inclusionAI/Ring-lite-rl-data huggingface dataset:
Bookman purchased 55 copies of a new book released recently, 10 of which are hardback and sold for $20 each, and the rest are paperback and sold for $10 each. If 14 copies were sold, what was the total value of the remaining books?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\$510}
Which type of quadrilateral is not necessarily a symmetrical figure? Provide your answer as the name of the quadrilateral.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{Parallelogram}
An apartment and an office are sold for $15,000 each. The apartment was sold at a loss of 25% and the office at a gain of 25%. Determine the net effect of the transactions.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{2000}
Let $f(t) = \frac{t}{1-t}$, where $t \neq 1$. If $y = f(x)$, express $x$ in terms of $y$. The original answer is in the form \frac{m}{n}, please give the value of m + n.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{2}
A frog starts at point $(2, 3)$ on a grid and makes jumps of length $1$ parallel to the coordinate axes. Each jump direction (up, down, right, or left) is chosen randomly. The jumping sequence stops when the frog reaches any point on the boundary of the rectangle defined by vertices $(0,0), (0,5), (5,5),$ and $(5,0)$. Calculate the probability that the sequence of jumps ends at either the top or bottom horizontal side of the rectangle.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\frac{1}{2}}
In $\triangle ABC$, $b=2$, $B=45^\circ$. If there are two possible values for $a$, find the range of $a$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{a\in\left(2,2 \sqrt{2}\right)}
In the sequence  $00$ ,  $01$ ,  $02$ ,  $03$ ,  $\cdots$ ,  $99$  the terms are rearranged so that each term is obtained from the previous one by increasing or decreasing one of its digits by  $1$  (for example,  $29$  can be followed by  $19$ ,  $39$ , or  $28$ , but not by  $30$  or  $20$ ). What is the maximal number of terms that could remain on their places?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{50}
Tristan is eating his favorite cereal, Tiger Crunch, which has marshmallows of two colors, black and orange. He eats the marshmallows by randomly choosing from those remaining one at a time, and he starts out with $17$ orange and $5$ black marshmallows. If $\frac{p}{q}$ is the expected number of marshmallows remaining the instant that there is only one color left, and $p$ and $q$ are relatively prime positive integers, find $p + q$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{37}
Given vectors a=(8, 1/2x) and b=(x, 1), where x > 0, find the value of x such that (a-2b) || (2a+b). Express your answer as a single number.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{4}
Consider the polynomial $f(x) = x^5 - 4x + 2$. Let $L$ be the complex splitting field of $f(x)$ over $\mathbb{Q}$. How many subfields $K$ of $L$ are there such that $(K : \mathbb{Q}) = 2$?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{1}
Find the value of \( \sin^{4} \frac{\pi}{8} + \sin^{4} \frac{3\pi}{8} + \sin^{4} \frac{5\pi}{8} + \sin^{4} \frac{7\pi}{8} \).
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\frac{3}{2}}
A sequence of consecutive positive integers starting with 1 is written on the blackboard. If one of the numbers is erased, the arithmetic mean of the remaining numbers is 35 7/17. Determine the erased number. Express your answer as a single integer.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{7}
Evaluate the following limit:

$$\lim_{h \rightarrow 0} \frac{\tan(a+3h)-3\tan(a+2h)+3\tan(a+h)-\tan a}{h}$$
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{0}
If 5 times a number is 2, then 100 times the reciprocal of the number is
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{$250$}
A 180 m long train is running at 72 kmph. It crossed a platform of length 220.03199999999998 m in a certain amount of time. How many seconds did it take for the train to cross the platform?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{20}
For how many integers $n$ between $1$ and $50$, inclusive, is $\frac{(n^2-1)!}{(n!)^n}$ an integer?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{34}
In a multinational office in Singapore, there are 60% female employees and 40% male employees, working in various job roles such as engineers, managers, and support staff. The engineers constitute 35% of the total workforce, the managers account for 25%, and the support staff make up the remaining 40%. Out of the total 1400 employees, 62% are computer literate. Furthermore, the computer literacy rates among the employees are different depending on their gender and job roles as follows:

- Male engineers: 80%
- Female engineers: 75%
- Male managers: 55%
- Female managers: 60%
- Male support staff: 40%
- Female support staff: 50%

