prompt list | ground_truth string |
|---|---|
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | Reception: Outpatients: $285,415, Admitted Patients: $332,985, Total: $618,400
Treatment: Outpatients: $1,127,778, Admitted Patients: $90,222, Total: $1,218,000
Cleaning: Outpatients: $160,518, Admitted Patients: $66,882, Total: $227,400 |
[
{
"content": "Find the smallest positive integer solution to $\\tan{19x^{\\circ}}=\\dfrac{\\cos{96^{\\circ}}+\\sin{96^{\\circ}}}{\\cos{96^{\\circ}}-\\sin{96^{\\circ}}}$.",
"role": "user"
}
] | 159 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | C_4H_8 + 6O_2 -> 4CO_2 + 4H_2O |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 11.23 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 3.075e-8 cm |
[
{
"content": "Find the number of elements of order 8 in the multiplicative group of the finite field $GF(p^n)$, where $p \\equiv 3 \\pmod{4}$ and $n$ is even.",
"role": "user"
}
] | 4 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 2 * 10^-8 C/m |
[
{
"content": "Find all positive integer solutions \\((c, d)\\) to the equation \\[1372c^4 - d^2 = 3.\\]",
"role": "user"
}
] | (1, 37) |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | $52 |
[
{
"content": "Determine whether there exists a connected, simple, undirected graph with a countably infinite number of vertices and a finite diameter, such that its complement graph also has a finite diameter.",
"role": "user"
}
] | Yes |
[
{
"content": "Evaluate the integral \\( \\int_{-\\infty}^{\\infty} x f(x) \\delta(x-a) \\, dx \\), where \\( f(x) \\) is a continuous function and \\( \\delta(x-a) \\) is the Dirac delta function.",
"role": "user"
}
] | a f(a) |
[
{
"content": "Determine whether the statement is true or false: For any prime number \\( p \\), the reciprocal of \\( p \\) in base 10 has a repeating set of digits with a period of \\( p-1 \\).",
"role": "user"
}
] | B |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 1.32 g |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 24 g |
[
{
"content": "What is the area of the region in the $xy-$plane that satisfies \\[\\lfloor x \\rfloor \\lfloor y \\rfloor = 16\\, ?\\]",
"role": "user"
}
] | 10 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | $949.10 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 970 g |
[
{
"content": "Let $z_1, z_2,$ and $z_3$ be complex numbers such that $z_1 + z_2 + z_3 = 2$, $z_1^2 + z_2^2 + z_3^2 = 3$, and $z_1z_2z_3 = 4$. Calculate the value of \\( \\sum_{i=1}^{3} \\frac{1}{z_i^2 - z_i + 4} \\).",
"role": "user"
}
] | \dfrac{23}{36} |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 1.694 MeV |
[
{
"content": "Given that \\(X_i \\sim \\text{Poisson}(\\theta)\\), find the maximum likelihood estimator (MLE) of \\(\\pi(\\theta) = \\exp(-\\theta)\\). Is \\(\\exp(-\\bar{X})\\) the MLE of \\(\\pi\\)?",
"role": "user"
}
] | e^{-\bar{X}} |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 5.56e15 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 66.6 s |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | $ \ddot x(t)=-\frac{Gm}{x^2(t)} $ |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 1.09 m |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | {\sqrt{Rg(\tan\theta + \mu_s)/(1-\mu_s\tan\theta)}} |
[
{
"content": "Evaluate the contour integral \\(\\oint\\limits_{|z-3|=4}^{}\\frac{z}{\\cos z-1}dz\\) using the residue theorem.",
"role": "user"
}
] | -8\pi i |
[
{
"content": "In the inscribed quadrilateral \\(ABCD\\), the diagonals intersect at point \\(O\\). The circumcircle of triangle \\(AOB\\) intersects lines \\(AD\\) and \\(BC\\) at points \\(K\\) and \\(L\\), respectively. Given that \\(\\angle BCA = \\angle BDC\\), determine the ratio \\(OK:OL\\).",
"role":... | 1 |
[
{
