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... | 44 seconds |
[
{
"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... | 16.97% |
[
{
"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... | 3867 |
[
{
"content": "Let $A \\in \\mathbb{R}^{n \\times p}$ and $B \\in \\mathbb{R}^{n \\times d}$ be matrices such that both have a spectral norm (largest singular value) equal to 1. If we concatenate the columns of $A$ and $B$ to construct $M = [A|B]$, determine the spectral norm of $M$.",
"role": "user"
}
] | \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... | 100,943.29 |
[
{
"content": "Determine the largest integer value of \\( k \\) such that the inequality \\[ k \\cdot \\left(\\frac{abc}{a+b+c}\\right) \\leq \\left( a+b \\right)^{2} + \\left( a+b+4c \\right)^{2} \\] holds for all positive real numbers \\( a, b, \\) and \\( c \\).",
"role": "user"
}
] | 100 |
[
{
"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... | 219934.64 |
[
{
"content": "Let $\\mathbf{v} = \\begin{pmatrix} 2 \\\\ 1 \\\\ -1 \\end{pmatrix}$ and $\\mathbf{w} = \\begin{pmatrix} 1 \\\\ 0 \\\\ 3 \\end{pmatrix}.$ The columns of a matrix are $\\mathbf{u},$ $\\mathbf{v},$ and $\\mathbf{w},$ where $\\mathbf{u}$ is a unit vector. Find the largest possible determinant of th... | \sqrt{59} |
[
{
"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... | 643.2 kJ/kg |
[
{
"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... | 42.84 |
[
{
"content": "Let $f(x) = 12x+7$ and $g(x) = 5x+2$ whenever $x$ is a positive integer. Define $h(x)$ to be the greatest common divisor of $f(x)$ and $g(x)$. What is the sum of all possible values of $h(x)$?",
"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... | 16.4 g sodium |
[
{
"content": "The least common multiple of $x$, $10$ and $14$ is $70$. What is the greatest possible value of $x$?",
"role": "user"
}
] | 70 |
[
{
"content": "Does there exist a continuous function $f$ such that $f$ is bounded with a codomain of $[0,1]$ and its second derivative $f''$ is unbounded with a codomain of $(-\\infty,+\\infty)$?",
"role": "user"
}
] | Yes |
[
{
"content": "Find $x.$\n\n[asy]\nunitsize(0.7 cm);\n\npair A, B, C, D, O;\n\nO = (0,0);\nA = 4*dir(160);\nB = 5*dir(160 + 180);\nC = 8*dir(20);\nD = 4*dir(20 + 180);\n\ndraw(A--B);\ndraw(C--D);\ndraw(A--C);\ndraw(B--D);\n\nlabel(\"$4$\", (A + O)/2, SW);\nlabel(\"$10$\", (C + O)/2, SE);\nlabel(\"$4$\", (D + O)/... | 9 \sqrt{2} |
[
{
"content": "Find the value of \\( \\alpha \\) that satisfies the equation:\n\\[ 2\\left(\\frac{1}{\\alpha}\\right) \\ln\\left(\\frac{1}{1-\\alpha}\\right) = \\frac{1}{1-\\alpha} \\]",
"role": "user"
}
] | 0.715 |
[
{
"content": "Evaluate the limit: $$\\lim_{x\\to 0^{+}}\\left[\\left(1+\\frac{1}{x}\\right)^x+\\left(\\frac{1}{x}\\right)^x+\\left(\\tan(x)\\right)^{\\frac{1}{x}}\\right]$$",
"role": "user"
}
] | 2 |
[
{
"content": "Evaluate the limit: \\[ \\lim_{x\\to1^{-}} (1-x)\\left(\\sum_{i=0}^{\\infty} x^{i^2}\\right)^{2} \\]",
"role": "user"
}
] | \dfrac{\pi}{4} |
[
{
"content": "On the Cartesian plane in which each unit is one foot, a dog is tied to a post on the point $(4,3)$ by a $10$ foot rope. What is the greatest distance the dog can be from the origin?",
"role": "user"
}
] | 15 |
[
{
"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... | ```cpp
#include <iostream>
using namespace std;
int main() {
double monthly_payment, outstanding_balance, annual_interest_rate = 7.49;