Calculate the joint probability of a randomly selected employee being both female and computer literate, considering the different job roles and computer literacy rates.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{36.75\%}
Determine the number of integers  $ n$  with  $ 1 \le n \le N\equal{}1990^{1990}$  such that  $ n^2\minus{}1$  and  $ N$  are coprime.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{591 \times 1990^{1989}}
Given two concentric circles, a tangent to the smaller circle divides the length of the arc of the larger circle in the ratio $1: 5$. Find the ratio of the areas of the circles bounded by these circles.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\frac{3}{4}}
Given that the function \( f(x) \) satisfies the equation \( 2 f(x) + x^{2} f\left(\frac{1}{x}\right) = \frac{3 x^{3} - x^{2} + 4 x + 3}{x + 1} \) and \( g(x) = \frac{5}{x + 1} \), determine the minimum value of \( f(x) + g(x) \).
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\frac{15}{4}}
Among the permutations of integers $1, 2, \cdots, n$, how many permutations are there such that each number is either greater than all the numbers preceding it or less than all the numbers preceding it?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{2^{n-1}}
Given $1994$ points on a plane, it is known that any $100$ of them can be selected such that $98$ of these can be enclosed by a circle with a diameter of $1$. Determine the minimum number of circles with a radius of $1$ required to cover all $1994$ points.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{21}
On side \( CB \) of triangle \( ABC \), a point \( D \) is taken such that \( |CD| = \alpha |AC| \). The radius of the circumcircle of \( \triangle ABC \) is \( R \). Find the distance between the center of the circumcircle of \( \triangle ABC \) and the center of the circumcircle of \( \triangle ADB \).
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\alpha R}
For each positive integer $n$, define $S(n)$ to be the smallest positive integer divisible by each of the positive integers $1, 2, 3, \ldots, n$. How many positive integers $n$ with $1 \leq n \leq 100$ have $S(n) = S(n+4)$?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{11}
Two spheres, each with a radius of 1, are externally tangent to each other and internally tangent to a cylinder with a radius of 1. Another smaller sphere is externally tangent to both of these spheres and internally tangent to the same cylinder. If the plane passing through the center of the small sphere and the center of one of the larger spheres intersects the cylinder to form an ellipse, find the maximum possible value of the eccentricity \( e \) of this ellipse.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\frac{4}{5}}
There are 3 females and 3 males to be arranged in a sequence of 6 contestants, with the restriction that no two males can perform consecutively and the first contestant cannot be female contestant A. Calculate the number of different sequences of contestants.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{132}
Evaluate the integral: $$\int_0^{\frac{\pi}{2}}\ln^2\left(\cos^2x\right)\text{d}x$$
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{2\pi\ln^2(2) + \frac{\pi^3}{6}}
Five apples have weights of 125g, $a$, 121g, $b$, and 127g respectively. If the median and the mean of the sample weights are both 124g, find the standard deviation $s$ of the sample.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{2}
\(ABCD\) is a convex quadrilateral where \(AB = 7\), \(BC = 4\), and \(AD = DC\). Also, \(\angle ABD = \angle DBC\). Point \(E\) is on segment \(AB\) such that \(\angle DEB = 90^\circ\). Find the length of segment \(AE\).
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{1.5}
A cryptographer devises the following method for encoding positive integers. First, the integer is expressed in base $5$. Second, a 1-to-1 correspondence is established between the digits that appear in the expressions in base $5$ and the elements of the set $\{V, W, X, Y, Z\}$. Using this correspondence, the cryptographer finds that three consecutive integers in increasing order are coded as $VYZ$, $VYX$, $VVW$, respectively. What is the base-10 expression for the integer coded as $XYZ$?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{108}
Let $a$, $b \in \mathbb{R}$, $c \in [0,2\pi)$. If for any real number $x$, the equation $2\sin (3x- \frac {\pi}{3})=a\sin (bx+c)$ holds, then how many sets of $(a, b, c)$ satisfy the condition? Express your answer as a single integer.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{4}
When 100 is divided by positive integer x, the remainder is 3. What is the remainder when 197 is divided by x?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{3}
Find the minimum value of the expression \(\frac{13 x^{2}+24 x y+13 y^{2}+16 x+14 y+68}{\left(9-x^{2}-8 x y-16 y^{2}\right)^{5 / 2}}\). Round the answer to the nearest hundredth if needed.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{0.26}
What is the sum of all $k \leq 25$ such that one can completely cover a $k \times k$ square with $T$ tetrominos without any overlap?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{84}
Cassandra sets her watch to the correct time at noon. At the actual time of $1:00$ PM, she notices that her watch reads $12:57$ and $36$ seconds. Assuming that her watch loses time at a constant rate, calculate the total time discrepancy in seconds between her watch and the actual time when her watch first reads $10:00$ PM. Please provide your answer as an integer representing the number of seconds.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{1500}
What is the sum of the six positive integer factors of 30?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{72}
From the set of integers $\{1,2,3,\dots,3009\}$, choose $k$ pairs $\{a_i,b_i\}$ with $a_i<b_i$ so that no two pairs share a common element. Each sum $a_i+b_i$ must be distinct and less than or equal to $3009$. Determine the maximum possible value of $k$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{1504}
5. In the Cartesian coordinate system, the "rectangular distance" between points $P\left(x_{1}, y_{1}\right)$ and $Q\left(x_{2}, y_{2}\right)$ is defined as $d(P, Q) = \left|x_{1}-x_{2}\right| + \left|y_{1}-y_{2}\right|$. If the "rectangular distance" from $C(x, y)$ to points $A(1,3)$ and $B(6,9)$ is equal, where the real numbers $x$ and $y$ satisfy $0 \leqslant x \leqslant 10$ and $0 \leqslant y \leqslant 10$, then the sum of the lengths of all the loci of points $C$ that satisfy the condition is . $\qquad$
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{5(\sqrt{2}+1)}
A game show offers a contestant three prizes A, B and C, each of which is worth a whole number of dollars from $\textdollar 1$ to $\textdollar 9999$ inclusive. The contestant wins the prizes by correctly guessing the price of each prize in the order A, B, C. As a hint, the digits of the three prices are given. On a particular day, the digits given were $1, 1, 1, 1, 3, 3, 3$. Find the total number of possible guesses for all three prizes consistent with the hint.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{$420$}
Two snails crossed the surface of a planet shaped like a torus, leaving trails behind them. One snail crawled along the outer equator, and the other along a helical line. Into how many parts did the snails' trails divide the surface of the planet? (It is sufficient to write only the answer.)
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{3}
There are 120 people that own pets. Out of these, 30 people own only dogs, 25 people own only cats, and 12 people own only snakes. Additionally, 15 people own both dogs and cats, 10 people own both cats and snakes, and 8 people own both dogs and snakes. Finally, 5 people own cats, dogs, and snakes. How many total snakes are there among these pet owners?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{35}
Arrange the $n$ consecutive positive integers from 1 to $n$ (where $n > 1$) in a sequence such that the sum of each pair of adjacent terms is a perfect square. Find the minimum value of $n$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{15}
The sum of the number of boys and girls in a school is 300. If the number of boys is a certain number, then the number of girls becomes that same number as a percentage of the total number of students. What is the number of boys?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{225}
Cells of a  $n*n$  square are filled with positive integers in the way that in the intersection of the  $i-$ th column and  $j-$ th row, the number  $i+j$  is written. In every step, we can choose two non-intersecting equal rectangles with one dimension equal to  $n$  and swap all the numbers inside these two rectangles with one another. ( without reflection or rotation ) Find the minimum number of moves one should do to reach the position where the intersection of the  $i-$ th column and  $j-$ row is written  $2n+2-i-j$ .
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{n-1}
In a board game played with dice, our piece is four spaces away from the finish line. If we roll at least a four, we reach the finish line. If we roll a three, we are guaranteed to finish in the next roll.

