unique_id stringlengths 2 7 | problem stringlengths 9 11.6k | answer stringlengths 0 2.49k | answer_type stringclasses 11
values | category stringclasses 16
values | difficulty stringclasses 5
values |
|---|---|---|---|---|---|
1131067 | Write an equation for the simple harmonic motion of a ball on a spring that starts at its lowest point of 6 inches below equilibrium, bounces to it maximum height of 6 inches above equilibrium and returns to its lowest point in a total of 2 seconds. (think about amplitude and period) | 6*sin(πt) | Expression | Physics | Senior High School |
2022282 | Balance the following reaction equation: {eq}N_2H_4 \to NH_3 + N_2
{/eq} | 3N_2H_4 -> 4NH_3 + N_2 | Expression | Chemistry | Senior High School |
667568 | Identify the term:
This WBC secretes histamine. | mast cells | String | Biology | Senior High School |
1319302 | How far is saturn from the sun in scientific notation? | 1.4 x 10 ^ 9 kilometers | Float | Physics | Junior High School |
879860 | Suppose $X$ is Nötherian, integral, separated, and regular in codimension one. If $\imath:Y\to X$ and $\jmath:Z\to X$ are closed immersions and $Y$ and $Z$ are integral schemes such that there exists a homeomorphism $\lvert\varphi\rvert:\lvert Y\rvert\to \lvert Z\rvert$ such that $\lvert\jmath\rvert\circ\lvert\varphi\r... | Yes | Boolean | Mathematics | PhD |
712060 | Which unit, megagrams or grams, would be more suitable for expressing the mass of an automobile? Why? | megagram | String | Physics | Junior High School |
632240 | Suppose $X_1$ and $X_2$ are independent exponential random variables with $E(X_1)=\theta$ and $E(X_2)=2\theta$. Find a most powerful test of $H_0: \theta=2$ versus $H_\alpha: \theta=4$. Given that $\frac{L(\theta_0;x_1,x_2)}{L(\theta_\alpha;x_1,x_2)}= 4e^{-\frac{2x_1+x_2}{8}}$ and $2X_1+X_2$ is a sufficient statistic, ... | Reject $H_0$ when $2X_1 + X_2 > T$, where $T$ satisfies $\mathbb{P}(\Gamma(2,4) > T) = 0.05$ | Expression | Mathematics | University |
2004481 | Assuming that the gases are ideal, calculate the amount of work done (in joules) in the following reaction. Is work done on or by the system?
A reaction in the Mond process for purifying nickel(0) tetracarbonyl at {eq}50-100 ^{\circ} C
{/eq}.
Assume one mole of nickel is used and a constant temperature of {eq}75 ^{\... | 8684J | Integer | Chemistry | Senior High School |
574118 | The problem with attempting to control interest rates while also controlling the exchange rate and maintaining free and open international capital flows is that
A. Capital will flow into those countries that maintain a rate of interest above the global mean rate (risk-adjusted) causing the nation to move off the peg
... | D | Multiple Choice | Economics | University |
1131704 | What is the limit of #x^2e^x# as x goes to infinity? | ∞ | String | Mathematics | University |
1904374 | If the firm could reduce the average age of its inventory from 73 days, to 63 day, by how much would it reduce its dollar investment in working capital? | 2.74% | Percentage | Business | Senior High School |
256471 | Suppose in the current year that there is a nation-wide drought for apple growers and a statewide bumper crop for oranges in both Florida and California. Which of the following statements correctly reflects the subsequent developments in the U.S. orange market?
a. Both equilibrium output and price will increase.
b. B... | e | Multiple Choice | Economics | Senior High School |
1628036 | Use Work and Mechanical Energy to derive the expression for the experimentally determined moment of inertia. | I=m[\frac{v^2-u^2}{\omega_i^2-\omega_f^2}]+2mg[\frac{h_f-h_i}{\omega_i^2-\omega_f^2}] | Expression | Physics | University |
518551 | Solve the following:
{eq}t\frac{dx}{dt} -x-3y = t\frac{dy}{dt} -x+y = 0
{/eq} | x=t/4(C1+3C2), y=t/4(C1-C2) | Expression | Mathematics | University |
1388635 | Which one of the following species has the same electron configuration as the Al{eq}^{3+}
{/eq} cation?
