inclusionAI/Ring-lite-rl-data huggingface dataset:
A certain commodity has a cost price of 200 yuan and a marked price of 400 yuan. What is the maximum discount that can be offered to ensure that the profit margin is not less than 40%?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{30\%}
Given the equations:
\[
\log_{2}\left[\log_{\frac{1}{2}}\left(\log_{2} x\right)\right]=\log_{3}\left[\log_{\frac{1}{3}}\left(\log_{3} y\right)\right]=\log_{5}\left[\log_{\frac{1}{5}}\left(\log_{5} z\right)\right]=0
\]
Determine the relationship among x, y, and z. Express your answer in the format x? y? z, where? represents <, >, or =.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{z < x < y}
Evaluate the expression $-20 + 15 \times (4^{\div -1} \times 2)$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{-12.5}
Given the function $f\left(x\right)=\cos 2x\cdot \ln x$, find the derivative of $f\left(x\right)$. Express your answer as a mathematical expression.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{-2\sin 2x\cdot \ln x + \frac{\cos 2x}{x}}
Given the function $f(x) = (x+1)^3 + 1$, a positive geometric sequence $\{a_{n}\}$ satisfies $a_{1012} = \frac{1}{10}$. Find $\sum_{k=1}^{2023} f(\log{a}_{k})$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{2023}
Two small rulers form a set square, where the small ruler can slide along the large ruler. Each unit on the large ruler is marked with natural numbers. The first small ruler divides 11 units on the large ruler into 10, and the second small ruler divides 9 units on the large ruler into 10. The starting points of both small rulers are 0, marked from 1 to 10 respectively. Now measure the distance between points \(A\) and \(B\), with point \(A\) at 0 units on the large ruler, and point \(B\) between 18 and 19 units on the large ruler. When the 0 unit of the first small ruler is placed at point \(B\), its 3rd unit coincides with a certain unit on the large ruler. If the 0 unit of the second small ruler is placed at point \(B\), then which unit of the second small ruler coincides with a certain unit on the large ruler?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{7}
Use the Newton-Raphson method to find the value of $t$ near $0.04$, correct to four decimal places, for which the amplitude $y$ is $0.880$ in the equation:
\[ y = \left(t + \frac{\pi}{4}\right) + \sin(t) + \frac{1}{8}\sin(3t) \]
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{0.0399}
A quadrilateral is inscribed in a circle with a radius of 13. The diagonals of the quadrilateral are perpendicular to each other. One of the diagonals is 18, and the distance from the center of the circle to the point where the diagonals intersect is \( 4 \sqrt{6} \).

Find the area of the quadrilateral.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{18 \sqrt{161}}
Determine the rank of the linear function $f: V \to W$, where $V$ is the vector space of all square matrices with trace 0, and $W$ is the set of real numbers.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{1}
Rectangle $W X Y Z$ has $W X=4, W Z=3$, and $Z V=3$. The rectangle is curled without overlapping into a cylinder so that sides $W Z$ and $X Y$ touch each other. In other words, $W$ touches $X$ and $Z$ touches $Y$. The shortest distance from $W$ to $V$ through the inside of the cylinder can be written in the form $\sqrt{\frac{a+b \pi^{2}}{c \pi^{2}}}$ where $a, b$ and $c$ are positive integers. What is the smallest possible value of $a+b+c$?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{18}
Find the domain of the function $f(x) = \ln(x - 1)$. Express your answer as a set of all x satisfying a certain condition.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\{x | x > 1\}}
The owner of an apartment rents it out for five years and receives 240,000 rubles from tenants at the end of each year. He does not spend his rental income, but keeps it in a term deposit at 10% annual interest (capitalized once at the end of each year). What amount will the owner have in the account after five years?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{1465224}
What is the smallest constant $\alpha$ such that, given 19 points on a solid, regular hexagon with side 1, there will always be 2 points with distance at most $\alpha$?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{0.5}
设点 $A$ 的坐标为 $(0,3)$, 点 $B, C$ 为圆 $O: x^{2}+y^{2}=25$ 上的两动点, 满足 $\angle B A C=90^{\circ}$.  $\triangle A B C$ 面积的最大值为$\frac{a+b \sqrt{c}}{d}$，求$a+b+c+d$的值。
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{71}
Pizzas are sized by diameter. What percent increase in area results if Lorrie’s pizza increases from a 16-inch pizza to an 18-inch pizza?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{26.5625\%}
The numbers \(a, b, c\) lie in the interval \((0 ; \pi / 2)\) and satisfy the equations: \(\cos a = a\), \(\sin (\cos b) = b\), \(\cos (\sin c) = c\). Arrange these numbers in ascending order.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{b < a < c}
In triangle \(ABC\), the angle bisector \(AP\) is drawn. It is known that \(BP = 16\), \(PC = 20\), and the circumcenter of triangle \(ABP\) lies on segment \(AC\). Find side \(AB\).
