}\\times\n\n{/eq} 10{eq}^5\n\n{/eq} J. How much energy does the same car have when it moves at 102 miles per hour? Answer in units of J.", "role": "user" } ]	1.85 * 10^6 J
[ { "content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> reasoning process here </think> <answer> answer here </answer>.", "role": "system" }, { "content": "If T-bills pay 2% per six months and the semiannual dividend yield is 1%, what is the parity value of the futures price? (Do not round intermediate calculations.)", "role": "user" } ]	$1.01
[ { "content": "Twenty-seven solid gold spherical beads each of radius 3 are melted down and recast into a larger, solid gold sphere. How many units are in the radius of this larger gold sphere?", "role": "user" } ]	9
[ { "content": "An $\\textit{annulus}$ is the region between two concentric circles. The concentric circles in the figure have radii $b$ and $c$, with $b>c$. Let $\\overline{OX}$ be a radius of the larger circle, let $\\overline{XZ}$ be tangent to the smaller circle at $Z$, and let $\\overline{OY}$ be the radius of the larger circle that contains $Z$. Let $a=XZ$, $d=YZ$, and $e=XY$. What is the area of the annulus? Express your answer in terms of $\\pi$ and at most one of the variables $a,b,c,d,e$.\n\n[asy]\npair O,X,Y,Z;\nO=(0,0);\nX=(16,12);\nY=(0,20);\nZ=(0,12);\nfill(Circle(0,20),gray(0.7));\nfill(Circle(0,12),white);\ndraw(Circle(O,20),linewidth(0.7));\ndraw(Circle(O,12),linewidth(0.7));\ndot(O);\ndot(X);\ndot(Y);\ndot(Z);\ndraw(O--X--Y--cycle,linewidth(0.7));\ndraw(Z--X,linewidth(0.7));\nlabel(\"$b$\",(8,6),SE);\nlabel(\"$a$\",(8,12),S);\nlabel(\"$e$\",(8,16),SW);\nlabel(\"$c$\",(0,6),W);\nlabel(\"$d$\",(0,16),W);\nlabel(\"$O$\",O,S);\nlabel(\"$X$\",X,NE);\nlabel(\"$Y$\",Y,N);\nlabel(\"$Z$\",Z,SW);\n[/asy]", "role": "user" } ]	\pi a^2
[ { "content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> reasoning process here </think> <answer> answer here </answer>.", "role": "system" }, { "content": "Calculate the amount of energy (in kJ) necessary to convert 317 g of liquid water from {eq}0^{\\circ }C\n\n{/eq} to water vapor at {eq}177^{\\circ }C.\n\n{/eq} The molar heat of vaporization ({eq}H_{vap}\n\n{/eq} ) of water is 40.79 kJ/mol. The specific heat for water Is 4.184 J/g. {eq}^{\\circ }C\n\n{/eq}, and for steam is 1.99 J/g{eq}.^{\\circ }C.\n\n{/eq}\n\n(Assume that the specific heat values do not change over the range of temperatures in the problem.)\n\n_____ KJ", "role": "user" } ]	897.63 kJ
[ { "content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> reasoning process here </think> <answer> answer here </answer>.", "role": "system" }, { "content": "X Company makes two products, A and B, and uses an activity-based costing overhead allocation system, with three cost pools and three cost drivers.\n\nBudgeted costs and driver information for 2015 were as follows :\n\n\n Cost Pool 1 Cost Pool 2 Cost Pool 3\n Budgeted costs $108,000 $54,000 $25,000\n Cost Drivers \n Product A 77,200 60,500 68,800\n Product B 76,100 52,400 52,800\nWhat was the allocation to Product A? (round overhead rates to the nearest cent).", "role": "user" } ]	$97,469.33
[ { "content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> reasoning process here </think> <answer> answer here </answer>.", "role": "system" }, { "content": "SCI just paid a dividend of $1.20 per share, and its annual dividend is expected to grow at a constant rate of 2.50% per year. SCI's expected stock price one year from today will be _____ per share.", "role": "user" } ]	$17.63
[ { "content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> reasoning process here </think> <answer> answer here </answer>.", "role": "system" }, { "content": "Is the doctrine that a business ought to be MAXIMIZING profits one arising from law or one derived from modern economics?", "role": "user" } ]	modern economics
[ { "content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> reasoning process here </think> <answer> answer here </answer>.", "role": "system" }, { "content": "How much lithium metal is needed to react with 15 grams of {eq}CH_3CH_2I\n\n{/eq} using a 15% excess of lithium to make methyllithium?\n\n{eq}CH_3CH_2I + Li \\to LiCH_2CH_3 + LiI\n\n{/eq}", "role": "user" } ]	1.54 g
[ { "content": "Let $X_1, X_2, X_3$ be independent and identically distributed random variables, each following a uniform distribution on the interval (0, 1). Calculate the expected value of the expression $E\\left(\\frac{X_1 + X_2}{X_1 + X_2 + X_3}\\right)$. What is the value?", "role": "user" } ]	\dfrac{2}{3}
[ { "content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> reasoning process here </think> <answer> answer here </answer>.", "role": "system" }, { "content": "Book Depot Inc sells on term 2/15, net 55. What is the implicit cost of trade credit under these terms ? Use a 365 day year.", "role": "user" } ]	18.62%
[ { "content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> reasoning process here </think> <answer> answer here </answer>.", "role": "system" }, { "content": "In a diesel engine, the piston compresses air at 305?K to a volume that is 0.0624 of the original volume and a pressure that is 48.5 times the original pressure. What is the temperature of the air after the compression?", "role": "user" } ]	923.05K
[ { "content": "Determine the possible leading digits that both $2^n$ and $5^n$ can have for certain natural numbers $n$. (The 14th All-Russian Mathematical Olympiad, 1988)", "role": "user" } ]	3
[ { "content": "Solve the congruence \\(x^3 + 2x + 2 \\equiv 0 \\pmod{125}\\) using Hensel's Lemma.", "role": "user" } ]	113
[ { "content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> reasoning process here </think> <answer> answer here </answer>.", "role": "system" }, { "content": "Classify the bond in NBr{eq}_3\n\n{/eq} as ionic or covalent.", "role": "user" } ]	covalent
[ { "content": "Calculate the average arc length between two randomly selected points on a sphere with a radius of 2.", "role": "user" } ]	\pi
[ { "content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> reasoning process here </think> <answer> answer here </answer>.", "role": "system" }, { "content": "A rigid cylinder contains 9.0 g of nitrogen at 20 {eq}^\\circ\n\n{/eq}C.\n\nWhat is the minimum amount of heat energy that must be removed to liquify the nitrogen?", "role": "user" } ]	3.22 kJ
[ { "content": "Stuart has drawn a pair of concentric circles, as shown. He draws chords $\\overline{AB}$, $\\overline{BC}, \\ldots$ of the large circle, each tangent to the small one. If $m\\angle ABC=75^\\circ$, then how many segments will he draw before returning to his starting point at $A$? [asy]\nsize(100); defaultpen(linewidth(0.8));\nreal rad1 = 1/Sin(37.5);\ndraw(Circle(origin,1)); draw(Circle(origin,rad1));\npair A = rad1dir(190), B = rad1dir(190 + 105), C = rad1dir(190 + 2105), D = rad1*dir(190 + 315);\ndraw(A--B--C--D,EndArrow(size=5));\nlabel(\"$A$\",A,W); label(\"$B$\",B,S); label(\"$C$\",C,E);\n[/asy]", "role": "user" } ]	24
[ { "content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> reasoning process here </think> <answer> answer here </answer>.", "role": "system" }, { "content": "Calculate the present value of the following payment stream, discounted at 6% annually: $1,500 at the end of year 1, $3,000 at the end of year 2, and $4,500 at the end of year 3.", "role": "user" } ]	$7,863.38
[ { "content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> reasoning process here </think> <answer> answer here </answer>.", "role": "system" }, { "content": "Assume that the market demand is given by P(Q) = 100 - Q and that the cost functions of the two firms in the industry are: {eq}C_i(q_i) = $20 q_i, i = 1,2\n\n{/eq}.\n\nCalculate the output of cash firm, the market price, and the profits of each firm that correspond to the Nash-Cournot equilibrium.", "role": "user" } ]	q1 = 80/3 q2 = 80/3 P = $46.67 Profit1 = $711.2 Profit2 = $711.2
[ { "content": "Evaluate the Fourier coefficient \\( \\hat{f}_k \\) for the function \\( f(t) = \\frac{1-r^2}{1+r^2-2r\\cos t} \\) where \\( t \\in \\mathbb{R} \\) and \\( \|r\| < 1/2 \\). Verify that the correct result is \\( \\hat{f}_k = r^{\|k\|} \\).", "role": "user" } ]	r^{\|k\|}
[ { "content": "Determine the range of values for \\( k \\) such that the equation \\( x^4 - 14x^2 + 24x - k = 0 \\) has four real and unequal roots.", "role": "user" } ]	(8, 11)
[ { "content": "In triangle $ABC$ with sides $AB=1$, $BC=\\sqrt{3}$, and $AC=2$, points $D$, $E$, and $F$ are located on $AB$, $BC$, and $AC$ respectively, such that $\\angle EDF = \\angle DFA = 90^{\\circ}$. If the maximum possible value of $[DEF]^2$ can be expressed as $\\frac{a}{b}$, where $a$ and $b$ are positive integers with $\\gcd(a, b) = 1$, find $a + b$. (Here $[DEF]$ denotes the area of triangle $DEF$.)", "role": "user" } ]	67
[ { "content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> reasoning process here </think> <answer> answer here </answer>.", "role": "system" }, { "content": "A spring-like trampoline dips down 0.08 m when a particular person stands on it. If this person jumps up to a height of 0.26 m above the top of the trampoline, how far with the trampoline compress when the person lands?", "role": "user" } ]	0.204 m

