prompt stringlengths 243 1.04k | gt stringlengths 2 77 |
|---|---|
<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A barn with a roof is rectangular in shape, $12$ yd. wide, $15$ yd. long, and $6$ yd. high. It is to be painted inside and outside, including the ceiling and the roof. Determine the total number of sq. y... | B) 1008 sq yd |
<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Let $ABCDEF$ be a regular octahedron with unit side length, such that $ABCD$ is a square. Points $G, H$ are on segments $BE, DF$ respectively. The planes $AGD$ and $BCH$ divide the octahedron... | \frac{9 - \sqrt{57}}{6} |
<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Average score of Alice and Charlie's test can be found. Let's think step by step and output the final answer within \boxed{}.<|im_end|>
<|im_start|>assistant
| 97 |
<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given that $f(x)$ is an odd function on $\mathbb{R}$, and when $x \geq 0$, $f(x) = x^2 - 2x$.
(I) Find the value of $f(f(-1))$;
(II) Find the analytic expression of $f(x)$;
(III) Solve the inequality $x ... | \{x \mid x \leq -2 \text{ or } x \geq 2\} |
<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Find an ordered pair $(x, y)$ that solves the system: \begin{align*} 6x &= -9 - 3y,\\ 4x &= 5y - 34 \end{align*} Let's think step by step and output the final answer within \boxed{}.<|im_end|>
<|im_start... | \left(\frac{1}{2}, -4\right) |
<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
If the probability that a baby born in a certain hospital will speak in the next day is \( \frac{1}{5} \), what is the probability that at least 3 babies out of a cluster of 7 babies will speak tomorrow?... | \frac{45349}{78125} |
<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Suppose $p(x), q(x), r(x)$ are linear functions defined as $p(x) = 2x + 1$, $q(x) = -x + 3$, and $r(x) = 0.5x + 2$. Define new functions $u(x)$ and $v(x)$ by
$$u(x) = \max\{p(x), q(x), r(x)\},$$
$$v(x) =... | (\sqrt{\frac{481}{9}} + \sqrt{\frac{181}{9}})^2 |
<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Three equally spaced parallel lines intersect a circle, creating three chords of lengths 40, 40, and 36. What is the distance between two adjacent parallel lines? Let's think step by step and output the ... | 6.16 |
<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The scores of 10 students were checked via two tests: $A$ and $B$. The scores on a 100-point scale are as follows (the first row indicates the scores for test $A$, and the second row indicates the score... | 0.51 |
<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The line $y=kx+1$ ($k \in \mathbb{R}$) always has a common point with the curve $\frac{x^2}{5} + \frac{y^2}{m} = 1$. Find the range of values for the non-negative real number $m$. Let's think step by ste... | \{m | m \geq 1 \text{ and } m \neq 5\} |
<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given that $F_1$ and $F_2$ are the left and right foci of the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1 (a > b > 0)$, find the range of the eccentricity of the ellipse. Let's think step by step and outp... | [\frac{2}{5},1) |
<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Find the sum of the absolute values of the roots of the polynomial $x^4 -4x^3 + 6x^2 + 14x - 12 = 0$. Let's think step by step and output the final answer within \boxed{}.<|im_end|>
<|im_start|>assistant... | \sqrt{17} |
<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A taxi company workshop needs to repair 7 taxis. The repair times for these 7 taxis by one worker are 12, 17, 8, 18, 23, 30, and 14 minutes respectively. Each minute a taxi is not in operation results in... | 364 |
<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
How many parts can two planes divide the space into? Let's think step by step and output the final answer within \boxed{}.<|im_end|>
<|im_start|>assistant
| 2 \text{ or } 4 |
<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Ivan Semyonov is taking the Unified State Exam in mathematics. The exam consists of three types of tasks: $A$, $B$, and $C$. Each type $A$ task offers four answer choices, only one of which is correct. T... | \approx 0.088 |
<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Find the integer solutions for the following equations:
(1) $11x + 5y = 7$; (2) $4x + y = 3xy$. Let's think step by step and output the final answer within \boxed{}.<|im_end|>
<|im_start|>assistant
| x = 1, y = 2 |
<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The function \( f(x, y) \) satisfies the following conditions for all non-negative integers:
1. \( f(0, y) = y + 1 \)
2. \( f(x + 1, 0) = f(x, 1) \)
3. \( f(x + 1, y + 1) = f(x, f(x + 1, y)) \)
Determi... | f(4, 1981) = 2^{2^{2^{1981 +1} + 1}} - 3 |
<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Four points are chosen uniformly at random on a circle. What is the probability that no set of three points among them form an obtuse triangle with the circle's center? Let's think step by step and outpu... | \frac{3}{32} |
<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given the function f(x) = x² - ax + 2lnx,
