problem
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1.17k
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1
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45
|
|---|---|---|---|---|---|
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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false,
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] | 0
|
$4 \sqrt{5}$
|
|
"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)
|
[
false,
false,
false,
false,
false,
false,
false,
false,
false,
false,
false,
false,
false,
false,
false,
false
] | 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)
|
[
true,
true,
true,
true,
true,
false,
true,
true,
true,
true,
true,
true,
true,
true,
false,
true
] | 0.875
|
49
|
|
"Compute the value of\n\n$$\n\\sin \\left(6^{\\circ}\\right) \\cdot \\sin \\left(12^{\\circ}\\right)(...TRUNCATED)
| ["<think>\nOkay, so I need to compute this expression:\n\n$$\n\\sin \\left(6^{\\circ}\\right) \\cdot(...TRUNCATED)
|
[
false,
false,
false,
false,
false,
false,
false,
false,
false,
false,
false,
false,
false,
false,
false,
false
] | 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)
|
[
false,
false,
false,
false,
false,
false,
false,
false,
false,
false,
false,
false,
false,
false,
false,
false
] | 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 over cosine x minus tangent x equ(...TRUNCATED)
|
[
false,
false,
false,
false,
false,
false,
false,
false,
false,
false,
false,
false,
false,
false,
false,
false
] | 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 see. I need to find the largest possible value of D + E given the equation wh(...TRUNCATED)
|
[
false,
false,
false,
true,
true,
true,
true,
false,
true,
false,
false,
true,
true,
true,
true,
true
] | 0.625
|
9
|
|
"Let $\\mathbb{Z}_{\\geqslant 0}$ be the set of non-negative integers, and let $f: \\mathbb{Z}_{\\ge(...TRUNCATED)
| ["<think>\nOkay, let's try to tackle this problem. It's about a bijection function f from non-negati(...TRUNCATED)
|
[
false,
false,
false,
false,
false,
false,
false,
false,
false,
false,
false,
false,
false,
false,
false,
false
] | 0
|
2500,7500
|
|
"If $x$ and $y$ are real numbers, determine all solutions $(x, y)$ of the system of equations\n\n$$\(...TRUNCATED)
| ["<think>\nOkay, so I need to solve this system of equations:\n\n$$\n\\begin{aligned}\n& x^{2} - x y(...TRUNCATED)
|
[
false,
false,
false,
false,
false,
false,
false,
false,
false,
false,
false,
false,
false,
false,
false,
false
] | 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)
|
[
false,
false,
false,
false,
false,
false,
false,
false,
false,
false,
false,
false,
false,
false,
false,
false
] | 0
|
$f(n)=n$
|
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