prompt list | ground_truth string |
|---|---|
[
{
"content": "Prove that \\(3^m + 3^n + 1\\) cannot be a perfect square for any positive integers \\(m\\) and \\(n\\).",
"role": "user"
}
] | 3^m + 3^n + 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... | $5.5 million |
[
{
"content": "Determine whether a bounded operator on a separable Banach space $X$ can always have an infinite-dimensional range contained in a closed, infinite-dimensional subspace $Y$ of $X$. 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... | 40734 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... | 27.5 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... | 66178 |
[
{
"content": "A parabola with equation $y = x^2 + bx + c$ passes through the points $(2,3)$ and $(4,3)$. What is $c$?",
"role": "user"
}
] | 11 |
[
{
"content": "Let $f: \\mathbb{R} \\rightarrow \\mathbb{R}$ be a continuous function satisfying $f(x) \\geq 0$ for all $x$ and \\(\\int_{-\\infty}^{\\infty} f(x) \\, dx = 1\\). For $r \\geq 0$, define\n\\[I_n(r) = \\int \\cdots \\int_{x_1^2 + x_2^2 + \\cdots + x_n^2 \\leq r^2} f(x_1)f(x_2)\\cdots f(x_n) \\, dx_... | 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... | 47.05m J |
[
{
"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... | K / (8*pi^2 + 1) |
[
{
"content": "For any integer \\( n (n \\geqslant 2) \\), if the positive numbers \\( a \\) and \\( b \\) satisfy \\( a^n = a + 1 \\) and \\( b^{2n} = b + 3a \\), determine the relationship between \\( a \\) and \\( b \\). Choose the correct option:\n\n(A) \\( a > b > 1 \\)\n\n(B) \\( b > a > 1 \\)\n\n(C) \\( a... | A |
[
{
"content": "For a specific value of \\(c\\), the limit \\(\\lim_{x \\to \\infty}\\left[\\left(x^{5} + 7x^{4} + 2\\right)^c - x\\right]\\) is finite and non-zero. Let \\(l\\) represent this limit. Find the value of \\(l - 2c\\).",
"role": "user"
}
] | 1 |
[
{
"content": "Let \\( f:(1,4)\\to \\mathbb{R} \\) be a uniformly continuous function and \\( \\{a_n\\} \\) be a Cauchy sequence in \\((1,2)\\). Define the sequences \\( x_n = a_n^2 f(a_n^2) \\) and \\( y_n = \\frac{1}{1+a_n^2} f(a_n^2) \\). Determine which of the following statements is correct:\n\n(A) Both \\(... | A |
[
{
"content": "What is the slope of the line determined by any two solutions to the equation $\\frac{2}{x}+\\frac{3}{y} = 0$? Express your answer as a common fraction.",
"role": "user"
}
] | - \frac 32 |
[
{
"content": "Determine whether the following statement is true or false: Let $(X, d)$ be a compact metric space and let $g_y:X\\to X$ be a continuous function for every $y\\in X$. If $f:X\\to X$ is defined by $f(x)=g_x(x)$, then $f$ must be continuous.",
"role": "user"
}
] | False |
[
{
"content": "Let $X_1, X_2, X_3, \\dots, X_n$ be identically independently distributed (i.i.d.) random variables from a probability distribution, and suppose there exists a positive constant $M$ such that $|E[X]| < M$. Does the strong law of large numbers imply that the sample mean $\\bar{X}_n$ is almost surel... | No |
[
{
"content": "Find the remainder when $10^{5^{102}}$ is divided by 35.",
"role": "user"
}
] | 10 |
[
{
"content": "Determine the radius of convergence of the series \\(\\sum^{\\infty}_{r=1}x^{r}\\cdot \\cos^2(r)\\).",
"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... | 7.360e6 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... | 2.09e-14 N, directed down the page |
[
{
"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... | $76,663 |
[
{
"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... | 5.26 mm |
[
{
"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... | $20.33 |
[
{
"content": "Determine whether there exist polynomials \\( P(x), Q(x), R(x) \\) with real coefficients such that the polynomials \\( P(x) \\cdot Q(x), Q(x) \\cdot R(x) \\), and \\( P(x) \\cdot R(x) \\) have the same degree, while the polynomials \\( P(x) + Q(x), P(x) + R(x), \\) and \\( Q(x) + R(x) \\) have pa... | 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... | 129 mL |
[
{
"content": "Given the polynomial \\(f(x) = x^2 + 3x + 1\\), let \\(\\alpha\\) and \\(\\beta\\) be its two zeroes. Evaluate the expression \\(\\frac{\\alpha^{2016} + \\beta^{2016} + \\alpha^{2014} + \\beta^{2014}}{\\alpha^{2015} + \\beta^{2015}}\\).",