[ { "content": "On segment $AC$, point $B$ is such that $AB = 14$ and $BC = 28$. Semicircles are constructed on segments $AB$, $BC$, and $AC$ as diameters in the same half-plane relative to line $AB$. Determine the radius of the circle that is tangent to all three semicircles.", "role": "user" } ]

6

[ { "content": "Find the limit of the sequence \$x_n\$ defined by \$x_1=1\$ and \$x_{n+1}=2+\\frac{3}{x_n}+\\frac{1}{n}\$.", "role": "user" } ]

3

[ { "content": "Suppose $f$ and $g$ are entire functions and $g(z) \\neq 0$ for all $z \\in \\mathbb{C}$. If $|f(z)| \\leq |g(z)|$, which of the following must be true about $f$? (a) $f(z) \\neq 0$ for all $z \\in \\mathbb{C}$ (b) $f$ is a constant function (c) $f(0) = 0$ (d) For some $c \\in \\mathbb{C}$, $f(z) = c g(z)$", "role": "user" } ]

D

[ { "content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> reasoning process here </think> <answer> answer here </answer>.", "role": "system" }, { "content": "How do you derive first order half life?", "role": "user" } ]

t_(1/2) = ln2/k

[ { "content": "Determine the number of zeros of the function \$ f(z) = z^2 + \\cosh(iz) \$ within the region \$ |z| < \\frac{1}{2} \$.", "role": "user" } ]

0

[ { "content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> reasoning process here </think> <answer> answer here </answer>.", "role": "system" }, { "content": "Suppose ABCD's stock price is currently $60. In the next six months it will either fall to $30 or rise to $80. What is the current value of a six-month call option with an exercise price of $70 using the delta hedging method? The six-month risk-free interest tale is 4% (periodic rate).", "role": "user" } ]

6.23

[ { "content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> reasoning process here </think> <answer> answer here </answer>.", "role": "system" }, { "content": "An average dairy cow produces 10,896 grams of methane gas, {eq}CH_4\n\n{/eq}, each year. What volume of {eq}CH_4\n\n{/eq} is produced at 25 degrees Celsius and 740 mmHg? (Hint: Convert grams to moles of {eq}CH_4\n\n{/eq}.)", "role": "user" } ]

17059 L

[ { "content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> reasoning process here </think> <answer> answer here </answer>.", "role": "system" }, { "content": "A student notice that the molar absorptivity was 504 mL/(mg*m). What is the molar absorptivity in units of L/(mol*cm)? The molar mass of the compound is 210g/mol.", "role": "user" } ]