cout << "Enter monthly mortgage payment: ";
cin >> monthly_payment;
cout << "Enter the amount still owed: ";
cin >> outstanding_balance;
double ... |
[
{
"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... | 1.8e-6 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... | Domestic: Ticketing $1,000,000, Baggage handling $600,000, Engine maintenance $1,400,000. Total $3,000,000. International: Ticketing $4,000,000, Baggage handling $2,400,000, Engine maintenance $5,600,000. Total $12,000,000. |
[
{
"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... | 6.95% |
[
{
"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... | 4.84 J |
[
{
"content": "Let \\( v \\) be a permutation of \\( \\{1, 2, \\ldots, 2n+1\\} \\) where \\( n \\) is odd. The permutation \\( v \\) must satisfy the condition that the middle element \\( v_{n+1} \\) has an equal number of elements less than \\( v_{n+1} \\) to its right as there are elements greater than \\( v_{... | (2n)! |
[
{
"content": "Consider a continuous and differentiable function \\(f\\) defined on the entire real line \\(\\mathbb{R}\\). Define a sequence of functions \\(f_n\\) as follows: \\(f_n(x) = n(f(x + \\frac{1}{n}) - f(x))\\). Determine which of the following statements is correct regarding the convergence of \\(f_n... | 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... | 179 |
[
{
"content": "As \\( n \\) becomes arbitrarily large, determine which number is greater: \\( a = (10^n - 1)^{(10^n)} \\) or \\( b = (10^n)^{(10^n - 1)} \\).",
"role": "user"
}
] | a |
[
{
"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... | 2.41 meters |
[
{
"content": "Determine the radius of convergence for the power series of \\( f(z) = \\frac{e^{z^2}}{1+z^3} \\) around \\( z = 0 \\).",
"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... | $3,360 |
[
{
"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 m |
[
{
"content": "Determine the number of units in the quotient ring $R/I$, where $R = \\mathbb{F}_7[x]$, $f(x) = x^3 + 4$, and $I = (f(x))$. The number of elements in $R/I$ is $343$. How many of these elements are units?",
"role": "user"
}
] | 342 |
[
{
"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... | Net cash provided by operating activities: 54
Net cash provided by investing activities: (39)
Net cash provided by financing activities: (16)
Net increase in cash: (1)
Cash balance, beginning of year: 22
Cash balance, end of year: 21 |
[
{
"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... | 150796 ft-lb |
[
{
"content": "Evaluate the limit \\( \\lim_{n\\rightarrow \\infty}\\sqrt[n]{f\\left(\\frac{1}{n}\\right)g\\left(\\frac{n}{n}\\right)+f\\left(\\frac{2}{n}\\right)g\\left(\\frac{n-1}{n}\\right)+\\cdots+f\\left(\\frac{n}{n}\\right)g\\left(\\frac{1}{n}\\right)} \\) where \\( f:[0,1]\\rightarrow [0,\\infty) \\) and ... | 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... | 9.6358% |
[
{
"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... | 0.235A |
[
{
"content": "A vessel with a capacity of 100 liters is filled with a brine solution containing 10 kg of dissolved salt. Every minute, 3 liters of water flows into it, and the same amount of the resulting mixture is pumped into another vessel of the same capacity, initially filled with water, from which the exc... | \dfrac{100}{3} |
[
{