1. Find the monotonic intervals of f(x) when a = 5.
2. If f(x) has two extreme points x₁ and x₂, and 1/3 < x₁ < 1/e < x₂, find the range of f(x₁) - f(x₂). (Wher... | (e² - \frac{1}{e²} - 4, \frac{80}{9} - 4ln3) |
<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The average (arithmetic mean) age of a group consisting of doctors, lawyers, and engineers is 45. If the doctors average 40 years old and the lawyers 55 years old, and the average age of the engineers is... | \text{C) } 3:1 |
<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
We want to color the edges of a complete graph with \( n \geq 3 \) vertices using \( k \) colors, where an edge can receive more than one color, but
(1) no single color appears on every edge,
(2) no s... | \left\lceil \log_2 n \right\rceil + 1 |
<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A chocolate egg manufacturer has announced a new collection featuring ten different crocodiles. The crocodiles are uniformly and randomly distributed in the chocolate eggs, meaning that each randomly cho... | 3.59 |
<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given that $f(x)$ is an odd function on $\mathbb{R}$, and for $x \in (-\infty, 0)$, $f(x) = -x\log(2-x)$, then $f(x) = \_\_\_\_\_\_$. Let's think step by step and output the final answer within \boxed{}.... | \begin{cases} -x\log(2-x), & (x < 0) \\ -x\log(2+x), & (x \geq 0) \end{cases} |
<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In an arithmetic sequence, the first four terms are $p+2$, $13$, $4p-r$, and $4p+r$. Find the $1010^\text{th}$ term of this sequence.
**A** $5692$
**B** $5690$
**C** $5691$
**D** $5693$ Let's think... | \textbf{(C)}\ 5691 |
<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Sarah needs to borrow $12,000 from a local credit union. The credit union offers her two options:
1. A twelve-year loan with an annual interest rate of $8\%$ compounded semi-annually. After 6 years, Sar... | \$2,427 |
<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given vectors $\overrightarrow{a} = (2\cos x, \sin x)$ and $\overrightarrow{b} = (\cos x, 2\sqrt{3}\cos x)$, define the function $f(x) = \overrightarrow{a} \cdot \overrightarrow{b} - 1$.
- (I) Determine ... | f(A) \in (-1, 2) |
<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Compute: $(1)(1+2i)^{2}$; $(2)(\frac{1+i}{1-i})^{6}+\frac{\sqrt{2}+\sqrt{3}i}{\sqrt{3}-\sqrt{2}i}$. Let's think step by step and output the final answer within \boxed{}.<|im_end|>
<|im_start|>assistant
| -\frac{5}{5}+\frac{\sqrt{6}}{5}+\frac{\sqrt{3}+\sqrt{2}}{5}i |
<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
By what factor does the impact of changes in oil production volume \(\left(Q_{N}\right)\) on the oil and gas revenues of the budget exceed the impact of changes in the price of Urals oil \(\left(P_{N}\ri... | 1.7 |
<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
What numbers can be expressed as the sum of two or more consecutive positive odd numbers? Let's think step by step and output the final answer within \boxed{}.<|im_end|>
<|im_start|>assistant
| \text{Multiples of 4 and odd composite numbers} |
<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Alex has 6 different math problems on pieces of paper and wishes to distribute them among his 10 friends. Each friend can receive exactly one problem, but not all problems need to be distributed. How man... | 349050 |
<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
On the complex plane, the parallelogram formed by the points 0, $z,$ $\frac{1}{z},$ and $z + \frac{1}{z}$ has area $\frac{12}{13}.$ If the imaginary part of $z$ is positive, let $c$ be the value of $\lef... | r^2 |
<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
If $\sin \theta = \frac{5}{13}$ and $\theta$ is in the first quadrant, determine the value of $\tan 3\theta$. Let's think step by step and output the final answer within \boxed{}.<|im_end|>
<|im_start|>a... | \tan 3\theta = \frac{145}{78} |
<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Calculate the sum:
\[\sum_{N=1}^{729} \lfloor \log_3 N \rfloor.\] Let's think step by step and output the final answer within \boxed{}.<|im_end|>
<|im_start|>assistant
| 2373 |
<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In the first week after his birthday, Bill's uncle gave him some money for his piggy bank. Every week after that Bill put $2 into his piggy bank. At the end of the ninth week after his birthday, Bill had... | \pounds 24 |
<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Ellie uses a mower to cut her rectangular 60-foot by 120-foot lawn. The swath width of the mower is 30 inches, but she overlaps each cut by 6 inches to ensure thorough coverage. She walks at different ra... | \textbf{(C) } 0.9 \text{ hours} |
<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
You have a set of 1000 switches, each with five positions labeled $A, B, C, D, E$, cycled in this order. Initially, each switch is in position $A$. The switches are labeled uniquely as $(2^{x})(3^{y})(5^... | 725 |
<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In a triangle \(PQR\), point \(Z\) lies on segment \(PR\) such that \(\angle QZP = \angle QZR\). Given \(PZ = 18\) units, \(QR = 42\) units, and \(RZ = 36\) units, find the length of \(QZ\). Let's think ... | 16.8 |
<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In a similar parlor game, the magician asks a participant to think of a three-digit number $(abc)$ and form the numbers $(acb)$, $(bca)$, $(bac)$, $(cab)$, and $(cba)$. They then add these five numbers, ... | 118 |
<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given that the sequence $\{a\_n\}$ is an arithmetic sequence with a common difference of $2$, and the sequence $\{b\_n\}$ satisfies $b\_1=1, b\_2= \frac {1}{2}$, if $a\_nb\__{n+1}-b\__{n+1}=nb\_n$ for al... | S\_n=10- \frac {2n+5}{2^{n-1}} |
<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Consider a natural number $ n $ for which it exist a natural number $ k $ and $ k $ distinct primes so that $ n=p_1\cdot p_2\cdots p_k. $ **a)** Find the number of functions $ f:\{ 1, 2,\ldots , ... | 580 |
<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A regular quadrilateral pyramid is intersected by a plane passing through a vertex of the base perpendicular to the opposite lateral edge. The area of the resulting cross-section is half the area of the ... | \frac{1 + \sqrt{33}}{8} |
<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given that $4x + y = 10$ and $x + 4y = 18$, find $16x^2 + 24xy + 16y^2$. Let's think step by step and output the final answer within \boxed{}.<|im_end|>
<|im_start|>assistant
| 424 |
<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Solve the equation $7x + 2 \equiv 11 \pmod{15}$ for $x$. Let's think step by step and output the final answer within \boxed{}.<|im_end|>
<|im_start|>assistant
| 27 |
<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Express the quotient $12320_4 \div 12_4$ in base 4. Let's think step by step and output the final answer within \boxed{}.<|im_end|>
<|im_start|>assistant
| 1121_4 |
<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
How many pounds of grain need to be milled so that after paying for the work, which is 10% of the milling, exactly 100 pounds of flour remains?
There is no loss during milling. Let's think step by step ... | 1976 \text{ at } a = 8, b = 2 |
<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The cards in a stack of $2n$ cards are numbered consecutively from 1 through $2n$ from top to bottom. The top $n$ cards are removed, forming pile $A$, and the remaining cards form pile $B$. The cards are... | 446 |
<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Square $EFGH$ has side length 5, and $N$ is the midpoint of $\overline{GH}$. A circle with radius 2.5 centered at $N$ intersects a circle with radius 5 centered at $E$ at points $Q$ and $H$. Determine th... | 1.33 |
<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In the Cartesian coordinate system $xOy$, the curve C: $x^2=6y$ intersects with the line l: $y=kx+3$ at points M and N.
(1) When $1<k<2$, find the range of values for the area of triangle MON.