1050 L/(mol*cm)

[ { "content": "Show that the order of the automorphism group of \$Z_3 \\times Z_3\$ is 48.", "role": "user" } ]

48

[ { "content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> reasoning process here </think> <answer> answer here </answer>.", "role": "system" }, { "content": "For the reaction {eq}N_2(g)+3H_2(g)<-->2NH_3(g) Kp = 4.20\\times10-3\n\n{/eq} at 339 C . What is K for the reaction at this temperature? Enter your answer numerically.", "role": "user" } ]

1.05e+1

[ { "content": "Consider the function \$f(x)=\\int_x^{2x}\\frac{\\sin t}{t}dt\$. Determine the value of \$x\$ on the interval \$(0,\\frac{3\\pi}{2})\$ at which this function attains a local maximum.", "role": "user" } ]

\dfrac{\pi}{3}

[ { "content": "Let $(n_k)$ be an increasing sequence of positive integers. Define $E$ as the set of all $x$ such that the sequence $\\sin(n_k x)$ converges. Prove that the Lebesgue measure of $E$, $\\mu(E)$, is zero.", "role": "user" } ]

0

[ { "content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> reasoning process here </think> <answer> answer here </answer>.", "role": "system" }, { "content": "Charlotte, a 65 kg scuba diver, shoots a 2 kg spear from her speargun with a speed of 15 m/s at a fish who darts quickly away without getting hit.\n\nWhat is Charlotte's recoil velocity?", "role": "user" } ]

0.46 m/s

[ { "content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> reasoning process here </think> <answer> answer here </answer>.", "role": "system" }, { "content": "A roller coaster (358 kg) moves from A (1.19 m above the ground) to B (26.2 m above the ground). Two non-conservative forces are present: friction does {eq}-2.12 \\times 10^4\\ J\n\n{/eq} of work on the car, and a chain mechanism does {eq}+5.09 \\times 10^4\\ J\n\n{/eq} of work to help the car up a long climb. What is the change in the car's kinetic energy {eq}KE_f - KE_i\n\n{/eq} from A to B?", "role": "user" } ]

-5.81e4 J

[ { "content": "Is there a Hausdorff compactification of the irrational numbers with its usual topology such that the remainder is a discrete space?", "role": "user" } ]

No

[ { "content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> reasoning process here </think> <answer> answer here </answer>.", "role": "system" }, { "content": "How to calculate momentum after a collision?", "role": "user" } ]

The total momentum after a collision is equal to the total momentum before the collision. For two objects in an elastic collision: p_{1i} + p_{2i} = p_{1f} + p_{2f}. For an inelastic collision: p_{1i} + p_{2i} = p_f, where p_f is the momentum of the combined object.

[ { "content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> reasoning process here </think> <answer> answer here </answer>.", "role": "system" }, { "content": "The Mundell-Fleming model takes the world interest rate r* as an exogenous variable. Briefly explain the two factors that can cause the world interest rate to change.", "role": "user" } ]

Changes in the policies of large open economies and changes in current account balances or terms of trade can cause changes in the world interest rate.

[ { "content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> reasoning process here </think> <answer> answer here </answer>.", "role": "system" }, { "content": "The objects listed below are placed at the top of a ramp, and roll down to the bottom without slipping. Assuming that there in no air resistance, rank them in order from fastest average rolling speed to slowest. bowling\n\nball\n\nhollow\n\nglobe\n\npenny\n\nwedding\n\nring", "role": "user" } ]

bowling ball > penny > hollow globe > wedding ring

[ { "content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> reasoning process here </think> <answer> answer here </answer>.", "role": "system" }, { "content": "An investment offers a 15.5 percent total return over the coming year. Bill Bernanke thinks the total real return on this investment will be only 6.5 percent. What does Bill believe the inflation rate will be over the next year?\n\na. 10.99%\n\nb. 8.45%\n\nc. 9.72%\n\nd. -7.79%\n\ne. 5.92%", "role": "user" } ]

8.45%

[ { "content": "Let $X \\subset \\mathbb{R}^n$ be a bounded and connected set, and let $f: X \\to \\mathbb{R}$ be a polynomial function. Consider a point $x \\in X$ and the nearest global maximum $m \\in X$ to $x$. Suppose that in every neighborhood of $x$, there exists a point $y$ and a path $p_t$ such that $p_0 = y$, $p_1 = m$, and for every $t < t'$, $f(p_t) < f(p_{t'})$ and $d(x, p_t) < d(x, p_{t'})$. Does this imply that $x$ is not a local maximum of $f$?", "role": "user" } ]

Yes

[ { "content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> reasoning process here </think> <answer> answer here </answer>.", "role": "system" }, { "content": "Your energy bill is expected to be $250 next month (month 1) and is expected to grow at 0.64% per month for the foreseeable future (aka forever), after your utility provider ran into financial trouble. You read recently that installing solar panels on your roof will reduce your energy bill by 20% (so month 1 would be $200) and decrease the growth of the bill to 0.23% per month for the foreseeable future. Assuming this is true, that you plan to stay in the house for the foreseeable future, and that the applicable discount rate is 11% per year, from a pure financial perspective what is the most you d be willing to pay today to have solar panels installed immediately? Assume the panels could be installed quickly and the cost savings would start in month 1.", "role": "user" } ]

$61,235.23

[ { "content": "Let $n$ be an odd integer with exactly 11 positive divisors. Find the number of positive divisors of $8n^3$.", "role": "user" } ]

124

[ { "content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> reasoning process here </think> <answer> answer here </answer>.", "role": "system" }, { "content": "The rate constant for this first-order reaction is 0.0770 s{eq}^{-1}\n\n{/eq} at 400 degrees Celsius.\n\n{eq}A \\to \\text{products}\n\n{/eq}\n\nAfter how many seconds will 19.3% of the reactant remain?", "role": "user" } ]

21.4 seconds

[ { "content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> reasoning process here </think> <answer> answer here </answer>.", "role": "system" }, { "content": "A conical water tank, vertex down, is filled with water. If the tank has a radius of 8 feet and height 10 feet, find the work required to pump the water {eq}(p = 62.4~lb/ft^3)\n\n{/eq} to top of the tank.", "role": "user" } ]