"role": "user"
}
] | -3 |
[
{
"content": "A machine-shop cutting tool has the shape of a notched circle, as shown. The radius of the circle is $\\sqrt{50}$ cm, the length of $AB$ is $6$ cm and that of $BC$ is $2$ cm. The angle $ABC$ is a right angle. Find the square of the distance (in centimeters) from $B$ to the center of the circle.\n[... | 26 |
[
{
"content": "Evaluate the limit: \\[ I = \\lim_{t\\to0^{+}}\\lim_{x\\to+\\infty}\\dfrac{\\displaystyle\\int_{0}^{\\sqrt{t}}dx\\int_{x^2}^{t}\\sin{y^2}dy}{\\left[\\left(\\dfrac{2}{\\pi}\\arctan{\\dfrac{x}{t^2}}\\right)^x-1\\right]\\arctan{t^{\\frac{3}{2}}}} \\]",
"role": "user"
}
] | -\dfrac{\pi}{7} |
[
{
"content": "Find the limit of the function \\( f(x,y) = x \\cdot \\ln{(x^2+2y^2)} \\) as \\((x,y)\\) approaches \\((0,0)\\).",
"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... | $65, 879. 50 |
[
{
"content": "Find the number of quadratic polynomials \\( ax^2 + bx + c \\) that satisfy the following conditions:\n\n1. \\( a, b, c \\) are distinct integers.\n2. \\( a, b, c \\in \\{1, 2, 3, \\ldots, 999\\} \\).\n3. \\( (x+1) \\) divides \\( ax^2 + bx + c \\).",
"role": "user"
}
] | 498002 |
[
{
"content": "Determine if the polynomial \\(k^6 - 5k^5 + 10k^4 - 10k^3 + 5k^2 - k\\) can be the chromatic polynomial of a graph.",
"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... | 0.9239 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... | 1.919 g $H_2$ |
[
{
"content": "Determine the number of positive integer solutions \\((k, n)\\) to the equation:\n\n$$(2k)! = (2^{2n} - 1)(2^{2n} - 2)(2^{2n} - 4) \\cdots (2^{2n} - 2^{2n-1})$$",
"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... | $106,490,632 |
[
{
"content": "To be able to walk to the center $C$ of a circular fountain, a repair crew places a 16-foot plank from $A$ to $B$ and then a 10-foot plank from $D$ to $C$, where $D$ is the midpoint of $\\overline{AB}$ . What is the area of the circular base of the fountain? Express your answer in terms of $\\pi$.... | 164 \pi \mbox{ square feet} |
[
{
"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... | 5.10 * 10^(-24) J |
[
{
"content": "Given the partial differential equation:\n\\[ \\frac{\\partial}{\\partial t} f(x,y,t) = x \\frac{\\partial f}{\\partial y} - y \\frac{\\partial f}{\\partial x} \\]\nand the initial condition:\n\\[ f(x,y,0) = x^2 + y^2 \\]\ndetermine the function \\( f(x,y,t) \\) for all time \\( t \\).",
"role... | x^2 + y^2 |
[
{
"content": "Calculate the determinant of the matrix \\(A=\\begin{pmatrix} \\sin\\alpha & \\cos\\alpha & a\\sin\\alpha & b\\cos\\alpha & ab \\\\ -\\cos\\alpha & \\sin\\alpha & -a^2\\sin\\alpha & b^2\\cos\\alpha & a^2b^2 \\\\ 0 & 0 & 1 & a^2 & b^2 \\\\ 0 & 0 & 0 & a & b \\\\ 0 & 0 & 0 & -b & a \\end{pmatrix}\\)... | a^2 + b^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... | DEBT 20%, EQUITY 80%, WACC 11.04% |
[
{
"content": "Determine whether the linear functional $J: L^1[0,1] \\rightarrow \\mathbb{R}$, defined by \\[ J(f) = \\int_0^1 (x^2 + 1)f(x)\\,dx \\] is bounded on the set $\\{f \\in L^1[0,1] : \\|f\\|_1 = 1, f(x) \\geq 0\\}$. 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... | 10.2 L |
[
{
"content": "Given two primes \\( p \\) and \\( q \\) such that \\( p = 2q + 1 \\) and \\( q \\equiv 3 \\pmod{5} \\), determine if 5 is a primitive root modulo \\( p \\).",
"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... | 1.665*10^5 Pa |
[
{
"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... | 9.95978% |
[
{
"content": "Find all positive integers $M$ such that if $M$ divides the sum of the divisors of $n$, then $M$ also divides $n-1$.",
"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... | 0.42 |
[
{
"content": "Evaluate the limit \\( \\lim_{a \\to 1} \\frac{1}{1-a} \\int _{a} ^{1} \\frac{\\ln(x)}{x-1}\\ dx \\) using L'Hopital's Rule and Leibniz Integral Rule.",
"role": "user"
}
] | 1 |
[
{
"content": "Assume that the time between emissions from a radioactive source is independent and exponentially distributed with rate one. Each emission is detected by a Geiger counter with probability \\( p \\). Compute the density of the distribution of the time between detections of particles and identify th... | p e^{-pt} |