A. F
B. Cl
C. S{eq}_2
{/eq}
D. O
E. Mg{eq}^+
{/eq} | F | Multiple Choice | Chemistry | Senior High School |
731652 | Statements: The national norm is 100 beds per thousand populations but in this state, 150 beds per thousand are available in the hospitals. Conclusions: Our national norm is appropriate. The state's health system is taking adequate care in this regard. Options are: answer A Only conclusion I follows; answer B Only conc... | B | Multiple Choice | Philosophy | Senior High School |
540001 | How much energy is produced when the sun converts one kg of hydrogen into helium?. | 6.3e14 J | Float | Physics | Senior High School |
773326 | Eight months ago, you purchased 400 shares of Winston stock at a price of $46.40 a share. The company pays quarterly dividends of $1.05 a share. Today, you sold all of your shares for $48.30 a share. What is your total percentage return on this investment?
a. 8.62%
b. 12.08%
c. 10.12%
d. 4.09%
e. 7.34% | a | Multiple Choice | Finance | Senior High School |
492022 | Use a triple integral to find the volume of the solid bounded below by the cone {eq}z = \sqrt{x^2+y^2} {/eq} and bounded above by the sphere {eq}x^2 +y^2 +z^2 = 392 {/eq}. | \frac{10976\pi}{3}(\sqrt2-1) | Fraction | Mathematics | University |
333240 | A thin nonconducting rod of length {eq}l
{/eq} carries a nonuniform charge density {eq}\lambda = Ax^2
{/eq}. The rod lies on the positive {eq}x
{/eq}-axis with one end at the origin and the other end at {eq}x = l
{/eq}. A point charge {eq}q_0
{/eq} lies on the {eq}x
{/eq}-axis at the point {eq}x_0 (x_0 > l)
{/eq... | 0.6555 N | Float | Physics | University |
565029 | The hollow plastic sphere at right has inner radius a, outer radius b, and uniform charge density \rho. Find the electric potential difference between a and b. | -(\rho/(3*\epsilon_0)) * (3*a^2/2 - b^2/2 - a^3/b) | Expression | Physics | University |
1150216 | Suppose that n balls are tossed, one at a time, into n bins such that each ball is equally likely to fall into any bin and that the tosses are independent. What is the probability that the first bin is empty? | (1-1/n)^n | Expression | Mathematics | University |
1638613 | Find the jacobian of the vector valued function $\begin{pmatrix} f(x,y,z)\\ g(x,y,z) \\ h(x,y,z)\end{pmatrix}$ where $f(x,y,z) = x$, $g(x,y,z) = \sqrt[3]{\frac{x}{y z^2}}$, and $h(x,y,z) = \sin ^{-1}\left(\frac{y}{z^2}\right)$ | \begin{pmatrix}
1 & 0 & 0 \\
\frac{1}{3 y z^2 \sqrt[3]{\frac{x}{y z^2}}^2} & -\frac{x}{3 y^2 z^2 \sqrt[3]{\frac{x}{y z^2}}^2} & -\frac{2 x}{3 y z^3 \sqrt[3]{\frac{x}{y z^2}}^2} \\
0 & \frac{1}{z^2 \sqrt{1-\frac{y^2}{z^4}}} & -\frac{2 y}{z^3 \sqrt{1-\frac{y^2}{z^4}}} \\
\end{pmatrix} | Matrix | Mathematics | University |
1810847 | Show that $$\ {u}=\frac{\cos\phi}{b}$$ and use this to show that u then solves the homogenous equation: $$\frac {d^2u}{d{\phi}^2}+{u}=0$$ given that the homogenous equation describes a hypothetical situation where light passes by the Sun in a straight line without changing direction, b is the minimum distance from the ... | Given u = cos(phi)/b, du/d(phi) = -sin(phi)/b, and d^2u/d(phi^2) = -cos(phi)/b. Substituting into the homogeneous equation: d^2u/d(phi^2) + u = -cos(phi)/b + cos(phi)/b = 0. Therefore, u = cos(phi)/b satisfies the homogeneous equation. | Expression | Mathematics | University |