"content": "In triangle $ABC$, it is given that $|AB| + |AC| = 3|BC|$. Point $T$ is located on segment $AC$ such that $|AC| = 4|AT|$. Points $K$ and $L$ are on the interior of line segments $AB$ and $AC$, respectively, such that $KL \\parallel BC$ and $KL$ is tangent to the incircle of $\\triangle ABC$. Let $... | \dfrac{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... | 35.71% |
[
{
"content": "Determine the number of real roots of the equation \\(11^x + 13^x + 17^x - 19^x = 0\\). Choose from the following options: \\(1\\) No real root, \\(2\\) Only one real root, \\(3\\) Two real roots, \\(4\\) More than two real roots.",
"role": "user"
}
] | 2 |
[
{
"content": "Determine the conditions that the matrix \\( A \\in \\mathbb{R}^{n \\times n} \\) must satisfy such that \\( \\lim_{k \\to \\infty} ||e_k|| = 0 \\), where the sequence is defined by \\( e_{k+1} = A e_k \\) and \\( e_0 \\) is given.",
"role": "user"
}
] | \rho(A) < 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... | 5.58 g |
[
{
"content": "Find the values of $x$ for which the integral \\( \\int_{0}^{2\\pi} \\ln \\left(x + \\sin t \\right)dt \\) is zero, given that $1 < x < 2$.",
"role": "user"
}
] | \dfrac{5}{4} |
[
{
"content": "Consider the diffusion equation:\n\\[ \\frac{\\partial ^2 u}{\\partial x^2} = \\frac{\\partial u}{\\partial t},\\; u = u(x,t),\\; u(0,t) =0 = u( \\pi ,t),\\; u(x,0) = \\cos x \\sin 5x \\]\nWhich of the following is a solution to the equation?\n\n1. \\( \\frac{e^{-36t}}{2} [\\sin 6x + e^{20t} \\sin... | 1 |
[
{
"content": "Consider a square matrix of size n, where the entries are filled with consecutive integers from 1 to n^2 in row-major order. Does the antidiagonal of this matrix always contain at least one prime number for n > 1?",
"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... | 117.94 months or 9.83 years |
[
{
"content": "Calculate the limit using the Maclaurin series: \\[ \\lim_{x \\to 0}\\frac{1-(\\cos{x})^{\\sin{x}}}{x^3} \\]",
"role": "user"
}
] | \dfrac{1}{2} |
[
{
"content": "Find the coefficient of $x^7$ in the Taylor series expansion of $\\arcsin(x)$ around $x=0$. Use any efficient method to determine this coefficient.",
"role": "user"
}
] | \dfrac{5}{112} |
[
{
"content": "In a regular 2017-gon, all diagonals are drawn. What is the smallest number of diagonals, \\( N \\), that must be selected to guarantee that at least two of them have the same length?",
"role": "user"
}
] | 1008 |
[
{
"content": "Calculate the mass of the surface of the ellipsoid \\(E=\\{\\frac{x^2}{a^2}+\\frac{y^2}{b^2}+\\frac{z^2}{c^2}=1\\}\\) given that the density at a point \\((x,y,z)\\) on the surface is \\(\\rho=\\frac{r}{4\\pi abc}\\), where \\(r\\) is the distance from the origin to the tangent plane at that point... | 1 |
[
{
"content": "What is the automorphism group of the symmetric group of degree three, $Sym(3)$?",
"role": "user"
}
] | S_3 |
[
{
"content": "Determine the maximum value of the positive number \\(r\\) such that the set \\(T=\\{(x, y) \\mid x, y \\in \\mathbf{R}, x^{2}+(y-7)^{2} \\leqslant r^{2}\\}\\) is a subset of the set \\(S=\\{(x, y) \\mid x, y \\in \\mathbf{R}, \\cos 2\\theta + x \\cos \\theta + y \\geqslant 0\\}\\) for any \\(\\th... | 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... | 4.2 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... | $285,100 |
[
{
"content": "Determine the maximum number of functions in the set \\( A = \\{ f \\in C^1[0,1] : f(0) = 0, f(1) = 1, |f'(t)| \\le 1 \\text{ for all } t \\in [0,1] \\} \\) that can have different slopes at a given point \\( c \\in (0,1) \\).",