313656.6105

[ { "content": "Suppose $f(x, y)$ is defined on some neighbourhood of $(0, 0)$. If $u(x, y) = \\sin f(x, y)$ is continuous at $(0, 0)$, does it imply that $f(x, y)$ is continuous at $(0, 0)$? Provide a justification for your answer.", "role": "user" } ]

No

[ { "content": "Determine whether the set \$I_3 = \\{[a,b) \\times [c,d) \\times [e,f) \\mid a,b,c,d,e,f\\in\\Bbb{R}\\}\$ forms a semiring over \$\\Bbb{R}^3\$.", "role": "user" } ]

Yes

[ { "content": "Given the quadratic equations \$x^2 - 10ax - 11b = 0\$ with roots \$c\$ and \$d\$, and \$x^2 - 10cx - 11d = 0\$ with roots \$a\$ and \$b\$, find the value of \$a + b + c + d\$.", "role": "user" } ]

1210

[ { "content": "Determine the value of $r$ that maximizes the expression: $$\\sum_{k=0}^{r} \\binom{20}{r-k} \\binom{20}{k}.$$", "role": "user" } ]

20

[ { "content": "Christine must buy at least $45$ fluid ounces of milk at the store. The store only sells milk in $200$ milliliter bottles. If there are $33.8$ fluid ounces in $1$ liter, then what is the smallest number of bottles that Christine could buy? (You may use a calculator on this problem.)", "role": "user" } ]

7

[ { "content": "Consider 9 distinct apples and 7 distinct bananas to be placed into 6 identical bins. Determine the number of ways to configure the bins such that exactly one bin contains 5 apples, exactly one bin contains 3 bananas, and the remaining 4 bins each contain 1 apple and 1 banana. Provide your answer as a single number.", "role": "user" } ]

105840

[ { "content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> reasoning process here </think> <answer> answer here </answer>.", "role": "system" }, { "content": "Calculate the mass (in mg) of solid chromium(III) nitrate needed to make 250 mL of an aqueous solution with a pH of 4.00. The {eq}K_a\n\n{/eq} of {eq}Cr(H_2O)_6^{3+}\n\n{/eq} is {eq}1.0 \\times 10^{-4}\n\n{/eq}.", "role": "user" } ]

12 mg

[ { "content": "Let \$ S = \\{ x \\in \\mathbb{R} : 2x^2 \\cos\\frac{1}{x} = 1 \\} \$ and \$ T = \\{ x \\in \\mathbb{R} : 2x^2 \\cos\\frac{1}{x} \\leq 1 \\} \\cup \\{0\\} \$. Under the usual metric on \$ \\mathbb{R} \$, which of the sets \$ S \$ or \$ T \$ is complete?", "role": "user" } ]

T

[ { "content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> reasoning process here </think> <answer> answer here </answer>.", "role": "system" }, { "content": "A stock is trading for 43, and just paid a dividend of 1.0 which is expected to grow at a fraction 0.18 per year. If Goldman Sacs charges a fraction 0.18 as a flotation cost, what is the required rate of return on the new stock issued?", "role": "user" } ]

21.34%

[ { "content": "If $\\sin x + \\sin y = \\frac{96}{65}$ and $\\cos x + \\cos y = \\frac{72}{65}$, then what is the value of $\\tan x + \\tan y$?", "role": "user" } ]

\frac{507}{112}

[ { "content": "Calculate the limit \$ \\lim_{n \\to \\infty}\\frac{\\sqrt[n]{(2n)!}}{2n} \$ using Stirling's approximation.", "role": "user" } ]

\infty

[ { "content": "Evaluate the contour integral \$ \\oint_{C_3 (0)} \\frac{z+7}{z^4 + z^3 - 2 z^2}\\,dz \$ using the Residue Theorem, where \$C_3(0)\$ is the circle of radius 3 centered at the origin, oriented counter-clockwise.", "role": "user" } ]

0

[ { "content": "What is the largest $4$ digit integer congruent to $15 \\pmod{22}?$", "role": "user" } ]

9981

[ { "content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> reasoning process here </think> <answer> answer here </answer>.", "role": "system" }, { "content": "Nike, Inc. reported the following plant assets and intangible assets for the year ended May 31, 2007 (in millions):\n\nother plant assets: $767.2\n\nland $193.8; patents and trademarks (at cost): $115.5\n\nmachinery and equipment: $1,817.2\n\nbuildings: $840.9\n\ngoodwill (at cost): $130.8\n\naccumulated amortization: $47.1\n\naccumulated depreciation: $1,940.8\n\nPrepare a partial balance sheet for Nike for these items.", "role": "user" } ]

Partial Balance Sheet Intangible Assets: Patents and Trademarks (at cost) $115.5 Goodwill (at cost) $130.8 Less: Accumulated Amortization $47.1 Total Intangible Assets $199.2 Plant Assets: Other Plant Assets $767.2 Land $193.8 Machinery and Equipment $1,817.2 Buildings $840.9 Less: Accumulated Depreciation $1,940.8 Total Plant Assets $678.3 Total Plant and Intangible Assets $1,877.5

[ { "content": "Evaluate the limit: $$\\lim_{u\\to 0}\\frac{(u+1)^2\\sin(3u-3)}{\\cos(u^3+u-1)\\sin^2(u^2-u)}.$$", "role": "user" } ]

-\infty

[ { "content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> reasoning process here </think> <answer> answer here </answer>.", "role": "system" }, { "content": "At STP a gas occupies a 69.5 kiloliter balloon. How many mol of the gas must be in the balloon?", "role": "user" } ]

3102.67 mole

[ { "content": "Let \$ a_{n} \$ be the coefficient of the \$ x \$ term in the expansion of \$ (3-\\sqrt{x})^{n} \$ for \$ n=2,3,4, \\cdots \$. Find \$ \\lim _{n \\rightarrow \\infty}\\left(\\frac{3^{2}}{a_{2}}+\\frac{3^{3}}{a_{3}}+\\cdots+\\frac{3^{n}}{a_{n}}\\right) \$.", "role": "user" } ]

18

[ { "content": "Suppose $A \\subset \\mathbb{R}^2$ is an open subset such that there exist infinitely many homeomorphisms that, when restricted to $A$, give self-maps that are also homeomorphisms. Does it follow that $A$ is an open disc?", "role": "user" } ]