What is the probability that we will reach the finish line in more than two rolls?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{1/12}
Let $z_1$, $z_2$, $z_3$, $\cdots$, $z_{2021}$ be the roots of the polynomial $z^{2021}+z-1$. Evaluate $$\frac{z_1^3}{z_{1}+1}+\frac{z_2^3}{z_{2}+1}+\frac{z_3^3}{z_{3}+1}+\cdots+\frac{z_{2021}^3}{z_{2021}+1}.$$
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{1347}
The opposite of $\sqrt{3}$ is ____.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{-\sqrt{3}}
Three red beads, two white beads, and one blue bead are placed in line in random order. What is the probability that no two neighboring beads are the same color?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{$1/6$}
Example 7.12 Find the number of second-kind circular permutations formed by selecting 6 elements with repetition from the 3-element set $A=\{a, b, c\}$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{92}
Diane has five identical blue disks, two identical red disks, and one yellow disk. She wants to place them on an 8-cell grid so that each cell contains exactly one disk. The two red disks must not be placed in cells that share a common edge. Calculate the total number of different-looking completed grids that Diane can produce.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{108}
Two trains of some length and 200 meters are 630 meters apart. They are moving towards each other on parallel tracks, at speeds of 90 km/h and 72 km/h. The trains will meet after 13.998880089592832 seconds. What is the length of the first train?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{430}
Mark has a cursed six-sided die that never rolls the same number twice in a row, and all other outcomes are equally likely. Compute the expected number of rolls it takes for Mark to roll every number at least once.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\frac{149}{12}}
Let the coefficient of \( x^{1992} \) in the power series \( (1 + x)^{\alpha} = 1 + \alpha x + \dots \) be \( C(\alpha) \). Find \( \int_{0}^{1} C(-y-1) \sum_{k=1}^{1992} \frac{1}{y+k} \, dy \).
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{1992}
We call a path Valid if:

1. It only comprises the following types of steps:
   - $(x, y) \rightarrow (x + 1, y + 1)$
   - $(x, y) \rightarrow (x + 1, y - 1)$

2. It never goes below the x-axis.

Let $M(n)$ be the set of all valid paths from $(0,0)$ to $(2n,0)$, where $n$ is a natural number. 