"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... | $5.2 million |
[
{
"content": "Evaluate the limit: $$\\lim\\limits_{x \\to 0} \\frac{x^4\\cos(\\frac{1}{x})} {\\sin^3x}.$$",
"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... | $990,000 |
[
{
"content": "Given a random variable $X$ with a binomial distribution, $X \\sim \\mathrm{Binom}(n,p)$, find the limit of its cumulative distribution function (CDF) as $n$ approaches infinity, with $p$ remaining constant:\n\\[\\lim_{n\\to\\infty}F_X(x)=\\lim_{n\\to\\infty}\\sum_{k=0}^{\\lfloor x\\rfloor}\\binom... | 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... | ZnSO_4(aq) + BaCl_2(aq) rarr ZnCl_2(aq) + BaSO_4(s) |
[
{
"content": "Evaluate the limit \\( \\lim_{a\\to1^+}\\int_0^{\\pi/2}\\frac{dx}{(1+\\cos2x)^a} \\). Determine if the integral converges and find its value if it does.",
"role": "user"
}
] | \infty |
[
{
"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... | Classical economics |
[
{
"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... | 2.30e-3 |
[
{
"content": "Find the sum of all integer values of \\( a \\) such that \\( a(x^2+x-1) \\leq (x^2+x+1)^2 \\) for all real numbers \\( x \\).",
"role": "user"
}
] | 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... | 17.9 L |
[
{
"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... | Metalloids |
[
{
"content": "Determine the values of \\(m\\) and \\(k\\) for which the series \\(\\sum_{n=1}^{\\infty} \\frac{\\sqrt[m]{n!}}{\\sqrt[k]{(2n!)}}\\) converges.",
"role": "user"
}
] | k \leq 2m |
[
{
"content": "Find the positive constant $c$ such that the matrix $B = cA$, where $A = \\begin{pmatrix} 2 & -1 & -1 \\\\ -1 & 2 & -1 \\\\ -1 & -1 & 2 \\end{pmatrix}$, is an orthogonal projection matrix.",
"role": "user"
}
] | \dfrac{1}{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... | $58.20 |
[
{
"content": "Let $A$ and $N$ be Banach spaces, and consider a linear transformation $L: A \\rightarrow N$. If $L$ is continuous, does the operator norm of $L$, denoted by $\\|L\\| = \\inf\\{ M \\geq 0 \\ : \\|L(v)\\| \\leq M\\|v\\|, \\ \\forall v \\in A \\}$, belong to the set $\\{ M \\geq 0 \\ : \\|L(v)\\| \\... | 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... | -4.15 m |
[
{
"content": "Compute the Weil divisor of poles and zeroes for the rational section \\( \\frac{x^2}{x+y} \\) of the sheaf \\( \\mathcal{O}(1) \\) on \\( \\mathbb{P}_{k}^1 \\).",
"role": "user"
}
] | 2[0:1] - [1:-1] |
[
{
"content": "Given a simple closed curve with winding number zero around each of several red points, is it possible to homotope the curve to a loop that does not intersect any of the red points?",
"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... | 1.42 m |
[
{
"content": "Calculate the number of permutations in the symmetric group S7 that can be expressed as a product of exactly three disjoint cycles.",
"role": "user"
}
] | 1624 |
[
{
"content": "Evaluate the limit \\( \\lim_{n\\to\\infty} \\frac{\\sqrt[n]{(2n)!}}{n} \\).",
"role": "user"
}
] | \infty |
[
{
"content": "Calculate the limit: $$\\lim \\limits_{x \\to \\infty} \\left[(x+a)^{1+\\frac{1}{x}}-(x)^{1+\\frac{1}{x+a}}\\right].$$",
"role": "user"
}
] | a |
[
{