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{ \frac{144 \sqrt{5}}{5} }
在正六棱锥中，侧面与底面的夹角均为 \df{\pi}{3}，则其外接球与内切球的半径的比值为__________.原始的答案是\frac{m}{n}的形式，其中m、n是互质的。请给出最终m + n的值
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{19}
18. Let $A B C$ be an equilateral triangle. Let $\overrightarrow{A B}$ be extended to a point $D$ such that $B$ is the midpoint of $\overline{A D}$. A variable point $E$ is taken on the same plane such that $D E=A B$. If the distance between $C$ and $E$ is as large as possible, what is $\angle B E D$ ?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{15}
Evaluate the integral: \[ \int_0^{2\pi} - \frac{\cos t \; ( 2 (\sin t)^2 + (\cos t)^2)}{(\cos t)^4 + (\sin t)^2} \, dt \]
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{0}
Let \( \omega \) be a circle, and let \( ABCD \) be a quadrilateral inscribed in \( \omega \). Suppose that \( BD \) and \( AC \) intersect at a point \( E \). The tangent to \( \omega \) at \( B \) meets line \( AC \) at a point \( F \), so that \( C \) lies between \( E \) and \( F \). Given that \( AE = 6 \), \( EC = 4 \), \( BE = 2 \), and \( BF = 12 \), find \( DA \).
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{2\sqrt{42}}
Let (1+√2)^2012 = a + b√2, where a and b are integers. Find the greatest common divisor of b and 81. Express your answer as a single integer.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{3}
Consider the set $\mathcal F$ consisting of all holomorphic functions $f$ in the unit disc $\Bbb D$ such that $f(\Bbb D)\subset\Bbb D$, and satisfying $f\left(\frac12\right)=f'\left(\frac12\right)=0$. Determine the supremum of $|f(0)|$ over all functions $f$ in $\mathcal F$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{1/4}
David has a collection of 40 rocks, 30 stones, 20 minerals and 10 gemstones. An operation consists of removing three objects, no two of the same type. What is the maximum number of operations he can possibly perform?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{30}
Evaluate the integral \( \int \frac{5z^2 - 3z + 2}{(z-1)^3} \, dz \) using the Cauchy Integral Formula.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{10\pi i}
Determine the maximal interval of definition for solutions of the autonomous differential equation $\dot{x}=f(x)$, where $f:\mathbb{R}\rightarrow \mathbb{R}$ is locally Lipschitz continuous, $f(0)=0=f(1)$, and at time zero, $\dot{x}$ lies in the interval $[0,1]$. What is this interval?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{(-\infty, \infty)}
Let $x$ and $y$ be positive real numbers and $\theta$ an angle such that $\theta \neq \frac{\pi}{2}n$ for any integer $n$.  Suppose
\[\frac{\sin\theta}{x}=\frac{\cos\theta}{y}\]
and
\[
\frac{\cos^4 \theta}{x^4}+\frac{\sin^4\theta}{y^4}=\frac{97\sin2\theta}{x^3y+y^3x}.
