inclusionAI/Ring-lite-rl-data huggingface dataset:
Michael scored 260 points during his freshman year on the school basketball team. In his sophomore year, he improved by 15% and scored P% more points during his junior year than he did in his sophomore year. Finally, in his senior year, he scored 12% more points than in his junior year, plus an extra 17 points from successful free throws. If the total number of points scored during all four years is 1,450, find the value of P.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{38\%}
In a caravan, in addition to 50 hens, there are 45 goats, 8 camels, 12 spiders, and 6 octopuses with some keepers. 3 of the keepers have a prosthetic leg, while 2 of the keepers have a missing leg. If the total number of feet is 372 more than the number of heads in the caravan, the number of keepers is:
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{39}
Determine the fifth-largest divisor of 2,500,000,000.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{156,250,000}
Determine the range of values for the real number \(\lambda\) such that the inequality \(\sqrt{x(x^2 + 8)(8-x)} < \lambda(x+1)\) holds for all real numbers \(x\) in the interval \((0, 2)\).
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{(4, \infty)}
Calculate the marginal probability \( P(X_1=27, X_2=20) \) given the joint probability distribution:
\[
f(X_1, X_2 \mid p_1, p_2) = p_1^{x_1} (1 - p_1)^{(n_1-x_1)}p_2^{x_2}(1-p_2)^{(n_2-x_2)},
\]
where \( p_1 \sim \text{Unif}(0,1) \) independently \( p_2 \sim \text{Unif}(0,1) \), \( n_1=34 \), and \( n_2 = 56 \).
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\dfrac{1}{1995}}
Jonsey is awake for 2/3 of the day and spends 1/2 her time awake playing outside and the rest inside. Her brother, Riley, is awake for 3/4 of the day and spends some fraction of his day outside and the rest inside. On average, they spend 10 hours inside. What fraction of his day does Riley spend outside?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\frac{8}{9}}
Identify the tensor product $H \otimes_{\mathbb R} \mathbb C$ in familiar terms, where $H$ is the Hamiltonian quaternions, $\mathbb C$ is the complex numbers, and $\mathbb R$ is the real numbers.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{M_2(\mathbb{C})}
A grocer creates a display of cans where the top row contains two cans and each subsequent lower row has three more cans than the row preceding it. If the total number of cans used in the display is 120, how many rows are there in the display?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{n = 9}
Rapidly spinning a coin that is standing upright (assuming the axis of rotation remains stationary), the three-dimensional shape formed by the rotation is ___.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\text{sphere}}
For 8-bit symbols, Reed-Solomon codes are of the form \((n,k) = (255-z,255-2t-z)\), where:

- \(n\) is the number of symbols in a codeword.
- \(k\) is the number of data symbols that can be encoded.
- \(t\) is the number of errors that can be corrected.
- \(z\) is the number of implicit zeros that can be used if the code is to be shortened.

Determine the maximum value of \(t\) for these codes.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{127}
Determine the values of $r$ for which there exists a finite $r$-dense subset in the unit ball of $C([0,1])$ with respect to the supremum norm $d_{	ext{inf}}$. A subset $Y \subset (X, d)$ is $r$-dense if for every $x \in X$, there exists a $y \in Y$ such that $d(x, y) < r$. Provide the set of values for $r$ where such a finite subset exists.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{(1, \infty)}
Equilateral $\triangle DEF$ has side length $300$. Points $R$ and $S$ lie outside the plane of $\triangle DEF$ and are on opposite sides of the plane. Furthermore, $RA=RB=RC$, and $SA=SB=SC$, and the planes containing $\triangle RDE$ and $\triangle SDE$ form a $150^{\circ}$ dihedral angle. There is a point $M$ whose distance from each of $D$, $E$, $F$, $R$, and $S$ is $k$. Find $k$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{300}
In triangle $A B C, \angle B A C=60^{\circ}$. Let \omega be a circle tangent to segment $A B$ at point $D$ and segment $A C$ at point $E$. Suppose \omega intersects segment $B C$ at points $F$ and $G$ such that $F$ lies in between $B$ and $G$. Given that $A D=F G=4$ and $B F=\frac{1}{2}$, find the length of $C G$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\frac{16}{5}}
Let  $\alpha\geq 1$  be a real number. Define the set  $$ A(\alpha)=\{\lfloor \alpha\rfloor,\lfloor 2\alpha\rfloor, \lfloor 3\alpha\rfloor,\dots\} $$  Suppose that all the positive integers that **does not belong** to the  $A(\alpha)$  are exactly the positive integers that have the same remainder  $r$  in the division by  $2021$  with  $0\leq r<2021$ . Determine all the possible values of  $\alpha$ .