No

[ { "content": "Given a matrix where the value at each index is determined by the XOR operation between the column and row indices, and a fixed amount is subtracted from each element (ensuring non-negative results), calculate the sum of all elements in the matrix. For example, consider a matrix with 5 rows and 8 columns:\n\n\\[\n\\begin{bmatrix}\n0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 \\\\\n1 & 0 & 3 & 2 & 5 & 4 & 7 & 6 \\\\\n2 & 3 & 0 & 1 & 6 & 7 & 4 & 5 \\\\\n3 & 2 & 1 & 0 & 7 & 6 & 5 & 4 \\\\\n4 & 5 & 6 & 7 & 0 & 1 & 2 & 3 \\\\\n\\end{bmatrix}\n\\]\n\nAfter subtracting a fixed amount from each element (ensuring non-negative results), the matrix becomes:\n\n\\[\n\\begin{bmatrix}\n0 & 0 & 1 & 2 & 3 & 4 & 5 & 6 \\\\\n0 & 0 & 2 & 1 & 4 & 3 & 6 & 5 \\\\\n1 & 2 & 0 & 0 & 5 & 6 & 3 & 4 \\\\\n2 & 1 & 0 & 0 & 6 & 5 & 4 & 3 \\\\\n3 & 4 & 5 & 6 & 0 & 0 & 1 & 2 \\\\\n\\end{bmatrix}\n\\]\n\nFind the sum of all elements in the modified matrix.", "role": "user" } ]

105

[ { "content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> reasoning process here </think> <answer> answer here </answer>.", "role": "system" }, { "content": "Dewitt Industries has adopted the following production budget for the first 4 months of 2017.\n\n \n \n \n Month \n Units \n \n \n \n \n January \n 10,240 \n \n \n February \n 8,340 \n \n \n March \n 5,150 \n \n \n April \n 4,130 \n \n \n\n\nEach unit requires 3 pounds of raw materials costing {eq}\\$2\n\n{/eq} per pound. On December 31, 2016, the ending raw materials inventory was 6,144 pounds. Management wants to have a raw materials inventory at the end of the month equal to {eq}20\\%\n\n{/eq} of next month's production requirements.\n\nPrepare a direct materials purchases budget by month for the first quarter.", "role": "user" } ]

$135,048

[ { "content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> reasoning process here </think> <answer> answer here </answer>.", "role": "system" }, { "content": "Physical Phitness, Inc., operates three divisions, Weak, Average, and Strong. As it turns out, the Weak division has the lowest operating income, and the president wants to close it. \"Survival of the fittest, I say!\" was his response when the Weak division's manager insisted that his division earned money for the company. Following is the most recent financial analysis for each division:\n\n \n \n \n \n Weak \n Average \n Strong \n \n \n Sales \n $125,600 \n $349,200 \n $543,800 \n \n \n Variable expenses \n 52,500 \n 198,700 \n 309,600 \n \n \n Contribution margin \n 73,100 \n 150,500 \n 234,200 \n \n \n Direct expenses \n 37,400 \n 75,100 \n 117,000 \n \n \n Allocated expenses \n 52,100 \n 52,100 \n 52,100 \n \n \n Operating income \n $(16,400) \n $23,300 \n $65,100 \n \n \n\n\nBy how much would total income change if the Weak division were dropped?", "role": "user" } ]

$35,700

[ { "content": "In an equilateral triangle \$\\triangle ABC\$ with side length 4, point \$D\$ is located on side \$BC\$ such that \$BD = 1\$. Let \$r\$ and \$s\$ be the radii of the inscribed circles of triangles \$\\triangle ADB\$ and \$\\triangle ADC\$, respectively. Calculate the product \$rs\$.", "role": "user" } ]

4 - \sqrt{13}

[ { "content": "Given the polynomial \$x^4 + px^3 + qx^2 + rx + s = 0\$ with rational coefficients and four complex roots, two of the roots add up to \$3 + 4i\$ and the other two have a product of \$13-i\$. Compute the value of \$q\$.", "role": "user" } ]

51

[ { "content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> reasoning process here </think> <answer> answer here </answer>.", "role": "system" }, { "content": "A horizontal vinyl record of radius 0.13 m rotates about a vertical axis through its center with an angular speed of 4.7 rad/s. The rotational inertia of the record about its axis of rotation is {eq}5.0 \\times 10^{-4} \\ {\\rm kgm^2}\n\n{/eq}. A wad of putty of mass 0.020 kg drops vertically onto the record from above and sticks to the edge of the record. What is the angular speed of the record immediately after the putty sticks to it?", "role": "user" } ]

2.80 kgm^2/s

[ { "content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> reasoning process here </think> <answer> answer here </answer>.", "role": "system" }, { "content": "The following information pertains to the Moline Facility for the month of May (all materials are added at the beginning of the process):\n\n \n \n \n \n Units \n Material Costs \n \n \n Beginning work in process \n 70,000 \n $30,000 \n \n \n Started in May \n 250,000 \n 103,400 \n \n \n Units completed \n 235,000 \n \n \n \n Ending work in process \n 85,000 \n \n \n \n\n\nCompute the cost per equivalent unit for materials using the FIFO method.", "role": "user" } ]

$0.42

[ { "content": "Determine the values of $p \\geq 0$ for which the integral \$ \\int_0^{\\infty} \\frac{dx}{x^{p}+x^{-p}} \$ converges.", "role": "user" } ]

p > 1

[ { "content": "Find the maximum volume of a rectangular solid in the first octant ($x \\geq 0$, $y \\geq 0$, $z \\geq 0$) with one vertex at the origin and the opposite vertex lying on the plane $x + y + z = 1$. Use the method of Lagrange multipliers to derive the system of equations needed to solve for the maximum volume.", "role": "user" } ]

\dfrac{1}{27}

[ { "content": "Find the orthogonal complement of the subset \$ C = \\{ u \\in L^2(0,2) : \\int_0^2 u(t) \\, dt = 1 \\} \$ in the space \$ L^2(0,2) \$.", "role": "user" } ]

\{0\}

[ { "content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> reasoning process here </think> <answer> answer here </answer>.", "role": "system" }, { "content": "Carotenoids, present in all organisms capable of photosynthesis, extend the range of light absorbed by the organism. They exhibit the maximal capacity for absorption of light in the range of 440-470 nm. Calculate the energy in kilojoules represented by absorption of an Avogadro's number of photons of wavelength 460 nm.", "role": "user" } ]