\]
Compute $\frac xy+\frac yx.$
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{14}
7. There are 5 power poles, 2 of which will leak electricity. There are 5 birds each randomly choosing one of the poles to rest (if a bird touches a leaking pole, it will be stunned by the electric shock and fall to the ground). The probability that only 2 of the poles have birds on them is $\qquad$
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\frac{342}{625}}
Find the principal on a certain sum of money at 5% per annum for 2 2/5 years if the amount being Rs. 2120. What is the principal amount in rupees?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{1892.86}
A fat coin is one which, when tossed, has a \(\frac{2}{5}\) probability of being heads, \(\frac{2}{5}\) of being tails, and \(\frac{1}{5}\) of landing on its edge. Mr. Fat starts at 0 on the real line. Every minute, he tosses a fat coin. If it's heads, he moves left, decreasing his coordinate by 1; if it's tails, he moves right, increasing his coordinate by 1. If the coin lands on its edge, he moves back to 0. If Mr. Fat does this indefinitely, what fraction of his time will he spend at 0?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\frac{1}{3}}
Determine the number of relatively prime dates in the month with the second fewest relatively prime dates.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{11}
There are 30 people sitting around a round table - knights and liars (knights always tell the truth, and liars always lie). It is known that each of them has exactly one friend at the table, and if one is a knight, their friend is a liar, and vice versa (friendship is always mutual). In response to the question "Is your friend sitting next to you?" the individuals who are sitting in every other seat answered "Yes." How many of the remaining individuals could also answer "Yes"?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{0}
Evaluate the integral \( \int_{0}^{\infty} \frac{\log(x) }{\sqrt{x} (x+1)^{2}}\,dx \).
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{-\pi}
When Betty makes cheesecake, she sweetens it with a ratio of one part sugar to four parts cream cheese. She flavors it with a certain ratio of vanilla to cream cheese. For every one teaspoon of vanilla, she uses two eggs. She used two cups of sugar and 8 eggs in her latest cheesecake. What is the ratio of vanilla to cream cheese?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{1:96}
Determine the smallest finite field in which the polynomial \((x^2+x+1)(x^5+x^4+1)\) is reducible.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\mathbb{F}_2}
In a configuration of 16 students, each positioned at the vertices of concentric regular pentagons, a total of 3360 coins are distributed such that students equidistant from the center receive the same number of coins. After a redistribution process where each student gives all their coins equally to their neighbors, each student ends up with the same number of coins they started with. How many coins did the student in the central circle originally have?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{280}
Let $F$ be a field of order $32$. Determine the number of non-zero solutions $(a, b) \in F \times F$ to the equation $x^2 + xy + y^2 = 0$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{0}
The diagonals of convex quadrilateral $BSCT$ meet at the midpoint $M$ of $\overline{ST}$.  Lines $BT$ and $SC$ meet at $A$, and $AB = 91$, $BC = 98$, $CA = 105$.  Given that $\overline{AM} \perp \overline{BC}$, find the positive difference between the areas of $\triangle SMC$ and $\triangle BMT$.

[i]Proposed by Evan Chen[/i]
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{336}
Random variable $Z$ has a mean of $15$ and a standard deviation of $2$. What is the minimum percentage of $Z$ values that lie between $8$ and $17$?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{42.45\%}
Let $G=(L\cup R,E)$ be a bipartite graph with $n$ nodes on each side. Determine the maximum value of $n$ such that if any two vertices in $L$ have at least two neighbors in $R$, then $G$ has a perfect matching.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{2}
Strain A had 9000 cells and decreased at a rate of 3000 cells per hour. Strain B started with 4000 cells and decreased at a rate of 2000 cells per hour. When will the strains have the same number of cells? Give the ordered pair please!
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{(3, 0)}
Consider an ellipse given by \(\frac{x^2}{4} + y^2 = 1\). A point \(P\) on the ellipse has an eccentric angle of \(45^\circ\). Through this point, variable pairs of chords are drawn such that they are perpendicular to each other and meet the ellipse at points \(A\) and \(B\). If the line joining \(A\) and \(B\) always passes through a fixed point \(Q(a, b)\), find the value of \(a^2 + b^2\).