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{["\\frac{2021}{2020}"]}
Find the maximum value of  $$ \int^1_0|f'(x)|^2|f(x)|\frac1{\sqrt x}dx $$  over all continuously differentiable functions  $f:[0,1]\to\mathbb R$  with  $f(0)=0$  and  $$ \int^1_0|f'(x)|^2dx\le1. $$
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\frac{2}{3}}
Let $f(x)$ be a strictly increasing function defined for all $x > 0$ such that $f(x) > -\frac{1}{x}$ for all $x > 0$, and
\[f(x) f \left( f(x) + \frac{1}{x} \right) = 1\]for all $x > 0$.  Find $f(1)$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\frac{1-\sqrt{5}}{2}}
Given the function $f(x) = \log_{3}(x^{2} + ax + a + 5)$, if $f(x)$ is a decreasing function in the interval $(-\infty, 1)$, then the range of the real number $a$ is:
_______ .
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{-3 \leq a \leq -2}
Unit size cubes are stacked inside a large rectangular box with dimensions corresponding to four consecutive multiples of a prime number p. Choose the exact number of cubes that can completely fill the box.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{6p^3}
Among the numbers $11n + 10^{10}$, where $1 \le n \le 10^{10}$ is an integer, how many are squares?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{44801}
On a horizontal plane, there are 4 touching spheres with a radius of \( 20 - 10 \sqrt{2} \), and their centers form a square. Above the center of the square, a fifth sphere of the same radius is placed on top of the four spheres. Find the distance from its highest point to the plane.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{20}
Alex is stuck on a platform floating over an abyss at $1 \mathrm{ft} / \mathrm{s}$. An evil physicist has arranged for the platform to fall in (taking Alex with it) after traveling 100ft. One minute after the platform was launched, Edward arrives with a second platform capable of floating all the way across the abyss. He calculates for 5 seconds, then launches the second platform in such a way as to maximize the time that one end of Alex's platform is between the two ends of the new platform, thus giving Alex as much time as possible to switch. If both platforms are 5 ft long and move with constant velocity once launched, what is the speed of the second platform (in $\mathrm{ft} / \mathrm{s}$)?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{3 \mathrm{ft} / \mathrm{s}}
the original price of a suit is $300. The price increased by 20%, and after this increase, the store published a 30% off coupon for a one-day sale. However, the day after the sale, the price was reduced by an additional 10%. Given that the consumers who used the coupon on the sale day were getting 30% off the increased price, how much did those who bought the suit the day after the sale pay for the suit?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\$324}
Given the hyperbola $my^{2}-x^{2}=1$ whose one vertex lies on the axis of the parabola $y= \frac {1}{2}x^{2}$, determine the eccentricity of the hyperbola. Express your answer as a numerical value.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\sqrt{5}}
A rectangular grass field is 75 m * 55 m, it has a path of 2.5 m wide all round it on the outside. The area of the path is 6750 sq m. If the cost of constructing the path is Rs. 10 per sq m, what is the total cost of constructing the path?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{Rs. 6750}
Let $M$ be a subset of the set of $2021$ integers $\{1, 2, 3, ..., 2021\}$ such that for any three elements (not necessarily distinct) $a, b, c$ of $M$ we have $|a + b - c | > 10$.
