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problem
stringlengths 73
1.17k
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sequencelengths 16
16
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sequencelengths 16
16
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float64 0
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45
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Quadrilateral $A R M L$ is a kite with $A R=R M=5, A M=8$, and $R L=11$. Compute $A L$. | ["<think>\nOkay, so I need to find the length of AL in this kite ARML. Let me recall what a kite is.(...TRUNCATED) | [
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|
"Triangle $A B C$ is inscribed in circle $\\omega$. The tangents to $\\omega$ at $B$ and $C$ meet at(...TRUNCATED) | ["<think>\nOkay, so I need to find the area of triangle PBC, given some information about triangle A(...TRUNCATED) | [
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] | 0 | $\frac{800}{3}$ |
|
"Given quadrilateral $A R M L$ with $A R=20, R M=23, M L=25$, and $A M=32$, compute the number of di(...TRUNCATED) | ["<think>\nOkay, so I need to figure out how many different integers could be the perimeter of quadr(...TRUNCATED) | [
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] | 0.9375 | 49 |
|
"Compute the value of\n\n$$\n\\sin \\left(6^{\\circ}\\right) \\cdot \\sin \\left(12^{\\circ}\\right)(...TRUNCATED) | ["<think>\nOkay, so I need to compute the value of this expression:\n\n$$\n\\sin \\left(6^{\\circ}\\(...TRUNCATED) | [
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] | 0 | $\frac{1}{16}$ |
|
"Tanner has two identical dice. Each die has six faces which are numbered 2, 3, 5, $7,11,13$. When T(...TRUNCATED) | ["<think>\nOkay, so I need to figure out the probability that the sum of two dice is a prime number.(...TRUNCATED) | [
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] | 0 | $\frac{1}{6}$ |
|
If $\frac{1}{\cos x}-\tan x=3$, what is the numerical value of $\sin x$ ? | ["<think>\nOkay, so I need to solve this trigonometric equation: 1/cos x minus tan x equals 3. And t(...TRUNCATED) | [
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] | 0 | $-\frac{4}{5}$ |
|
"Let $T=2030$. Given that $\\mathrm{A}, \\mathrm{D}, \\mathrm{E}, \\mathrm{H}, \\mathrm{S}$, and $\\(...TRUNCATED) | ["<think>\nOkay, let's try to tackle this problem. So, we have T = 2030. The digits W, A, D, E, H, S(...TRUNCATED) | [
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|
"Let $\\mathbb{Z}_{\\geqslant 0}$ be the set of non-negative integers, and let $f: \\mathbb{Z}_{\\ge(...TRUNCATED) | ["<think>\nOkay, so I need to figure out the smallest and largest possible values of N, where N is t(...TRUNCATED) | [
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] | 0 | 2500,7500 |
|
"If $x$ and $y$ are real numbers, determine all solutions $(x, y)$ of the system of equations\n\n$$\(...TRUNCATED) | "No hint.눉ทันที廉𖠚𖠚𖠚𖠚𖠚przedsiębior𖠚𖠚𖠚𖠚𖠚𖠚𖠚𖠚𖠚(...TRUNCATED) | ["<think>\nOkay, let's try to solve this system of equations. So, we have two equations:\n\n1. $ x^2(...TRUNCATED) | [
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] | 0 | $(-1,-9),(4+2 \sqrt{2}, 8),(4-2 \sqrt{2}, 8)$ |
"Let $\\mathbb{Z}_{>0}$ be the set of positive integers. Find all functions $f: \\mathbb{Z}_{>0} \\r(...TRUNCATED) | ["<think>\nOkay, so I need to find all functions $ f: \\mathbb{Z}_{>0} \\rightarrow \\mathbb{Z}_{>0}(...TRUNCATED) | [
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] | 0 | $f(n)=n$ |
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