1984151 | In the case of multiple wage attachments, a garnishment for a student loan has priority over any other garnishment. True or False? | False | Boolean | Law | Senior High School |
1256871 | Give some specific sets of quantum numbers and determine if the set given is possible. | Possible combinations:
n=3, l=0, ml=0, ms=+1/2 or -1/2
n=3, l=1, ml=-1, 0, or +1, ms=+1/2 or -1/2
n=3, l=2, ml=-2, -1, 0, +1, or +2, ms=+1/2 or -1/2
Impossible combination: n=3, l=2, ml=3, ms=+1/2 or -1/2 | List | Chemistry | Senior High School |
129235 | At a particular location in the room, there is an electric field = {eq}\displaystyle \langle 7940,\ 0,\ 0 \rangle\ N/C
{/eq}. Where would you place a single negative point particle of charge {eq}2.0\ \mu C
{/eq} in order to produce this electric field? | 1.505 m on the right side of origin on the x-axis | Float | Physics | University |
379436 | How do I proceed to discover an expression for $I_l$ given $$I_l = V_1 \int_0^1 P_l(x)dx+V_2 \int_{-1}^0 P_l(x)dx$$ and $$\Phi(r,x) = K\sum_{l=0}^\infty r^l P_l(x) I_l $$ where I am solving for the potential of a conducting sphere with hemispheres at opposite potentials? | $\frac{\sqrt{\pi}}{2\Gamma(1-\frac{l}{2})\Gamma(\frac{l+3}{2})}$ | Expression | Mathematics | University |
1686544 | Write the equation that represents "nitrogen and oxygen react to form nitrogen dioxide." | N_2 + 2O_2 -> 2NO_2 | Expression | Chemistry | Senior High School |
1779388 | Use power series methods to express {eq}S=\int_{0}^{1}\frac{\sin (x)}{x}dx{/eq} as an alternating series {eq}\sum_{n=0}^{\infty } a_{n}{/eq} with rational terms alternating in sign and satisfying the condition {eq}\left | a_{n} \right |\rightarrow 0{/eq}, then use the alternating series test remainder estimate to appro... | \sum_{n=0}^{\infty} \frac{(-1)^n}{(2n+1)!(2n+1)} | Expression | Mathematics | University |
1538372 | What is the length of the longest pipe that can be carried horizontally around a corner from a 9 ft wide hallway into a 6 ft wide hallway? | 21.07 | Float | Mathematics | University |
1808790 | A 24.0 kg wombat is moving horizontally at 1.90 m/s when it strikes an empty aluminum can attached to a wall and comes to rest after crumpling the can by 4.00 cm against the wall. What was the average force exerted on the can? | 1080 N | Integer | Physics | Senior High School |
588488 | If there is s large amount of lactose present, how does bacteria respond?
A the gene for beta-galactosidase turns on.
B the gene for beta-galactosidase turns off.
C beta-galactosidase production increases.
D lactose is produced. | A | Multiple Choice | Biology | Senior High School |
1211937 | After takeoff, an airplane climbs at an angle of 30 degrees at a speed of 215 ft/sec. How long does it take for the airplane to reach an altitude of 13,000 ft? (round your answer to one decimal place.) | 120.9 s | Float | Physics | Senior High School |
2028912 | When the following equation is balanced using the smallest possible integers, what is the coefficient in front?