Determine the largest possible number of elements of $M$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{1006}
In rectangle $ABCD$ with center $O$, where $AB=10$ and $BC=8$, circle $\gamma$ is centered at $O$ and is tangent to both $\overline{AB}$ and $\overline{CD}$. Points $M$ and $N$ are located on $\overline{AD}$ and $\overline{BC}$, respectively. The segment $MN$ intersects $\gamma$ at two distinct points $P$ and $Q$, with $P$ between $M$ and $Q$. Given that the ratio $MP : PQ : QN = 3 : 5 : 2$, the length $MN$ can be expressed as $\sqrt{a} - \sqrt{b}$, where $a$ and $b$ are positive integers. Determine the value of $100a + b$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{16808}
Given the universal set U = A ∪ B = {x ∈ ℤ | 0 ≤ x ≤ 6} and A ∩ (∁_U B) = {1, 3, 5}, deduce the set B. Express your answer as a set of integers, including all elements of the set.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{{0, 2, 4, 6}}
In how many ways can 1 apple, 2 peaches, 3 cucumbers, and 2 plums be distributed among Annus, Bözsi, Cili, and Dóra so that each girl gets 2 whole fruits? (Fruits of the same type cannot be distinguished from each other.)
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{204}
Juvy has a garden that is divided into 60 equally spaced rows with 18 plants in each row. She plants parsley in 3/5 of the rows, rosemary in 1/4 of the rows, mint in 1/6 of the remaining rows, thyme in 7/12 of the remaining rows after mint, and basil in 2/3 of the remaining rows after thyme. The rest of the rows will be planted with chives. How many chives will Juvy plant?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{36}
已知两圆$$x^{2}+y^{2}=9$$和$$(x-3)^{2}+y^{2}=27$$，求大圆被小圆截得劣弧的长度.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\sqrt{3}\pi}
Evaluate the integral:

$$\int_{0}^{1} (1-x^7)^{\frac{1}{3}}-(1-x^3)^{\frac{1}{7}} \: dx$$
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{0}
Each face of a cube is painted either red or blue, each with probability $1/2$. The color of each face is determined independently. What is the probability that the painted cube can be placed on a horizontal surface so that the four vertical faces are all the same color? The original answer is in \frac{k}{m} format, please give the value of k + m.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{21}
Find the angle between the line of intersection of the planes $2 x-y-3 z+5=0$ and $x+y-2=0$ and the plane passing through the points $M(-2 ; 0 ; 3), N(0 ; 2 ; 2)$ and $K(3 ;-3 ; 1)$.

#
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\arcsin\frac{22}{3\sqrt{102}}}
A bagel is cut into sectors. A total of 10 cuts were made. How many pieces were formed?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{11}
Let \( k \) be a positive constant. The sequence \( x_i \) of positive real numbers has a sum equal to \( k \). What are the possible values for the sum of \( x_i^2 \)?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{(0, k^2)}
Karina took several matches from a box and assembled from them a $3 \times 7$ grid of squares with sides equal to one match, as shown in the picture below.

What is the minimum number of matches she needs to take from the box so that with all the matches she can assemble a square grid? (The squares in the grid must again have a side equal to one match. There should not be any extra matches left.)
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{8}
Four points $B,$ $A,$ $E,$ and $L$ are on a straight line, as shown. The point $G$ is off the line so that $\angle BAG = 120^\circ$ and $\angle GEL = 80^\circ.$ If the reflex angle at $G$ is $x^\circ,$ then what does $x$ equal?