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\dfrac{9}{10}}
Pikachu, Charmander, and Vulpix are three of the four equally-skilled players in a Pokemon bracket tournament. Because they are equally skilled, whenever any two of the players battle, they are equally likely to win. In the bracket tournament, the four players are randomly paired into two rounds, each round consisting of two players. The winners of the first two rounds then play each other in the final round. The winner of the final match ranks first; the loser of the final round ranks second; and the two losers of the previous rounds jointly rank third. What is the probability that Charmander plays Vulpix in a round, but ranks lower than Pikachu? Express your answer in the form \(\frac{k}{m}\) where the fraction is in simplest form, and provide the value of \(k + m\).
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{9}
The algebraic expression $4x^{2}+3mx+9$ is a perfect square trinomial. Then, $m=$ \_\_\_\_\_\_ .
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\pm 4}
Calculate the expected number of turns required to jump from the ground floor (floor 0) to the 5th floor in a building with 5 floors. The probability of jumping from the ground to floor 1 is 1. For each floor i (where i ranges from 1 to 4), the probability of jumping to the next floor (i+1) is \( \frac{1}{3^i} \), the probability of staying on the same floor is \( \frac{3^i-1}{2 \times 3^i} \), and the probability of jumping back to the previous floor (i-1) is \( \frac{3^i-1}{2 \times 3^i} \).
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{14543}
A quadrilateral has side lengths of 70, 90, 130, and 110, in that order. It is both inscribed in a circle and has an incircle. The points where the incircle touches the side of length 130 divide it into segments of lengths \( x \) and \( y \). Determine the value of \( |x - y| \).
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{13}
In a circuit with 2000 components, every pair of components is initially connected by a wire. Vasya and Petya take turns cutting wires, with Vasya starting. Vasya cuts one wire per turn, while Petya cuts two or three wires per turn. The player who cuts the last wire connected to any component loses. Determine which player has a winning strategy.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{Petya}
To make the inequality $0\leqslant x^{2}+ax+6\leqslant 4$ have exactly one solution with respect to $x$, then $a=\_\_\_\_\_\_$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\pm2\sqrt{2}}
Find the value of \(x\) that satisfies the equation: \[ 1 + x + \frac{1\cdot3}{2!}x^2 + \frac{1\cdot3\cdot5}{3!}x^3 + \ldots = \sqrt{2} \]
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\dfrac{1}{4}}
Yan is at a point between his house and a park. He has two options to reach the park: He can either walk directly to the park or he can walk back to his house and use his scooter to reach the park. He scoots 10 times faster than he walks, and both routes take the same amount of time. Determine the ratio of Yan's distance from his house to his distance to the park.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\frac{9}{11}}
Consider a Wiener-Hopf integral equation of the first kind with unknown function $\phi(x)$ for $x\geq 0$: $$f(x)=\int_0^\infty \phi(y)\min\{x,y\}\,\mathrm{d}y.$$ If $f(x)=\sin(x)$, find the solution for $\phi(x)$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\sin(x)}
Let $a_d$ be the number of non-negative integer solutions $(a, b)$ to $a + b = d$ where $a \equiv b \pmod{n}$ for a fixed $n \in \mathbb{Z}^+$. Consider the generating function $M(t) = a_0 + a_1t + a_2t^2 + \ldots$ Consider
$$P(n) = \lim_{t\to 1} \left( nM(t) - \frac{1}{(1 - t)^2} \right).$$
Then $P(n)$, $n \in \mathbb{Z}^+$ is a polynomial in $n$, so we can extend its domain to include all real numbers while having it remain a polynomial. Find $P(0)$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{0}
An even perfect square in the decimal system is of the form: $\overline{a b 1 a b}$. What is this perfect square?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{76176}
Let $S$ be the set of monic polynomials in $x$ of degree 6, all of whose roots are members of the set $\{-1, 0, 1\}$. Let $P$ be the sum of the polynomials in $S$. What is the coefficient of $x^4$ in $P(x)$?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{70}