{eq}\displaystyle \rm C_2H_6 + O_2 \to CO_2 + H_2O
{/eq}
(a) 1
(b) 7
(c) 4
(d) 6
(e) 2 | (e) | Multiple Choice | Chemistry | Senior High School |
1541803 | Slow U.S. economic growth rate impacts the size of the Fed's balance sheet as:
a. The Fed reduces the discount rate to 0%,
b. Banks maintain high levels of excess reserves,
c. Businesses reduce spending, keeping more money in their demand accounts,
d. Individuals move money from checking ti saving accounts. | b | Multiple Choice | Economics | University |
958236 | It takes a boat 5 hours to travel upstream. It takes the same boat 4 hours to travel the same distance downstream. If the current is 1 mile per hour, what is the speed of the boat in still water? | 9 mph | Integer | Physics | Junior High School |
1365733 | How do you find the integral ln(x)/(x^2)? | #-lnx /x -1/x +C# | Expression | Mathematics | University |
84215 | An object of mass m travels along the parabola {eq}y=6x^{2}
{/eq} with a constant speed of {eq}6 \, units/s
{/eq}. What is the force on the object due to its acceleration at {eq}(2^{\frac{1}{2}}, 12)
{/eq}? | {eq}F = \frac{432m}{4913}{/eq} | Fraction | Physics | University |
1584889 | Is there any standard function that outputs $1$ if an inequality is true and $0$ otherwise? | Indicator function $\Bbb{1}_{x>D}$ | Expression | Mathematics | University |
69045 | Amanda likes to eat bananas and apples with her lunch between classes. She also keeps a close eye on her spending each week since she is in college and cannot afford the time to work too much. She has budgeted a certain amount of money each week for apples and bananas. If she spends all of this budget on apples, she ca... | 0.6 apples | Float | Economics | Senior High School |
1823993 | I want to correct visual odometry (VO) trajectory with GPS and assign each point of the VO curve a computed GPS coordinate. Data I have: I have a curve that represents the VO trajectory (blue in the picture) - this trajectory was calculated via some computer vision algorithms and I know coordinates of every point of th... | $f(\begin{bmatrix} x \\ y \end {bmatrix}) = S + \frac{\|G-S \|}{\|F-S\|}R (\begin{bmatrix} x \\ y \end {bmatrix} - S)$ | Expression | Other STEM | University |
1935339 | Which of the following is false?
A. Fixed costs increase in the long run.
B. In the long run, both the amount of capital and labor used by the firm can be changed.
C. Long-run average variable costs equal long-run average total costs.
D. As a firm produces more output, eventually it experiences diseconomies of scal... | C | Multiple Choice | Economics | University |
928969 | A portable CD player was recently introduced that has a "special power saving technology." The manufacturer claims that with only two standard AA batteries (together: 3.0 V, 20 kJ energy storage), the player can be played for about 25 hours. What is the approximate resistance in the CD player's electrical circuitry? | 39Ω | Integer | Physics | Senior High School |
1563943 | Which statement best describes the relationship between the pope and the monarchs of Europe during the medieval period?
The monarchs controlled the pope and the bishops.
They kept one another from gaining too much power.
They helped one another maintain power over people.
The pope controlled the flow of money for ... | C | Multiple Choice | History | Junior High School |
2073102 | How many siblings did Booker T. Washington have? | 3 | Integer | History | Junior High School |
404414 | Find the volume of the solid generated by revolving the region bounded by {eq}\; y = 2x^{\frac{2}{3}} - x \;{/eq} and {eq}\; y = 0 \;{/eq} around the {eq}x{/eq}-axis. | 128\pi / 21 | Fraction | Mathematics | University |
201749 | Suppose you need to decide whether to keep a machine or replace it with a new one:
Old machine: Old machine can operate for 5 years with operating cost of $120,000 per year.
New machine: Replacing old machine with new one requires capital cost of $250,000 in year zero (zero salvage value for old machine).
Capital co... | -$3357.48 | Float | Finance | University |
604267 | In the sentence, "Tim's family took a trip to Paris last September," what is the direct object? | Trip | String | Other | Junior High School |
1578469 | Evidence from which type of data supports the common origin of all life on Earth? | Genetic Data | String | Biology | Senior High School |
1830700 | Construct a 90% confidence interval for the population mean of life insurance policy premiums, given a sample of 45 policy holders with an average premium of $345 and a sample standard deviation of $65. Make a statement about this in context of the problem. | (328.719, 361.281) | List | Mathematics | University |
1247821 | An object, after being released from its circular path, travels the distance OA at the same time it would have moved from O to P on the circle. The speed of the object on and off the circle remains constant at the same value. Suppose that the radius of the circle is 3.6 m and the angle is 25C. What is the distance OA? | 1.570 m | Float | Physics | Senior High School |
1832425 | A 149 g bullet is fired from a rifle having a barrel 0.504 m long. Assuming the origin is placed where the bullet begins to move, the force exerted on the bullet by the expanding gas is {eq}F = a + bx - cx^2
{/eq}, where {eq}a = 8130 N
{/eq}, {eq}b = 123000 N/m
{/eq}, {eq}c = 37800 N/m^2
{/eq}, with {eq}x
{/eq} in... | 18106.40079 J | Float | Physics | University |
1234162 | The Starship Enterprise returns from a warp drive to ordinary space with a forward speed of {eq}53\text{ km/s}
{/eq}. To the crew's great surprise, a Klingon ship is {eq}150\text{ km}
{/eq} directly ahead, traveling in the same direction at a mere {eq}22\text{ km/s}
{/eq}. Without evasive action, the Enterprise will... | 6.5 km/s^2 | Float | Physics | Senior High School |
969019 | Hall Company's fixed budget performance report for June follows.