2.60e+05 J

[ { "content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> reasoning process here </think> <answer> answer here </answer>.", "role": "system" }, { "content": "A solution of aqueous nitric acid contains 5.00% nitric acid by mass. Calculate the molarity of the solution. The molar mass of nitric acid is 61.01 g/mol.", "role": "user" } ]

0.820 mol/L

[ { "content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> reasoning process here </think> <answer> answer here </answer>.", "role": "system" }, { "content": "Where are critical biodiversity hotspots located?", "role": "user" } ]

Critical biodiversity hotspots are located across the globe, spanning Africa, Asia-Pacific, Europe and Central Asia, North and Central America, and South America. Examples include the Cape Floristic Region, Madagascar and the Indian Ocean Islands, Japan, the forests of Eastern Australia, the Mediterranean Basin, Madrean pine-oak woodlands, the Atlantic forest, and the tropical Andes.

[ { "content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> reasoning process here </think> <answer> answer here </answer>.", "role": "system" }, { "content": "A student kept her 60-watt, 120-volt study lamp turned on from {eq}2:00 \\, \\mathrm{PM}\n\n{/eq} until {eq}6:00 \\, \\mathrm{PM}\n\n{/eq}. How many coulombs of charge went through it?", "role": "user" } ]

7200 C

[ { "content": "Find the Fourier series representation of the function \$W(t)\$ given by:\n\\[\nW(t) = \\begin{cases} 2, & \\text{for } -2 \\leq t < 4 \\\\ 0, & \\text{otherwise} \\end{cases}\n\\]\nUse the formulas for \$a_n\$ and \$b_n\$ extended for an interval of length \$2l\$.", "role": "user" } ]

2

[ { "content": "Solve the inequality $$-13(r+5) + 25 > 4(r-10)$$for $r$. Express your answer in interval notation.", "role": "user" } ]

(-\infty,0)

[ { "content": "Determine whether there exists a Lebesgue measurable set $D \\supset [0,1]$ such that $D \\neq [0,1]$ and $\\lambda^{*}(D) = 1$. Provide a justification for your answer.", "role": "user" } ]

Yes

[ { "content": "Determine the spectrum of the $C^*$-algebra formed by the direct sum $C(K) \\oplus C(K')$, where $K$ and $K'$ are compact Hausdorff spaces.", "role": "user" } ]

K \sqcup K'

[ { "content": "Let $X$ be a metric space and let $U, V \\subset X$ be open and bounded subsets. Is the Hausdorff metric \$ h(U,V) = \\max(\\sup_{x\\in U}\\inf_{y\\in V}d(x,y),\\sup_{x\\in V}\\inf_{y\\in U}d(x,y)) \$ defined for all possible choices of $U$ and $V$?", "role": "user" } ]

Yes

[ { "content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> reasoning process here </think> <answer> answer here </answer>.", "role": "system" }, { "content": "A motorist drives south at 20m/s for 3 mins, then turns west and travels at 25m/s for 2 mins, and finally travels northeast at 30m/s for 1min. For this 6 min trip, find the total vector displacement.", "role": "user" } ]

2898 m from origin at an angle 233.4 degrees from the positive x-axis

[ { "content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> reasoning process here </think> <answer> answer here </answer>.", "role": "system" }, { "content": "How does an infinite geometric series apply to being pushed on a swing?", "role": "user" } ]

21 m

[ { "content": "Find \$\\lim\\limits_{x\\to +\\infty} \\frac{x^{2}e^{-x}}{x^{2}+1}\\sin(xe^{x^{2}})\$.", "role": "user" } ]

0

[ { "content": "Does the uniform convergence of a sequence of Lipschitz continuous functions imply that the limit function is also Lipschitz continuous?", "role": "user" } ]

No

[ { "content": "Suppose we have \$n\$ independent variables from \$U[0,1+\\theta]\$ and let \$\\lambda=1+\\theta\$. The estimator of \$\\theta\$ is given by \$\\bar{\\theta}=2 \\bar{X} - 1\$. Find the bias of \$\\bar{\\theta}\$ given that the distribution of \$\\bar{X}\$ for \$n\$ variables from \$U[0,1]\$ is the Bates distribution.", "role": "user" } ]

0

[ { "content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> reasoning process here </think> <answer> answer here </answer>.", "role": "system" }, { "content": "Mitchell Company had the following budgeted sales for the first half of next year:\n\n \n \n \n \n Cash Sales \n Credit Sales \n \n \n January \n $90,000 \n $190,000 \n \n \n February \n $95,000 \n $210,000 \n \n \n March \n $52,000 \n $170,000 \n \n \n April \n $57,000 \n $152,000 \n \n \n May \n $67,000 \n $240,000 \n \n \n June \n $120,000 \n $420,000 \n \n \n\n\nThe company is in the process of preparing a cash budget and must determine the expected cash collections by month. To this end, the following information has been assembled.\n\n \n \n \n Collections on credit sales: \n \n \n 50% in month of sales \n \n \n 25% in month of following sales \n \n \n 25.0% in second month following sales \n \n \n\n\nAssume that the accounts receivable balance on January 1 was $68,000. Of this amount, $46,000 represented uncollected December sales and $22,000 represented uncollected November sales. Given these data the total cash collected during January would be:", "role": "user" } ]

$230,000

[ { "content": "Simplify the expression: \\[ \\frac{\\left(a^{2} b \\sqrt{b}-6 a^{5 / 3} b^{5 / 4}+12 a b \\sqrt[3]{a}-8 a b^{3 / 4}\\right)^{2 / 3}}{a b \\sqrt[3]{a}-4 a b^{3 / 4}+4 a^{2 / 3} \\sqrt{b}} \\]", "role": "user" } ]

1

[ { "content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> reasoning process here </think> <answer> answer here </answer>.", "role": "system" }, { "content": "A light meter reports that a camera setting of 1/500 s at f/1.0 will give a correct exposure. But the photographer wishes to use f/22 to increase the depth of the field. what should the shutter speed be?", "role": "user" } ]

0.968 s

[ { "content": "Find the Shnirelman density of the set \$ A = \\{ \\lfloor n \\ln (n) \\rfloor : n = 1,2,3,... \\} \$.", "role": "user" } ]