(2) Does t... | x^2+(y+3)^2=36 |
<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Let \(S = \{8^k : k \text{ is an integer}, 0 \le k \le 4000\}\). Given that \(8^{4000}\) has 3617 digits and that its first (leftmost) digit is 8, how many elements of \(S\) have 8 as their leftmost digi... | 384 |
<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
If the function $f(x) = x^2 - ax + \ln x$ has a tangent line perpendicular to the y-axis, then the range of the real number $a$ is
\_\_\_\_ Let's think step by step and output the final answer withi... | (2, +\infty) |
<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Find the angles that have the same terminal side as the angle -2010° and satisfy the following conditions:
(1) The smallest positive angle;
(2) The largest negative angle;
(3) Angles within the ran... | -570°, -210°, 150°, 510° |
<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Let \( M \) be the number of positive integers that are less than or equal to \( 1500 \) and whose base-\( 2 \) representation has more \( 1 \)'s than \( 0 \)'s. Find the remainder when \( M \) is divide... | 152 |
<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
For nonzero values of $a$ and $b$, calculate the expression $\left( 3a + \frac{b}{3} \right)^{-1} \left[(3a)^{-1} + \left( \frac{b}{3} \right)^{-1} \right]$.
**A)** $ab$
**B)** $a^{-1}b$
**C)** $ab^{-1}... | \textbf{(D)}\ (ab)^{-1} |
<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Solve the equation \(\left(\frac{7}{2} \cos 2 x+2\right) \cdot|2 \cos 2 x-1|=\cos x(\cos x+\cos 5 x)\). Let's think step by step and output the final answer within \boxed{}.<|im_end|>
<|im_start|>assista... | x = \pm \frac{\pi}{6} + \frac{k\pi}{2}, \, k \in \mathbb{Z} |
<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Let $[r,s]$ denote the least common multiple of positive integers $r$ and $s$. Find the number of ordered triples $(a,b,c)$ of positive integers for which $[a,b] = 1200$, $[b,c] = 2400$, and $[c,a] = 300... | 96 |
<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In a convex \( n \)-gon, several diagonals are drawn. A drawn diagonal is called good if it intersects exactly one other drawn diagonal (at interior points). Find the maximum possible number of good diag... | n-2 \text{ for even } n, \ n-3 \text{ for odd } n |
<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The domain of the function $f(x)= \sqrt {4-x^{2}}$ is __________. Let's think step by step and output the final answer within \boxed{}.<|im_end|>
<|im_start|>assistant
| \{x|-2\leqslant x\leqslant 2\} |
<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
$ABC$ is a right triangle with $∠ACB = 90°$, side $\overline{AB} = 3$ cm, and side $\overline{BC} = 4$ cm. $\overline{AB}$ is extended to point $D$ such that $D$ is twice the distance from $A$ to $B$. Po... | 12 \text{ cm}^2 |
<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Several natural numbers with a sum of 20 are written in a row. No number and no sum of several consecutive numbers is equal to 3. Could more than 10 numbers have been written? Let's think step by step an... | \text{Yes, more than 10 numbers can be listed} |
<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
P(ξ ≤ 78) = 0.12 + 0.3. Let's think step by step and output the final answer within \boxed{}.<|im_end|>
<|im_start|>assistant
| 0.23 |
<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Solve the inequality with respect to $x$: $ax^2 - (a+1)x + 1 < 0$ where $a > 0$. Let's think step by step and output the final answer within \boxed{}.<|im_end|>
<|im_start|>assistant
| \{x \mid \frac {1}{a} < x < 1\} |
<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The incircle of a triangle \(ABC\) is tangent to \(BC\) at \(D\). Let \(H\) and \(\Gamma\) denote the orthocenter and circumcircle of \(\triangle ABC\). The \(B\)-mixtilinear incircle, centered at \(O_B\... | \sqrt{\frac{1}{3}(7+2\sqrt{13})} |
<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Several different points are marked on a line, and all possible line segments are constructed between pairs of these points. One of these points lies on exactly 80 of these segments (not including any se... | 22 |
<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given the universal set $U=\mathbb{R}$, set $A=\{x|x+2<0\}$, and set $B=\{x|2^{x}<8\}$, then the set $(C_{U}A) \cap B=$ ? Let's think step by step and output the final answer within \boxed{}.<|im_end|>
<... | \{x|-2\leq x<3\} |
<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The average weight of 8 boys is 160 pounds, and the average weight of 3 girls is 110 pounds. What is the average weight of all 11 children?
A) 140 pounds
B) 142 pounds
C) 144 pounds
D) 146 pounds
E) 148 ... | The correct answer is **D) 146 pounds**. |
<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Compute the sum: $1 - 2 + 3 - 4 + \cdots - 100 + 101$.
A) 49
B) 50
C) 51
D) 52
E) 100 Let's think step by step and output the final answer within \boxed{}.<|im_end|>
<|im_start|>assistant
| C) 51 |
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