The $660,000 budgeted expenses include $450,000 variable expenses and $210,000 fixed expenses. Actual expenses include $200,000 fixed expenses.
Prepare a flexible budget performance report that shows any variances between budgeted results and actual res... | Accounts titleFlexible budget (A)Actual results (B)Variance (C = A - B)Favorable/Unfavorable
Sales632,000647,80015,800Unfavorable
Less: Variable costs395,000406,85011,850Unfavorable
Contribution margin237,000240,9503,950Unfavorable
Less: Fixed costs210,000200,00010,000Favorable
Income from operations27,00040,95... | Other | Business | University |
1167276 | A solid 0.3 kg ball rolls smoothly from rest (starting at height H = 6.0 m) until it leaves the horizontal section at the end of the track, at height h = 2.3 m. How far horizontally from end point does the ball hit the floor. | 5.0 m | Float | Physics | Senior High School |
1751237 | Is the stability region $-2 < (1+ \lambda h)^2<0$ for the explicit midpoint method correct, and how do I find the correct stability region? | The stability region is defined by |1+z+0.5z^2|<=1, where z = Δtλ. The boundary of the stability region can be found by setting |1+z+0.5z^2|=1 and solving for the imaginary part b as a function of the real part a, where z=a+bi. This yields b=±sqrt(-a^2-2a+2sqrt(-a(a+2))). Plotting this expression will reveal the stab... | Expression | Mathematics | University |
818894 | An estimate of the efficiency-loss ratio of taxes on labor income is 15 percent.
The efficiency-loss ratio of taxes on capital income is estimated to be 45 percent.
Assuming that these estimates are accurate, calculate the change in well-being that would result from a $10 billion reduction in taxes on capital income,... | 3 billion | Integer | Economics | University |
411229 | Given a 3D cartesian system with known origo position and z-direction $\vec{e}_z' = (\cos\theta\sin\phi, \sin\theta\sin\phi, \cos\phi)$ in global coordinates, and knowing there is no rotation around the z-axis, how can I find rotation angles $\alpha, \beta$ around the x and y axes respectively such that $R = R_xR_y$, w... | β = sin⁻¹(x₃), α = Atan2(y₃,-y₂) where (x₃,y₃,z₃) represents the new z-direction | Expression | Mathematics | University |
1172983 | _____ is the movement of water across a membrane.
Select all that apply.
a. Diffusion
b. Facilitated diffusion
c. Osmosis
d. Active transport | c | Multiple Choice | Biology | Senior High School |
1432606 | Which of the following is an example of inductive reasoning?
A. June is the coolest summer month where I live, so it will probably be cool this June.
B. It was cool on the first day of summer, so the entire summer will be cool.
C. I heard on the radio that the first day of summer will be cool, so it will be cool tha... | A | Multiple Choice | Philosophy | Senior High School |
1126854 | Assume that the uncovered interest parity condition holds. Also assume that the Australian interest rate is greater than the U.K. interest rate. Given this information, we know that investors expect:
a. the pound to appreciate.
b. the Australian interest rate to fall.
c. the pound to depreciate.