[
{
"content": "Given that $a + b + c = 2$ where $0 < a, b, c < 1$, find the range of the expression \\[ \\frac{a}{1-a} \\cdot \\frac{b}{1-b} \\cdot \\frac{c}{1-c}. \\]",
"role": "user"
}
] | [8, \infty) |
[
{
"content": "The settlements $A$, $B$, and $C$ are connected by straight roads. The distance from settlement $A$ to the road connecting settlements $B$ and $C$ is 100 km. The sum of the distances from settlement $B$ to the road connecting settlements $A$ and $C$, and from settlement $C$ to the road connecting ... | \dfrac{30}{7} |
[
{
"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... | -1925 |
[
{
"content": "Evaluate the integral \\( \\int_\\gamma \\frac{dz}{z} \\) where \\( \\gamma = a \\cos(t) + i b \\sin(t) \\) for \\( t \\in [0, 2\\pi] \\), using the complex logarithm function as the primitive of \\( \\frac{dz}{z} \\).",
"role": "user"
}
] | 2\pi i |
[
{
"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... | 171658.144 N/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... | $2,428,320.20 |
[
{
"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... | 63.53 kg/m^3 |
[
{
"content": "Determine whether the following statement is true or false:\n\nLet \\( f, g: [a, b] \\to \\mathbb{R} \\) be continuous and either both monotone increasing or both monotone decreasing. If Chebyshev's integral inequality holds as equality, i.e.,\n\\[\n\\left(\\int_a^b f(x) \\, \\mathrm{d}x\\right)\\... | 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... | 60830 |
[
{
"content": "In the polynomial ring \\(\\mathbb{Z}_7[x]\\), find the number of monic divisors of degree three for the polynomial \\(3x^3+2x^2+5x+6\\).",
"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... | 5MR^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... | 1292.10 |
[
{
"content": "Evaluate the limit: \\[ \\lim _{x\\to 0}\\left(\\frac{\\left(1-\\cos^2\\left(2x\\right)\\right)}{4-4\\sin^2\\left(x\\right)}\\cdot \\left(x^{-2x}+x^{1-2x}\\right)^{\\frac{1}{x}}\\right) \\]",
"role": "user"
}
] | e |
[
{
"content": "Let $M$ be an $n$-cell, a metric space homeomorphic to the closed unit disk $D^n \\subset \\mathbb{R}^n$. Consider the group $\\text{Isom}(M)$ of bijective isometries from $M$ to itself. Determine whether there exists a point $p \\in M$ such that $\\varphi(p) = p$ for all $\\varphi \\in \\text{Iso... | 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... | $2.4 per unit |
[
{
"content": "Evaluate the integral \\( I = \\int_0^{\\pi} e^{\\cos\\theta}\\cos(\\sin\\theta)\\ d\\theta \\).",
"role": "user"
}
] | \pi |
[
{
"content": "Express \\( \\left(\\frac{i-\\sqrt{3}}{i-1}\\right)^{24} \\) in algebraic form.",
"role": "user"
}
] | 4096 |
[
{
"content": "Let $f: A \\to \\mathbb{R}$ be a differentiable function on an open convex set $A \\subset \\mathbb{R}^{n}$. If $\\| \\nabla f \\| \\leq M$ on $A$ for some $M > 0$, determine whether it is possible to have \\(|f(x) - f(y)| \\leq M \\| x - y \\|\\) for all $x, y \\in A$. Justify your answer.",
... | Yes |
[
{
"content": "Find the minimum value of the function \\( u = \\frac{4}{4 - x^2} + \\frac{9}{9 - y^2} \\) given that \\( x \\) and \\( y \\) are within the interval \\((-2, 2)\\) and \\( x y = -1 \\).",
"role": "user"
}
] | \dfrac{12}{5} |
[
{
"content": "Let \\( f \\) be a differentiable function such that both \\( f \\) and \\( f' \\) are in \\( L^1(\\mathbb{R}) \\). Prove that \\( \\int_{\\mathbb{R}} f'(x) \\, dx = 0 \\).",
"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... | $10,128,000 |
[
{
"content": "Let $r,$ $s,$ and $t$ be the roots of the equation $4x^3 - 59x^2 + 32x - 32 = 0.$ Find the value of $f(r) + f(s) + f(t)$, where $f(x) = 4x^3 - 59x^2$.",
"role": "user"
}
] | -376 |
[
{
"content": "Find all prime numbers $p$ such that $p$ divides $2^p + 1$. Provide your answer as a list of primes.",
"role": "user"
}
] | 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... | 20/3 ft/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... | 1.97 * 10^8 m/s |
[
{
"content": "Determine the value of \\( \\alpha \\) that results in the fastest convergence of the given iteration formula.",