[asy]
draw((0,0)--(30,0),black+linewidth(1));
draw((10,0)--(17,20)--(15,0),black+linewidth(1));
draw((17,16)..(21,20)..(17,24)..(13,20)..(14.668,16.75),black+linewidth(1));
draw((17,16)..(21,20)..(17,24)..(13,20)..(14.668,16.75),Arrows);
label("$B$",(0,0),S);
label("$A$",(10,0),S);
label("$E$",(15,0),S);
label("$L$",(30,0),S);
label("$G$",(17,20),N);
label("$120^\circ$",(10,0),NW);
label("$80^\circ$",(15,0),NE);
label("$x^\circ$",(21,20),E);
[/asy]
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{340}
Konsistent Karl is taking this contest. He can solve the first five problems in one minute each, the next five in two minutes each, and the last five in three minutes each. What is the maximum possible score Karl can earn? Recall that this contest is $15$ minutes long, there are $15$ problems, and the $n$th problem is worth $n$ points. Assume that entering answers and moving between or skipping problems takes no time.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{70}
For $n \geq 1$, let $a_n$ be the number beginning with $n$ 9's followed by 744; for example, $a_4 = 9999744$. Define \[ f(n) = \max \{ m \in \mathbb{N} \mid 2^m \text{ divides } a_n \}, \] for $n \geq 1$. Find $f(1) + f(2) + f(3) + \cdots + f(10)$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{75}
In a football game, wristbands were given to every spectator for both their hands. There were two types of wristbands - type A and type B. Type A wristbands were given to 3 spectators for each hand, while Type B wristbands were given to 2 spectators for each hand. In total, 460 wristbands were distributed. How many spectators received both type A wristbands for both hands?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{138}
At a crossroads, if vehicles are not allowed to turn back, calculate the total number of possible driving routes.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{12}
Two non-intersecting circles with centers at points \(A\) and \(B\) are inscribed in an angle measuring \(\alpha\) \((0 < \alpha < 180^\circ)\). The distance \(A B\) is \(n\). A segment \(M N\) with its endpoints on the sides of the angle touches both circles. Find the difference in the areas of triangles \(B M N\) and \(A M N\).
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\frac{n^2 \sin(\alpha)}{4}}
A positive integer is written on each corner of a square such that numbers on opposite vertices are relatively prime while numbers on adjacent vertices are not relatively prime. What is the smallest possible value of the sum of these 4 numbers?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{60}
In a faraway kingdom, there are coins of three types in circulation: bronze coins worth 1 ruble, silver coins worth 9 rubles, and gold coins worth 81 rubles. From a treasury that has an unlimited supply of each type of coin, a certain amount of money less than 700 rubles was issued using 23 coins. Find this amount, given that it is not possible to issue this amount with fewer coins.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{647 \text{ } \text{rubles}}
Let $A, B, C, D, E, F$ be 6 points on a circle in that order. Let $X$ be the intersection of $AD$ and $BE$, $Y$ is the intersection of $AD$ and $CF$, and $Z$ is the intersection of $CF$ and $BE$. $X$ lies on segments $BZ$ and $AY$ and $Y$ lies on segment $CZ$. Given that $AX=3, BX=2, CY=4, DY=10, EZ=16$, and $FZ=12$, find the perimeter of triangle $XYZ$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\frac{77}{6}}
During what year after 1994 did sales increase the most number of dollars?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{2000}
For a positive integer $n$, let $p(n)$ denote the smallest prime divisor of $n$. Find the maximum number of divisors $m$ can have if $p(m)^4 > m$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{6}
Consider triangle $A B C$ with side lengths $A B=4, B C=7$, and $A C=8$. Let $M$ be the midpoint of segment $A B$, and let $N$ be the point on the interior of segment $A C$ that also lies on the circumcircle of triangle $M B C$. Compute $B N$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\frac{\sqrt{210}}{4}}
Triangle $A B C$ has incircle $\omega$ which touches $A B$ at $C_{1}, B C$ at $A_{1}$, and $C A$ at $B_{1}$. Let $A_{2}$ be the reflection of $A_{1}$ over the midpoint of $B C$, and define $B_{2}$ and $C_{2}$ similarly. Let $A_{3}$ be the intersection of $A A_{2}$ with $\omega$ that is closer to $A$, and define $B_{3}$ and $C_{3}$ similarly. If $A B=9, B C=10$, and $C A=13$, find \left[A_{3} B_{3} C_{3}\right] /[A B C].