d. the Australian d... | a | Multiple Choice | Economics | University |
1351328 | Let $Q$ be a finite quiver with vertex set $I$. Let $kQ = \bigoplus_{n \ge 0} k^{(n)}Q$ be the vector space direct sum decomposition of the path algebra $kQ$, where $k^{(n)}Q$ is the $k$-linear span of all paths of length $n$. Find a closed formula for the Poincaré series $P_{kQ}(t) = \sum_{n \ge 0} \text{dim}_k (k^{(n... | The generating function is the sum of the entries of the matrix $\sum_{n\ge0} A^nt^n=({
m Id}-At)^{-1}$ | Expression | Mathematics | University |
1746352 | Define asset turnover | Net Sales / Total Assets | Expression | Business | University |
1323766 | At room temperature, what fraction of the nitrogen molecules in the air are moving at less than 300 m/s? | 0.218 | Float | Physics | University |
1798038 | What is the amount assigned to each share of stock that is printed on the stock certificate called? | par value | String | Business | Senior High School |
695635 | Find the Maclaurin series of the function {eq}\displaystyle (2 x^2) (e^{\displaystyle -8 x})
{eq}. Then, find the coefficients from {eq}\displaystyle c_1
{eq} to {eq}\displaystyle c_5
{eq}. | c1=0, c2=2, c3=-16, c4=64, c5=-512/3 | List | Mathematics | University |
752663 | A light, unstressed spring has length d. Two identical particles, each with charge q, are connected to the opposite ends of the spring. The particles are held stationary a distance d apart and are then released at the same moment. The system then oscillates on a frictionless, horizontal table. The spring has a bit of i... | 5Cq^2/9d | Expression | Physics | University |
748386 | A corporate manager decides to build a new store on a lot owned by the corporation that could be sold to a local developer for $250,000. The lot was purchased for $50,000. How do you determine the value of the new store project? | NPV = \displaystyle \frac{CF1}{1 + I} + \frac{CF2}{(1 + I)^2} + \frac{CF3}{(1 + I)^3} + ... + \frac{CFn}{(1 + I)^n} - Total\:initial\:costs | Expression | Economics | University |
523483 | Use the Divergence Theorem to calculate the surface integral {eq}\displaystyle \iint_S \mathbf F \cdot d\mathbf S
{/eq}; that is, calculate the flux of {eq}\mathbf F
{/eq} across {eq}S
{/eq}.
{eq}\mathbf F(x,\ y,\ z) = x^2 y\mathbf i + x y^2\mathbf j + 3 x y z \mathbf k,\ S
{/eq} is the surface of the tetrahedron... | 56/15 | Fraction | Mathematics | University |
1998751 | How to determine a parametrization of the border of the $R$ region in a clockwise direction, where $R$ is defined by $y\geq \left | x \right |+2$ and $y\leq 4-x^{2}$? | $(1-|t|, |1-|t||+2)$ for $0\le t<2$ and $(t-3,-t^2+6t-5)$ for $2 \le t < 4$ | Expression | Mathematics | University |
202497 | How can we construct a 2x2 positive semi-definite matrix $A = \begin{pmatrix} a & b \\ c & d \end{pmatrix}$ such that $x^TAx = x^2a+xyb+xyc+dy^2 \geq 0$ for all vectors $(x, y)$? | A matrix is positive semi-definite if $x^TAx \geq 0$ for all vectors $x$. An example of 2x2 positive semi-definite matrix is $\begin{pmatrix}1&0\\ 0&1\end{pmatrix}$ | Matrix | Mathematics | University |
1958878 | An engine rejects energy {eq}1,933\ J
{/eq} to the cold reservoir while performing {eq}731\ J
{/eq} of work. Calculate the engine's efficiency. | 27.44% | Percentage | Physics | Senior High School |
626294 | An investment offers a total return of 12 percent over the coming year. Janet Jello thinks the total real return on this investment will be only 8.8 percent. What does Janet believe the inflation rate will be over the next year? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 dec... | 3.20% | Percentage | Finance | Senior High School |
1972347 | Evaluate the indefinite integral: $$\int{1\over (x+a)^2\cdot(x+b)^2} dx$$ | $$\frac{1}{(a-b)^2} \left( \frac{1}{x+a} - \frac{1}{x+b} \right) + \frac{2}{(a-b)^3}\ln\left|\frac{x+b}{x+a}\right| + C$$ | Expression | Mathematics | University |
1838514 | A prankster drops a water balloon from the top of a building on an unsuspecting person on the sidewalk below. If the balloon is travelling 35.4 m/s when it strikes a person's head (1.5 m above the ground), how tall is the building? Neglect air resistance. | 65 m | Integer | Physics | Senior High School |
1013795 | Let $A=\begin{pmatrix} 1 & 1 & -1\\ -1 & 3 & -1\\ -1 & 1 & 1 \end{pmatrix}$ and $f\in L(\mathbb R^3)$ be canonically associated to $A$. Given the diagonal matrix $B=\begin{pmatrix} 1 & 0 & 0\\ 0 & 2 & 0\\ 0 & 0 & 2 \end{pmatrix}$ and $P=\begin{pmatrix} 1 & -1 & 1\\ 0 & 1 & -1\\ -1 & 2 & -1 \end{pmatrix}$, how to calcul... | $A^n = P B^n P^{-1}$, where $B^n = \begin{pmatrix} 1^n & 0 & 0 \\ 0 & 2^n & 0 \\ 0 & 0 & 2^n \end{pmatrix}$ | Matrix | Mathematics | University |
5255 | Three identical charges of 3.0 {eq}\mu
{/eq}C are placed at the vertices of an equilateral triangle which measures 30 cm on a side. What is the magnitude of the electrostatic force which acts on an one of the charges?