0

[ { "content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> reasoning process here </think> <answer> answer here </answer>.", "role": "system" }, { "content": "Apple Inc has a beta of 1.35. The tax rate is 40%, and Apple is financed with 30% debt. What is Apple's unlevered beta?", "role": "user" } ]

1.073

[ { "content": "Calculate the circulation of the vector field \$ \\vec{F}(x, y, z) = \\langle \\sin(x^2+z)-2yz, 2xz + \\sin(y^2+z), \\sin(x^2+y^2)\\rangle \$ along the circle parameterized by \$ \\vec{r}(t)=\\langle\\cos(t), \\sin(t), 1\\rangle \$ for \$ t \\in [0, 2\\pi] \$. Use Stoke's Theorem to evaluate the integral.", "role": "user" } ]

4\pi

[ { "content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> reasoning process here </think> <answer> answer here </answer>.", "role": "system" }, { "content": "Determine what is the increase in volume (in {eq}cm^3\n\n{/eq}) of an Aluminum sphere with a radius of 11.1 cm when it is heated from {eq}0^oC{/eq} to {eq}80^oC{/eq}?", "role": "user" } ]

34 cm^3

[ { "content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> reasoning process here </think> <answer> answer here </answer>.", "role": "system" }, { "content": "A vertical right circular cylindrical tank measures 28 ft high and 8 ft in diameter. It is full of liquid weighing {eq}62.4 1b / ft^3\n\n{/eq}. How much work does it take to pump the liquid to the level of the top of the tank?\n\nThe amount of work required is ft-1b.", "role": "user" } ]

1229534 ft-lb

[ { "content": "If $\\frac{1}{x} + \\frac{1}{y} = 3$ and $\\frac{1}{x} - \\frac{1}{y} = -7$ what is the value of $x + y$? Express your answer as a common fraction.", "role": "user" } ]

-\frac{3}{10}

[ { "content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> reasoning process here </think> <answer> answer here </answer>.", "role": "system" }, { "content": "A 60.0 gram lead bullet hits a steel plate, both initially at 28 degrees C. The bullet melts and splatters on impact. Assuming that the bullet receives 82% of its kinetic energy as heat energy, at what minimum speed must it be traveling to melt on impact? (The melting temperature of Lead is 327 degrees C)", "role": "user" } ]

385.635 m/s

[ { "content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> reasoning process here </think> <answer> answer here </answer>.", "role": "system" }, { "content": "A car is moving at 53 miles per hour. The kinetic energy of that car is 5 {eq}\\times\n\n{/eq} 10{eq}^5\n\n{/eq} J. How much energy does the same car have when it moves at 102 miles per hour? Answer in units of J.", "role": "user" } ]

1.85 * 10^6 J

[ { "content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> reasoning process here </think> <answer> answer here </answer>.", "role": "system" }, { "content": "If T-bills pay 2% per six months and the semiannual dividend yield is 1%, what is the parity value of the futures price? (Do not round intermediate calculations.)", "role": "user" } ]

$1.01

[ { "content": "Twenty-seven solid gold spherical beads each of radius 3 are melted down and recast into a larger, solid gold sphere. How many units are in the radius of this larger gold sphere?", "role": "user" } ]

9

[ { "content": "An $\\textit{annulus}$ is the region between two concentric circles. The concentric circles in the figure have radii $b$ and $c$, with $b>c$. Let $\\overline{OX}$ be a radius of the larger circle, let $\\overline{XZ}$ be tangent to the smaller circle at $Z$, and let $\\overline{OY}$ be the radius of the larger circle that contains $Z$. Let $a=XZ$, $d=YZ$, and $e=XY$. What is the area of the annulus? Express your answer in terms of $\\pi$ and at most one of the variables $a,b,c,d,e$.\n\n[asy]\npair O,X,Y,Z;\nO=(0,0);\nX=(16,12);\nY=(0,20);\nZ=(0,12);\nfill(Circle(0,20),gray(0.7));\nfill(Circle(0,12),white);\ndraw(Circle(O,20),linewidth(0.7));\ndraw(Circle(O,12),linewidth(0.7));\ndot(O);\ndot(X);\ndot(Y);\ndot(Z);\ndraw(O--X--Y--cycle,linewidth(0.7));\ndraw(Z--X,linewidth(0.7));\nlabel(\"$b$\",(8,6),SE);\nlabel(\"$a$\",(8,12),S);\nlabel(\"$e$\",(8,16),SW);\nlabel(\"$c$\",(0,6),W);\nlabel(\"$d$\",(0,16),W);\nlabel(\"$O$\",O,S);\nlabel(\"$X$\",X,NE);\nlabel(\"$Y$\",Y,N);\nlabel(\"$Z$\",Z,SW);\n[/asy]", "role": "user" } ]

\pi a^2

[ { "content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> reasoning process here </think> <answer> answer here </answer>.", "role": "system" }, { "content": "Calculate the amount of energy (in kJ) necessary to convert 317 g of liquid water from {eq}0^{\\circ }C\n\n{/eq} to water vapor at {eq}177^{\\circ }C.\n\n{/eq} The molar heat of vaporization ({eq}H_{vap}\n\n{/eq} ) of water is 40.79 kJ/mol. The specific heat for water Is 4.184 J/g. {eq}^{\\circ }C\n\n{/eq}, and for steam is 1.99 J/g{eq}.^{\\circ }C.\n\n{/eq}\n\n(Assume that the specific heat values do not change over the range of temperatures in the problem.)\n\n_____ KJ", "role": "user" } ]

897.63 kJ

[ { "content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> reasoning process here </think> <answer> answer here </answer>.", "role": "system" }, { "content": "X Company makes two products, A and B, and uses an activity-based costing overhead allocation system, with three cost pools and three cost drivers.\n\nBudgeted costs and driver information for 2015 were as follows :\n\n\n Cost Pool 1 Cost Pool 2 Cost Pool 3\n Budgeted costs $108,000 $54,000 $25,000\n Cost Drivers \n Product A 77,200 60,500 68,800\n Product B 76,100 52,400 52,800\nWhat was the allocation to Product A? (round overhead rates to the nearest cent).", "role": "user" } ]