Let $T: \mathbb{R}^4 \to \mathbb{R}^4$ be a linear map with a null space defined by the condition $(x, y, w, z) \in \mathbb{R}^4$ such that $x + y + w + z = 0$. If the rank of $(T - 4I_4)$ is 3, and the minimal polynomial of $T$ is $x(x - 4)^{\alpha}$, what is the value of $\alpha$?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{1}
Given a cyclic quadrilateral \(ABCD\). The rays \(AB\) and \(DC\) intersect at point \(K\). It turns out that points \(B\), \(D\), and the midpoints of segments \(AC\) and \(KC\) lie on the same circle. What values can the angle \(ADC\) take?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{90^\circ}
设函数$f\left( x \right)$在定义域(0，+∞)上是单调函数，$\forall x\in \left( 0,+\infty  \right),f\left[ f\left( x \right)-{{e}^{x}}+x \right]=e$，若不等式$f\left( x \right)+{f}'\left( x \right)\ge ax$对$x\in \left( 0,+\infty  \right)$恒成立，则实数$\textit{a}$的取值范围是______．
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{$\left( -\infty ,2e-1 \right]$}
Given the rational numbers $a$, $b$, $c$, $d$ satisfy $2006 = 9a = 15b = 32c = 68d$, arrange the numbers $a$, $b$, $c$, $d$ in descending order.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{a > b > c > d}
Car A and Car B start simultaneously from locations A and B, respectively, and they travel between these two locations at constant speeds. After the first time they meet, Car A takes 4 hours to reach B, while Car B takes 1 hour to reach A. How many hours have both cars traveled by the 15th time they meet (excluding meetings at locations A and B)?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{86}
The workday at the enterprise was 8 hours. During the first six hours, labor productivity met the planned level, but then it fell by 25%. The director, in agreement with the workforce, extended the shift by an hour. It turned out that for the added hour, the first six hours were again at the planned productivity level, but afterward, productivity dropped by 30%. By what percent did the overall productivity for the shift increase as a result of extending the workday?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{8 \%}
In a movie theater, five friends took seats from 1 to 5 (the leftmost seat is number 1). During the movie, Anya went to get popcorn. When she returned, she found that Varya had moved one seat to the right, Galya had moved two seats to the left, and Diana and Ella had swapped seats, leaving the end seat for Anya. In which seat was Anya sitting before she got up?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{4}
1. Milan moved 10 steps forward, then returned 2 steps back, then 10 forward and 1 back, then again 10 forward and 2 back, etc. How many steps does Milan need to take to be 1000 steps away from the starting point?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{1356}
Evaluate the limit: \[ \lim_{n \to \infty} \sum_{k=1}^{\infty}\frac{1}{k^{2}\sqrt[k]{n}}\sin^{2}\left(\frac{n \pi}{k}\right) \]
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{0}
Every week Roger pays for a movie ticket and a soda out of his allowance. Last week, Roger's allowance was $A$ dollars. The cost of his movie ticket was $20\%$ of the difference between $A$ and the cost of his soda, while the cost of his soda was $5\%$ of the difference between $A$ and the cost of his movie ticket. To the nearest whole percent, what fraction of $A$ did Roger pay for his movie ticket and soda?

Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{23%}
Calculate the limit using Taylor expansions or the Generalized Binomial Theorem:

$$\lim_{x \rightarrow 0} \frac{(1+3x)^{\frac{1}{2x}} - (1+2x)^{\frac{3}{x}}}{x}$$
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{-\infty}
Every week Roger pays for a movie ticket and a soda out of his allowance. Last week, Roger's allowance was $A$ dollars. The cost of his movie ticket was $20\%$ of the difference between $A$ and the cost of his soda, while the cost of his soda was $5\%$ of the difference between $A$ and the cost of his movie ticket. To the nearest whole percent, what fraction of $A$ did Roger pay for his movie ticket and soda?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{$23\%$}
Starting with a $5 \times 5$ grid, choose a $4 \times 4$ square in it. Then, choose a $3 \times 3$ square in the $4 \times 4$ square, and a $2 \times 2$ square in the $3 \times 3$ square, and a $1 \times 1$ square in the $2 \times 2$ square. Assuming all squares chosen are made of unit squares inside the grid, in how many ways can the squares be chosen so that the final $1 \times 1$ square is the center of the original $5 \times 5$ grid?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{36}