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{14/65}
In the given diagram, a circle of radius 3 has two tangents that intersect at a point, forming an angle of 60 degrees. Calculate the shaded area, which consists of the interior of the circle and the area between the circle and the two tangents. Express your answer in terms of pi and the square root of 3.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{6\pi + 9\sqrt{3}}
Given the quadratic function y = x^2 - (m-2)x + 4, find the value of m that does not satisfy the condition that the vertex lies on the coordinate axis.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{0}
Given $f(x) = x^2 - ax$, the inequality $|f(f(x))| \leqslant 2$ holds for all $x$ in the interval $[1, 2]$. Determine the maximum possible value of the real number $a$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\frac{3 + \sqrt{17}}{4}}
Five members of the Lexington Math Team are sitting around a table. Each flips a fair coin. Given that the probability that three consecutive members flip heads is $\frac{m}{n}$, where $m$ and $n$ are relatively prime positive integers, find $m+n$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{43}
Mrs. Delta's language class has 52 students, each with unique initials, and no two students have initials that are alphabetically consecutive (e.g., AB cannot follow AC directly). Assuming Y is considered a consonant, what is the probability of randomly picking a student whose initials (each first and last name starts with the same letter, like AA, BB) are both vowels? Express your answer as a common fraction.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\frac{5}{52}}
In the expansion of \((x + y + z)^8\), determine the sum of the coefficients of all terms of the form \(x^2 y^a z^b\) (\(a, b \in \mathbf{N}\)).
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{1792}
Given the equation $\dfrac{x-1}{x-4}=\dfrac{m}{x-4}$, find the value of $m$ that makes the equation have a root. Express your answer as a single integer.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{3}
Calculate the degree of the field extension \([F_{p^2}(t)(t^{1/p}):F_p(t)]\) using the tower of fields \(F_p \subseteq F_{p^2} \subseteq F_{p^2}(t) \subseteq F_{p^2}(t)(t^{1/p})\).
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{2p}
Calculate $T(10, 4) \pmod{7}$, where $T(n, k) = \sum_{j=1}^{\min(k,n)} j T(n - j, j)$ for a positive integer $n$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{0}
5. On a sheet of paper, 14 parallel lines $L$ and 15 lines $P$ perpendicular to them are drawn. The distances between adjacent lines from $L$ from the first to the last are given: 2;4;6;2;4;6;2;4;6;2;4;6;2. The distances between adjacent lines from $P$ are also known: 3;1;2;6;3;1;2;6;3;1;2;6;3;1. Find the greatest length of the side of a square whose boundaries lie on the lines $L$ and $P$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{40}
Raymonde's financial institution publishes a list of service charges as follows: Autodebit costs $0.60 per transaction, cheque costs $0.50 per transaction, and cash withdrawal costs $0.45 per transaction. For her first twenty-five transactions, she uses Autodebit three times as often as she writes checks, and she also writes as many checks as she makes cash withdrawals. After her twenty-fifth transaction, she begins to make single transactions. Calculate the smallest number of transactions she needs to make so that her monthly service charges will exceed the $15.95 "all-in-one" fee. Express your answer as a whole number.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{29}
Evaluate the contour integral $\oint_{|z|=1} z^{-1+i} \,dz$ using the principal branch of the logarithm, defined on the set $\{z: 0 \leq \arg(z) < 2\pi\}$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{i(1-e^{-2\pi})}
The circles $k_{1}$ and $k_{2}$, both with unit radius, touch each other at point $P$. One of their common tangents that does not pass through $P$ is the line $e$. For $i>2$, let $k_{i}$ be the circle different from $k_{i-2}$ that touches $k_{1}$, $k_{i-1}$, and $e$. Determine the radius of $k_{1999}$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\frac{1}{1998^2}}
Given a positive integer \( n \), find the number of positive integer solutions \((x, y)\) for the equation \(\frac{1}{n} = \frac{1}{x} + \frac{1}{y}\) where \( x \neq y \).
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{d(n^2) - 1}
Geli is committed to her workout routine. On her first day, she started doing 10 push-ups. Her fitness trainer encouraged her to add 5 more push-ups each day. Geli did a total of 45 push-ups throughout her first week. How many times a week does Geli workout?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{3}
The GooGoo brand of clothing manufactures four types of shirts: Type A with 3 buttons, Type B with 5 buttons, Type C with 6 buttons, and Type D with 4 buttons. A large department store ordered GooGoo to manufacture 200 of Type A, 300 of Type B, 150 of Type C, and 250 of Type D shirts. Additionally, GooGoo provides a discount on button usage for bulk orders, reducing button usage by 10% for orders over 200 shirts. Calculate the total number of buttons GooGoo brand will use to manufacture all the shirts for this order, taking the discount into account.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{3750}