"content": "Let $A$ be a C*-algebra. If for every cyclic representation $\\pi: A \\rightarrow B(H)$, we have $\\pi(a) \\geq 0$ for all $a \\in A$, can we conclude that $a \\geq 0$?",
"role": "user"
}
] | Yes |
[
{
"content": "Given a nice functional $F: \\mathcal B \\to \\mathbb R$ on a Banach space $\\mathcal B$, define the map $\\phi_x: \\mathbb R \\to \\mathbb R$ for a fixed $x \\in \\mathcal B$ and $c \\in \\mathbb R$ by $\\phi_x(c) = F(cx)$. Find an expression for $\\frac{d}{dc}\\phi_x(c)$. Assume that $F$ is diff... | DF(cx)(x) |
[
{
"content": "In triangle \\( \\triangle ABC \\), \\(\\angle ABC = 40^\\circ\\), \\(\\angle ACB = 20^\\circ\\). Point \\( N \\) is located inside the triangle such that \\(\\angle NBC = 30^\\circ\\) and \\(\\angle NAB = 20^\\circ\\). Determine the measure of \\(\\angle NCB\\).",
"role": "user"
}
] | 10^\circ |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 0.12 M |
[
{
"content": "Determine the smallest integer $n$ for which the number of pairs $(x, y)$ satisfying $x \\ge y$, $\\operatorname{lcm}(x, y) = n!$, and $\\gcd(x, y) = 2023$ is greater than 2023. Note that $2023 = 7 \\times 17^2$. What is this value of $n$?",
"role": "user"
}
] | 41 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 0.025 mg |
[
{
"content": "Let $G$ be a group, and let $e \\ne x \\in G$ and $y \\in G$ such that $\\langle y \\rangle \\subseteq \\langle x \\rangle$. Can $\\langle y \\rangle$ be equal to $G$?",
"role": "user"
}
] | Yes |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | human capital |
[
{
"content": "The graph of the equation $y=ax^2+bx-6$ is completely below the $x$-axis. If $a^2=49$, what is the largest possible integral value of $b$?",
"role": "user"
}
] | 12 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | -1.275e+6 V |
[
{
"content": "In a group of $N$ boys and $N$ girls, each person shakes hands with $d$ random members of the opposite sex. If one person is initially infected with a disease that spreads through handshakes, what is the probability that everyone in the group will eventually become infected, given that $d > 1$?",
... | 1 |
[
{
"content": "Let $M^n$ be a topological manifold of dimension $n=3$ or $n=4$, which has the same homotopy type as the standard torus $T^n$. Is $M^n$ homeomorphic to the standard torus $T^n$?",
"role": "user"
}
] | Yes |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 29,984.25 J |
[
{
"content": "Let \\( p(x) = x^2 + bx + c \\), where \\( b \\) and \\( c \\) are integers. If \\( p(x) \\) is a factor of both \\( x^4 + 6x^2 + 25 \\) and \\( 3x^4 + 4x^2 + 28x + 5 \\), find the value of \\( p(1) \\).",
"role": "user"
}
] | 4 |
[
{
"content": "Calculate the present value of a continuously varying, continuously paid annuity with payments $(8k + tk)$ made to an account, where $0 \\leq t \\leq 10$. The interest is credited at a force of interest $\\delta_t = \\frac{1}{8+t}$. After 10 years, the account's value is $20,000$. Find the value o... | \dfrac{1000}{9} |
[
{
"content": "Determine whether it is possible to find 100 positive integers $x_1, x_2, \\ldots, x_{100}$ such that $x_1!x_2! \\cdots x_{100}!=n!$ for some positive integer $n$. Provide a justification for your answer.",
"role": "user"
}
] | Yes |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | $2.20 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 3.17m/s^2 |
[
{
"content": "Consider the polynomial \\( f(x) \\) of degree 11 defined such that \\( f(x) = \\frac{1}{x+1} \\) for \\( x = 0, 1, 2, \\ldots, 11 \\). What is the value of \\( f(12) \\)?\n\n(A) \\( \\frac{1}{13} \\)\n(B) \\( \\frac{1}{12} \\)\n(C) \\( 0 \\)\n(D) \\( \\frac{1}{7} \\)",
"role": "user"
}
] | C |
[
{