"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... | 163.94 g/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... | 4.4e+05 V |
[
{
"content": "Determine the number of solutions to the equation $x^2 - x\\sin x - \\cos x = 0$ for $x \\in (-\\infty, +\\infty)$. Provide your answer as a single integer.",
"role": "user"
}
] | 2 |
[
{
"content": "Determine the expected profit from a game where a fair die with $n$ sides is rolled at each step, and you can choose to stop and keep the last roll's value as your profit or pay $1$ to continue playing. Find an asymptotic formula for the expectation as $n$ approaches infinity.",
"role": "user"... | n - \sqrt{2n} |
[
{
"content": "Evaluate the integral \\( \\int_{|z|=3} \\frac{z^9}{z^{10} - 1} \\, dz \\) using the residue theorem.",
"role": "user"
}
] | 2\pi i |
[
{
"content": "Calculate the value of \\( \\sup_{f \\in \\mathscr{H}} \\inf_{z \\in D} [f_x^2(z) + f_y^2(z)] \\), where \\( f: \\mathbb{R}^2 \\to \\mathbb{R} \\) is continuous, has partial derivatives in \\( D = \\{(x,y) : x^2 + y^2 \\leq 1\\} \\), and satisfies \\( \\sup_D |f| \\leq 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... | | k|
|eeefffk|
| ddd k|
| ccc|
| bbb |
|aaa | |
[
{
"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... | 9.62% |
[
{
"content": "Determine the point on the curve \\(x^2 + 2y^2 = 6\\) that is closest to the line \\(x + y - 7 = 0\\).",
"role": "user"
}
] | (2, 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... | 352 |
[
{
"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... | Current liabilities:
Accounts payable: $13,200
Current portion of long-term debt: $8,000
Salary payable: $6,500
Interest payable: $2,400
FICA taxes payable: $1,900
Total current liabilities: $32,000
Non-current liabilities:
Bond payable: $400,000
Premium on bonds payable: $12,000
Total non-current liabilities: $412,000... |
[
{
"content": "Determine whether the following statement is true or false: For any natural numbers \\(m\\) and \\(n\\), if \\((2n+1)^2 + 1\\) is divisible by \\(m(m+1)\\), then \\(m\\) and \\(m+1\\) must be consecutive.",
"role": "user"
}
] | True |
[
{
"content": "In a circle \\(\\omega\\), quadrilateral \\(ABCD\\) is inscribed such that the center of \\(\\omega\\) lies on side \\(AB\\). Another circle \\(\\omega_{1}\\) is externally tangent to \\(\\omega\\) at point \\(C\\). A third circle \\(\\omega_{2}\\) is tangent to both \\(\\omega\\) and \\(\\omega_{... | 90^\circ |
[
{
"content": "Determine the number of elements of order 6 in the group \\(D_{12} \\times Z_2\\).",
"role": "user"
}
] | 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... | -0.274 kJ |
[
{
"content": "Thor, Captain America, and Spiderman are to split 2001 candies among themselves. Thor must receive more candies than Captain America, who must receive more candies than Spiderman, and Spiderman must receive at least one candy. How many ways can this distribution be done?",
"role": "user"
}
] | 332667 |
[
{
"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... | 916.08 |
[
{
"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... | 3411.71 |
[
{
"content": "The function \\( y = f(x) \\) defined on \\( \\mathbb{R} \\) has the following properties:\n1. For any \\( x \\in \\mathbb{R} \\), \\( f(x^3) = f^3(x) \\).\n2. For any \\( x_1, x_2 \\in \\mathbb{R}, \\quad x_1 \\neq x_2 \\), \\( f(x_1) \\neq f(x_2) \\).\n\nDetermine the value of \\( f(0) + f(1) + ... | 0 |
[
{
"content": "Let $F(x)$ be a continuous function defined on the interval $[0, 1]$. If $F(x) = 0$ for all irrational numbers in this interval, determine whether $F(1/2) = 0$.",
"role": "user"
}
] | 0 |
[
{
"content": "If \\(\\sum_{n=1}^\\infty\\tan^{-1}\\left(\\frac{4}{n^2+n+16}\\right)=\\tan^{-1}\\left(\\frac{\\alpha}{10}\\right)\\), find the value of \\(\\alpha\\).",
"role": "user"
}
] | 40 |
[
{
"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... | 10.0 rad |
[
{
"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... | 54.6 |
[
{
"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... | 13.75% |
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