$97,469.33

[ { "content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> reasoning process here </think> <answer> answer here </answer>.", "role": "system" }, { "content": "SCI just paid a dividend of $1.20 per share, and its annual dividend is expected to grow at a constant rate of 2.50% per year. SCI's expected stock price one year from today will be _____ per share.", "role": "user" } ]

$17.63

[ { "content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> reasoning process here </think> <answer> answer here </answer>.", "role": "system" }, { "content": "Is the doctrine that a business ought to be MAXIMIZING profits one arising from law or one derived from modern economics?", "role": "user" } ]

modern economics

[ { "content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> reasoning process here </think> <answer> answer here </answer>.", "role": "system" }, { "content": "How much lithium metal is needed to react with 15 grams of {eq}CH_3CH_2I\n\n{/eq} using a 15% excess of lithium to make methyllithium?\n\n{eq}CH_3CH_2I + Li \\to LiCH_2CH_3 + LiI\n\n{/eq}", "role": "user" } ]

1.54 g

[ { "content": "Let $X_1, X_2, X_3$ be independent and identically distributed random variables, each following a uniform distribution on the interval (0, 1). Calculate the expected value of the expression $E\\left(\\frac{X_1 + X_2}{X_1 + X_2 + X_3}\\right)$. What is the value?", "role": "user" } ]

\dfrac{2}{3}

[ { "content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> reasoning process here </think> <answer> answer here </answer>.", "role": "system" }, { "content": "Book Depot Inc sells on term 2/15, net 55. What is the implicit cost of trade credit under these terms ? Use a 365 day year.", "role": "user" } ]

18.62%

[ { "content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> reasoning process here </think> <answer> answer here </answer>.", "role": "system" }, { "content": "In a diesel engine, the piston compresses air at 305?K to a volume that is 0.0624 of the original volume and a pressure that is 48.5 times the original pressure. What is the temperature of the air after the compression?", "role": "user" } ]

923.05K

[ { "content": "Determine the possible leading digits that both $2^n$ and $5^n$ can have for certain natural numbers $n$. (The 14th All-Russian Mathematical Olympiad, 1988)", "role": "user" } ]

3

[ { "content": "Solve the congruence \$x^3 + 2x + 2 \\equiv 0 \\pmod{125}\$ using Hensel's Lemma.", "role": "user" } ]

113

[ { "content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> reasoning process here </think> <answer> answer here </answer>.", "role": "system" }, { "content": "Classify the bond in NBr{eq}_3\n\n{/eq} as ionic or covalent.", "role": "user" } ]

covalent

[ { "content": "Calculate the average arc length between two randomly selected points on a sphere with a radius of 2.", "role": "user" } ]

\pi

[ { "content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> reasoning process here </think> <answer> answer here </answer>.", "role": "system" }, { "content": "A rigid cylinder contains 9.0 g of nitrogen at 20 {eq}^\\circ\n\n{/eq}C.\n\nWhat is the minimum amount of heat energy that must be removed to liquify the nitrogen?", "role": "user" } ]

3.22 kJ

[ { "content": "Stuart has drawn a pair of concentric circles, as shown. He draws chords $\\overline{AB}$, $\\overline{BC}, \\ldots$ of the large circle, each tangent to the small one. If $m\\angle ABC=75^\\circ$, then how many segments will he draw before returning to his starting point at $A$? [asy]\nsize(100); defaultpen(linewidth(0.8));\nreal rad1 = 1/Sin(37.5);\ndraw(Circle(origin,1)); draw(Circle(origin,rad1));\npair A = rad1*dir(190), B = rad1*dir(190 + 105), C = rad1*dir(190 + 2*105), D = rad1*dir(190 + 315);\ndraw(A--B--C--D,EndArrow(size=5));\nlabel(\"$A$\",A,W); label(\"$B$\",B,S); label(\"$C$\",C,E);\n[/asy]", "role": "user" } ]

24

[ { "content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> reasoning process here </think> <answer> answer here </answer>.", "role": "system" }, { "content": "Calculate the present value of the following payment stream, discounted at 6% annually: $1,500 at the end of year 1, $3,000 at the end of year 2, and $4,500 at the end of year 3.", "role": "user" } ]

$7,863.38

[ { "content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> reasoning process here </think> <answer> answer here </answer>.", "role": "system" }, { "content": "Assume that the market demand is given by P(Q) = 100 - Q and that the cost functions of the two firms in the industry are: {eq}C_i(q_i) = $20 q_i, i = 1,2\n\n{/eq}.\n\nCalculate the output of cash firm, the market price, and the profits of each firm that correspond to the Nash-Cournot equilibrium.", "role": "user" } ]

q1 = 80/3 q2 = 80/3 P = $46.67 Profit1 = $711.2 Profit2 = $711.2

[ { "content": "Evaluate the Fourier coefficient \$ \\hat{f}_k \$ for the function \$ f(t) = \\frac{1-r^2}{1+r^2-2r\\cos t} \$ where \$ t \\in \\mathbb{R} \$ and \$ |r| < 1/2 \$. Verify that the correct result is \$ \\hat{f}_k = r^{|k|} \$.", "role": "user" } ]

r^{|k|}

[ { "content": "Determine the range of values for \$ k \$ such that the equation \$ x^4 - 14x^2 + 24x - k = 0 \$ has four real and unequal roots.", "role": "user" } ]

(8, 11)

[ { "content": "In triangle $ABC$ with sides $AB=1$, $BC=\\sqrt{3}$, and $AC=2$, points $D$, $E$, and $F$ are located on $AB$, $BC$, and $AC$ respectively, such that $\\angle EDF = \\angle DFA = 90^{\\circ}$. If the maximum possible value of $[DEF]^2$ can be expressed as $\\frac{a}{b}$, where $a$ and $b$ are positive integers with $\\gcd(a, b) = 1$, find $a + b$. (Here $[DEF]$ denotes the area of triangle $DEF$.)", "role": "user" } ]

67

[ { "content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> reasoning process here </think> <answer> answer here </answer>.", "role": "system" }, { "content": "A spring-like trampoline dips down 0.08 m when a particular person stands on it. If this person jumps up to a height of 0.26 m above the top of the trampoline, how far with the trampoline compress when the person lands?", "role": "user" } ]

0.204 m