"content": "Evaluate the limit: $$\\lim_{t\\rightarrow\\infty} \\frac{1-\\exp\\left(-\\frac{1}{1+tx}\\right)}{1-\\exp\\left(\\frac{1}{1+t}\\right)}$$",
"role": "user"
}
] | -\dfrac{1}{x} |
[
{
"content": "What is \\( \\mathbb{E}[g(X)|X] \\) for a continuous random variable \\( X \\) with distribution \\( f_X \\) and a continuous function \\( g \\)?",
"role": "user"
}
] | g(X) |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 9.67% |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | $531 |
[
{
"content": "Determine the degree of the map \\( f: \\mathbb{P}_{\\mathbb{R}}^3 \\rightarrow \\mathbb{P}_{\\mathbb{R}}^3 \\) given by \\( f([x_0:x_1:x_2:x_3])=[x_0^2: x_1^2: x_2^2 :x_3^2] \\).",
"role": "user"
}
] | 0 |
[
{
"content": "Determine the number of solutions for the following system of equations: \\[(2-y)e^{x} = e^{-y} \\] \\[ x(2-y)e^{y} = -e^{-x} \\]",
"role": "user"
}
] | 1 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | W = 200 - 2Q |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | $280,000 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 71.747 degrees |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | -$200,000 |
[
{
"content": "Determine whether the following statement is true or false: If a differentiable function $f(x)$ satisfies $(f(x))^{n} = f(nx)$ for all $x \\in \\mathbb{R}$, then $f'(x)f(nx) = f(x)f'(nx)$. Justify your answer.",
"role": "user"
}
] | True |
[
{
"content": "Given the digits 0 and 9, form the smallest positive number that is a multiple of a given integer \\( n \\). For example, if \\( n = 7 \\), the smallest number is 9009. Determine this number for a given \\( n \\).",
"role": "user"
}
] | 9009 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 27 degrees Celsius |
[
{
"content": "Determine the constant $b$ such that the functions $\\sin(3x)$ and $1 - e^{bx}$ overlap on the interval $(-1,1)$ when graphed.",
"role": "user"
}
] | -3 |
[
{
"content": "Two fair 6-sided dice are rolled. What is the probability \"doubles\" are rolled (i.e., that the two dice show the same number)?",
"role": "user"
}
] | \dfrac{1}{6} |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | $44 Unfavorable |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | $3,432,005 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 4.62 g P4 |
[
{
"content": "Let \\((a, b, c)\\) be a Pythagorean triple, where \\(a, b, c\\) are positive integers. If \\(\\gcd(a, b) = 1\\), is it always true that \\(\\gcd(b, c) = \\gcd(a, c) = 1\\)? Provide a proof or counterexample.",
"role": "user"
}
] | Yes |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 14.8 kJ/mol |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 3.9 s |
[
{
"content": "Compute\n\\[\\prod_{n = 0}^\\infty \\left[ 1 - \\left( \\frac{1}{2} \\right)^{3^n} + \\left( \\frac{1}{4} \\right)^{3^n} \\right].\\]",
"role": "user"
}
] | \frac{2}{3} |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | Co_2(SO_4)_3 |
[
{
"content": "For which of the following functions does the series \\( \\sum_{x \\in S(f)} \\frac{1}{x} \\) converge, where \\( S(f) = \\{x:x>0, f(x)=x\\} \\)?\n\nA.) \\( \\tan x \\)\n\nB.) \\( \\tan x^2 \\)\n\nC.) \\( \\tan 2x \\)\n\nD.) \\( \\tan\\sqrt{x} \\)\n\nE.) \\( \\sqrt{|\\tan x|} \\)",
"role": "us... | D |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | Cash $25,300
Sales $22,000
Sales tax payable $1,540
Excise tax payable $1,760 |
[
{
"content": "Find the value of the following sum:\n\\[\n\\left(1+ \\frac{1}{2}+\\frac{1}{3}+\\cdots +\\frac 1{2015}+\\frac{1}{2016}\\right)^2 \\\\\n+\\left(\\frac{1}{2}+\\frac{1}{3}+\\cdots +\\frac 1{2015}+\\frac{1}{2016}\\right)^2 \\\\\n+ \\left(\\frac{1}{3}+\\cdots +\\frac 1{2015}+\\frac{1}{2016}\\right)^2 \... | 4032 |
[
{
"content": "Evaluate the integral: $$\\int_0^{2\\pi}\\arctan \\biggl( \\frac{\\sin \\theta} {\\cos \\theta +3}\\biggr)d\\theta$$",