A) 2.4 N
B) 1.6 N
C) 1.8 N
D) 2.2 N
E) 2.0 N | B | Multiple Choice | Physics | Senior High School |
2100135 | In 1961, two neurosurgeons were able to reduce seizure activity in epileptic patients by severing the corpus callosum. the neurosurgeons were: | Vogel and Bogen | String | Biology | University |
371017 | Convert the following matrix to reduced row echelon form:
$\left(
\begin{array}{cccccc}
8 & -1 & 9 & -5 & -2 & 7 \\
0 & -1 & 7 & -4 & 5 & -9 \\
9 & 0 & 10 & -7 & -7 & 10 \\
\end{array}
\right)$. | $\left(
\begin{array}{cccccc}
1 & 0 & 0 & \frac{2}{31} & -\frac{28}{31} & \frac{70}{31} \\
0 & 1 & 0 & -\frac{81}{62} & -\frac{261}{62} & \frac{55}{31} \\
0 & 0 & 1 & -\frac{47}{62} & \frac{7}{62} & -\frac{32}{31} \\
\end{array}
\right)$ | Matrix | Mathematics | University |
1402034 | Consider a 35 year coupon bond that pays $80 annual coupons (beginning one year from today). What is the future value of the coupons at maturity if you can invest them at 8%? | $13785.3 | Float | Finance | University |
378724 | Find an equation of the plane tangent to the paraboloid f(x, y, z) = 32 - 3x^2 - 4y^2 - z at (2, 1, 16). | T(x,y) = 48-12x-8y | Expression | Mathematics | University |
649984 | Consider the flow of a fluid with viscosity{eq}\mu
{/eq} through a circular pipe. The velocity profile in the pipe is given as u(r) = umax(1 - r^n/R^n), where umax is the maximum flow velocity, which occurs at the centerline; r is the radial distance from the centerline; and u(r) is the flow velocity at the position r... | F/L = 2nμπu_max | Expression | Physics | University |
337786 | Set up the integrals that represent the area inside r = 6, but outside r = 12 cos(θ). | \int_{\frac{\pi}{3}}^{\frac{2\pi}{3}} \int_{6}^{12 \cos \theta} r \ dr \ d \theta | Expression | Mathematics | University |
24720 | A variable force of {eq}x^2 - 2x
{/eq} pounds moves an object along a straight line when it is {eq}x
{/eq} feet from the origin. Determine the work {eq}W
{/eq} done in moving the object from {eq}x = 2
{/eq} to {eq}x = 3
{/eq} feet. | 4/3 ft⋅lb | Fraction | Physics | Senior High School |
1432523 | The following data refer to Industrial Manufacturing Pty Ltd for the current year:
Sales revenue
$3,157,500
Raw material inventory, 1 January
133,500
Purchases of raw material
1,096,500
Raw material inventory, 31 December
88,500
Direct... | $45,000 reduction | Integer | Business | University |
1687450 | Let $G$ be a weighted graph with edge weights greater than one and $G’$ be the graph constructed by squaring the weights of edges in $G$. Let $T$ and $T’$ be the minimum spanning trees of $G$ and $G’$, respectively, with total weights $t$ and $t’$. Which of the following statements is TRUE?