Consider a Valid path $T \in M(n)$. Denote:

$$\phi(T) = \prod_{i=1}^{2n} \mu_i$$

where $\mu_i$ is defined as:

- $1$, if the $i^{th}$ step is $(x, y) \rightarrow (x + 1, y + 1)$
- $y$, if the $i^{th}$ step is $(x, y) \rightarrow (x + 1, y - 1)$

Now, let $f(n) = \sum_{T \in M(n)} \phi(T)$. Evaluate the number of zeroes at the end of the decimal expansion of $f(2021)$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{0}
The minute hand of a clock moves 2 small units. How many circles does the second hand move in the same time? Express your answer as a whole number.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{2}
Arrange 1, 2, 3, a, b, c in a row such that letter 'a' is not at either end and among the three numbers, exactly two are adjacent. The probability is $\_\_\_\_\_\_$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\frac{2}{5}}
The side of the base of a regular triangular prism $A B C A_1 B_1 C_1$ is 4, and the lateral edge is 3. On the edge $B B_1$, a point $F$ is taken, and on the edge $C C_1$, a point $G$ is taken such that $B_1 F=1, C G=\frac{2}{3}$. Points $E$ and $D$ are the midpoints of edges $A C$ and $B_1 C_1$ respectively. Find the minimum possible value of the sum $E P+P Q$, where point $P$ belongs to the segment $A_1 D$, and point $Q$ belongs to the segment $F G$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\sqrt{\frac{51}{2}}}
Let  $ABC$  be a scalene triangle whose side lengths are positive integers. It is called *stable* if its three side lengths are multiples of 5, 80, and 112, respectively. What is the smallest possible side length that can appear in any stable triangle?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{20}
A player throwing a die scores as many points as on the top face of the die and is to play until his score reaches or passes a total $n$. Denote by $p(n)$ the probability of making exactly the total $n$, and find the value of $\lim _{n\to\infty} p(n)$. The original answer is in \frac{m}{n} format, please give the value of m + n.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{9}
Define the "distance" between two sets of numbers A and B as the minimum value of $|a-b|$, where $a \in A, b \in B$. If $A=\{y|y=2x-1, x\in\mathbb{R}\}$ and $B=\{y|y=x^2+1, x\in\mathbb{R}\}$, then the "distance" between A and B is
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{0}
Let $n$ be the answer to this problem. Hexagon $ABCDEF$ is inscribed in a circle of radius 90. The area of $ABCDEF$ is $8n$, $AB=BC=DE=EF$, and $CD=FA$. Find the area of triangle $ABC$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{2592}
If the probability of producing a Grade B product is $0.03$, and the probability of producing a Grade C product is $0.02$, calculate the probability of randomly inspecting a product and finding it to be a qualified product.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{0.95}
Claudia has a total of 12 coins consisting of 5-cent and 10-cent coins, with which she can combine to make exactly 17 different values using some or all of these coins. Find the number of 10-cent coins Claudia has. Express your answer as a whole number.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{5}
Given that $y$ is the unique solution to the IVP $xy''+y'-xy=0, y(0)=1, y'(0) = 0,$ how can we compute $\int_0^{\infty} xe^{-x^2/2}y \, dx$? The series for $y$ is given as $y = \sum\limits_{n \ge 0} \frac{(x/2)^{2n}}{(n!)^2}$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{e^{1/2}}
Find the largest integer \( A \) such that for any permutation of natural numbers from 1 to 100, there always exists a sequence of 10 consecutive numbers whose sum is greater than or equal to \( A \).
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{505}
For a positive integer $n,$ let $P_n$ be the set of sequences of $2n$ elements, each $0$ or $1,$ where there are exactly $n$ $1$’s and $n$ $0$’s. I choose a sequence uniformly at random from $P_n.$ Then, I partition this sequence into maximal blocks of consecutive $0$’s and $1$’s. Define $f(n)$ to be the expected value of the sum of squares of the block lengths of this uniformly random sequence. What is the largest integer value that $f(n)$ can take on?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{121}
In 60 chandeliers (each with 4 shades), the shades need to be replaced. Each electrician takes 5 minutes to replace one shade. A total of 48 electricians will be working. No more than one shade can be replaced in a chandelier at the same time. What is the minimum time required to replace all the shades in all the chandeliers?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{25}
The numbers \(1000^{2}, 1001^{2}, 1002^{2}, \ldots\) have their last three digits discarded. How many of the first terms in the resulting sequence form an arithmetic progression?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{32}
Given the proposition $p$: the inequality $2x-x^{2} < m$ holds for all real numbers $x$; and the proposition $q$: $|m-1|\geqslant 2$. If "$\neg p$" and "$p\wedge q$" are both false propositions, find the range of values for the real number $m$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{m\in(1,3)}