"role": "user"
}
] | 0 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | ytterbium |
[
{
"content": "Determine if the recurrence \\(x_0 = n, x_{i + 1} = x_i - \\log x_i, \\forall i \\geq 0\\) satisfies that the smallest integer \\(N_n\\) such that \\(x_{N_n} < 10\\) is in \\(\\omega(\\log(n))\\).",
"role": "user"
}
] | Yes |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 1.11e-6 T |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 459.36 km |
[
{
"content": "Determine whether the matrix direct sum is distributive over matrix multiplication. Specifically, is the following statement true or false? $$\\bigoplus_{i=1}^n A_iB_i = \\left(\\bigoplus_{i=1}^n A_i\\right)\\left(\\bigoplus_{i=1}^n B_i\\right)$$ where $A_iB_i$ denotes the product of matrices $A_i... | True |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 33.6 g |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 2.50e7 N; 5.63e6 lbs |
[
{
"content": "Solve the equation \\(x^2 = \\log^2(x)\\) for \\(x\\).",
"role": "user"
}
] | W(1) |
[
{
"content": "Evaluate the integral \\( \\int_0^{2\\pi}\\sqrt{1+\\sin x}\\,dx \\).",
"role": "user"
}
] | 4\sqrt{2} |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 9.1 * 10^8 J |
[
{
"content": "Calculate the Jacobian determinant for the transformation from variables \\((u, v, w)\\) to \\((x, y, z)\\) given by the equations:\n\n\\[ u = x + y + z, \\quad v = x + 2z, \\quad w = x + 2y + 3z. \\]",
"role": "user"
}
] | -\dfrac{1}{3} |
[
{
"content": "Determine the number of solutions to the congruence $x^{20} \\equiv 1 \\pmod{121}$. Provide your answer as a single integer.",
"role": "user"
}
] | 10 |
[
{
"content": "Evaluate the integral: $$ \\int\\limits_0^{\\pi/2} \\frac{\\cos^3x + \\sin^3x}{\\sqrt{\\sin 2x}}dx $$",
"role": "user"
}
] | \dfrac{3\pi}{4} |
[
{
"content": "Mohan is selling cookies at the economics fair. As he decides how to package the cookies, he finds that when he bags them in groups of 4, he has 3 left over. When he bags them in groups of 5, he has 2 left over. When he bags them in groups of 7, he has 4 left over. What is the least number of cook... | 67 |
[
{
"content": "Does the uniform continuity of a function $f$ on the interval $[0, \\\\infty)$ ensure that the limit $\\\\lim_{x\\\\to\\\\infty} f(x)$ exists?",
"role": "user"
}
] | No |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 12.5 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 12:1 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 5.71% |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 2.86 m/s |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 563 Hz |
[
{
"content": "Provide a counterexample to the conjecture that for any positive integer $N$ and $\\alpha_i \\in [0,1)$ such that $e^{2\\pi i \\alpha_1} + \\cdots + e^{2\\pi i \\alpha_N} = 0$, if any non-empty proper subset of the $\\alpha_i$ does not sum to zero, then $N$ must be prime.",
"role": "user"
}
... | 4 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 107 uC |
[
{
"content": "Evaluate the limit: \\[ \\lim_{x \\to 0} \\frac{|x|^{1/2} \\cos(\\pi^{1/x^2})}{2 + (x^2 + 3)^{1/2}} \\]",
"role": "user"
}
] | 0 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 4.174 W |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 5.25 hp |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 1.12e5 years |
[
{
"content": "Let $X=(X_1,X_2,X_3)$ be a continuous random vector with the joint probability density function given by \\( f(x_1,x_2,x_3)= 12x_2 \\) for \\( 0<x_3<x_2<x_1<1 \\) and \\( 0 \\) elsewhere. Calculate the probability of the event \\( B = \\{ x_3 \\leq \\frac{1}{3} \\} \\).",
"role": "user"
}
] | \dfrac{49}{81} |
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