"content": "Given a closed, orientable, smooth manifold $M$ and a cohomology class $\\alpha \\in H^2(M)$, consider a closed, orientable submanifold $N \\subset M$ that is Poincaré dual to $\\alpha$. Let $E \\rightarrow M$ be the complex line bundle with Euler class $e(E) = \\alpha$, and suppose there exists a... | 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... | 1.17 m |
[
{
"content": "Given that \\( \\{a_n\\} \\) is a sequence of positive real numbers that converges to a number \\( A \\), determine if the sequence \\( \\left\\{\\left(\\frac{a_1+a_2+\\cdots+a_n}{n}\\right)^{1/n}\\right\\} \\) converges.",
"role": "user"
}
] | 1 |
[
{
"content": "Calculate \\( \\operatorname{Cov}(X + 3, XZ) \\) given that \\( f_X(x) = \\begin{cases} 4x^3 &, \\text{if} \\ 0 < x < 1 \\\\\\ 0 &, \\text{otherwise} \\end{cases} \\), where \\( Z \\sim N(1,2) \\) and \\( X \\) and \\( Z \\) are independent.",
"role": "user"
}
] | \dfrac{2}{75} |
[
{
"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... | Na2SO4 * 10H2O |
[
{
"content": "Suppose $A, B, C \\sim U(-1, 1)$ are mutually independent random variables. Calculate the probability $P(A + B + C < 0)$. Express your answer as a decimal or a fraction.",
"role": "user"
}
] | \dfrac{1}{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... | 838.75 |
[
{
"content": "Find the limit of the sequence defined by \\(S_n= n\\,p^n \\sum_{k=n}^{+\\infty} \\frac{1}{k}\\, \\binom{k-1}{n-1} \\, (1-p)^{k-n}\\) where \\(0<p<1\\).",
"role": "user"
}
] | p |
[
{
"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... | 5.88e6 N |
[
{
"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... | 1.125 g |
[
{
"content": "Find an integer \\( m \\geq 2 \\) such that the congruence equation \\( x^2 \\equiv 1 \\pmod{m} \\) has more than two distinct solutions in the residue class ring \\( \\mathbb{Z}/m\\mathbb{Z} \\).",
"role": "user"
}
] | 8 |
[
{
"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... | $100,000, $112,150, $115,596, $113,043, $108,000, $115,385 |
[
{
"content": "Determine whether there exist two finite complex measures \\( \\mu \\) and \\( \\nu \\) with compact supports on the real line, both singular with respect to the Lebesgue measure, such that their convolution \\( \\mu \\ast \\nu \\) has a nonzero absolutely continuous component.",
"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... | Moles of solute/Volume of solution |
[
{
"content": "Given two independent random variables $X$ and $Y$, both uniformly distributed from $2.16$ to $6.81$, find the expected value of the squared absolute difference, $E(|X - Y|^2)$. Express your answer as a single number.",
"role": "user"
}
] | 3.60375 |
[
{
"content": "Consider a compact Riemann surface $C$ of genus $g$. The vector space of holomorphic 1-forms on $C$, denoted by $\\mathrm{H}^0(C,\\mathrm{K}_C)$, has a basis $\\eta_1, \\ldots, \\eta_g$. A holomorphic 1-form on $C^{\\times 2}$ is called a bidifferential. A bidifferential $\\omega$ is symmetric if ... | Yes |
[
{
"content": "Find the values of $k$ for which the function $f(x) = x^k|x|$ is thrice differentiable at $x = 0$.",
"role": "user"
}
] | k \geq 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... | 5.25 |
[
{
"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... | 2606.7K |
[
{
"content": "Evaluate the integral \\(\\int_{|z-\\pi|=\\pi} \\frac{\\sin(\\pi z)}{z^{2}-\\pi^{2}} \\, dz\\) using Cauchy's integral formula.",
"role": "user"
}
] | i \sin(\pi^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... | $7,486.68 |
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