(A) $T’ = T$ with total weig... | B | Multiple Choice | Mathematics | University |
2059639 | Karl is going to visit the local community mental health center. He is most likely to see a:
a. pastoral counselor
b. psychoanalyst
c. psychiatrist
d. clinical psychologist | c | Multiple Choice | Psychology | Senior High School |
1262419 | Given the process $X_t = (2+t+\exp(W_t))_t$ where $W_t$ is Brownian motion, find functions $\sigma, \tau$ such that $X_t = X_0 + \int_0^t \sigma(W_s,s)dW_s + \int_0^t\tau(W_s,s)ds$. | $dX_t = \exp(W_t)dW_t + (1+0.5\exp(W_t))dt = (X_t-2-t)dW_t + (1+0.5(X_t - 2 - t))dt$ | Expression | Mathematics | University |
1619111 | find the coefficient of $z^n$ in expansion of $e^z \cos z$ | $\frac{1}{n!} \sum_{0\leq 2k\leq n} \binom{n}{k}(-1)^k$ | Expression | Mathematics | University |
546798 | Drug side effects are endless and can vary depending on the ____________. | Individuals | String | Biology | Senior High School |
1449529 | Why are some producers forced to sell their products at the prevailing market price?
a) Price takers find market analysis is too costly.
b) They can increase output without affecting quality.
c) High degree of similarity to competitors products.
d) They are very small players in the overall market | d | Multiple Choice | Economics | Senior High School |
555080 | What is Stefan Boltzmann law? | L=A*sigma*T^4 | Expression | Physics | Senior High School |
1678101 | Determine the time required for a 1.25 cm diameter Carbon Steel (1% C) sphere to cool from 500 {eq}^o{/eq}C to 100 {eq}^o{/eq}C if exposed to a cooling airflow at 25 {eq}^o{/eq}C. Assume h = 110 W/m{eq}^2{/eq}-K. Assume the thermal conductivity of 1% C steel is 40 W/m-K. | 128.99s | Float | Physics | University |
580323 | How many partitions of $n$ distinct objects are there, given that all parts are equinumerous, excluding the empty partition and the identity partition? What is the number of such partitions when $n = p^2$ with $p$ prime, specifically when $n = 9,$ or $25,$ or $49$? | $\frac{(p^2)!}{(p!)^{p+1}}$ | Expression | Mathematics | University |
983999 | Construct a {eq}95\%{/eq} confidence interval for the mean incubation period of the SARS virus interpret the interval, based on the information that the mean incubation period was {eq}5{/eq} days, with a standard deviation of {eq}14.7{/eq} days from interviews with {eq}96{/eq} SARS patients. | (2.0218, 7.9781) | List | Mathematics | University |
1986691 | A force {eq}\vec{F} = 2\vec{i} + \vec{j} - 3\vec{k}{/eq} is applied to a spacecraft with velocity {eq}\vec{V} = 3\vec{i} - \vec{j}{/eq}. Express {eq}\vec{F}{/eq} as a vectors parallel and orthogonal to two vectors parallel and orthogonal to {eq}\vec{V}{/eq}. | The parallel component is (1.5i - 0.5j) N and the orthogonal component is (0.5i + 1.5j - 3k) N | List | Physics | University |
1713444 | Let $X$ be a random variable having a normal distribution with mean $\mu$ and standard deviation $\sigma$. The observations $(x_i; i=1,2,\cdots,n)$ have measurement errors that are normally distributed with zero mean and known standard deviation $\delta$. Use the method of maximum likelihood to estimate $\mu$ and $\sig... | $\widehat{\sigma}^2 = \max\{s^2,\delta^2\} - \delta ^2 = \max\{s^2-\delta^2, 0\}$ | Expression | Mathematics | University |
824609 | The wavelength of yellow sodium light is 589 nm.
What is its frequency? | 5.09 * 10^14 Hz | Float | Physics | Senior High School |
1848114 | A 4.6-kg block slides down an inclined plane that makes an angle of 26 with the horizontal. Starting from rest, the block slides a distance of 2.6 m in 4.9 s. Find the coefficient of kinetic friction between the block and plane. | 0.46 | Float | Physics | Senior High School |
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