prompt list | ground_truth string |
|---|---|
[
{
"content": "Find the minimum value of the expression:\n\n$$\\frac{18}{a+b} + \\frac{12}{ab} + 8a + 5b$$\n\nwhere $a$ and $b$ are positive real numbers.",
"role": "user"
}
] | 30 |
[
{
"content": "Let \\( y(x) \\) be the unique solution of the differential equation \\[ \\frac{\\mathrm{d} y}{\\mathrm{~d} x}=\\log_{e} \\frac{y}{x}, \\] where \\( x > 0 \\) and \\( y > 0 \\), with the initial condition \\( y(1) = 2018 \\). Determine the number of positive real numbers \\( x \\) that satisfy the... | 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... | 7.2e5 lb-ft |
[
{
"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_{52}H_{82}N_{6}O_{14} |
[
{
"content": "Consider a smooth projective variety $M$ of dimension $n$ over the complex numbers, where the cotangent bundle $T^*M$ forms a completely integrable system with $n$ independent regular functions $f_1, \\ldots, f_n$ in involution. The moment map is given by $\\mu: T^*M \\to \\mathbb{C}^n$, defined b... | 2 |
[
{
"content": "A random variable $X$ has the cumulative distribution function $$F(x)=\\begin{cases} 0 & x<1\\\\\\frac{x^2-2x+2}{2}&x\\in[1,2)\\\\1&x\\geq2\\end{cases}.$$ Calculate the variance of $X$. \\( \\boxed{\\text{Variance}} \\)",
"role": "user"
}
] | \dfrac{5}{36} |
[
{
"content": "Suppose $f: [0,1] \\rightarrow \\mathbb{R}$ is a continuous, strictly increasing function with $f(0) = 0$, $f(1) = 1$, and $f'(x) > 0$. If $\\int_0^1 f(x) \\, dx = \\frac{1}{3}$, find the value of the integral $\\int_0^1 f^{-1}(y) \\, dy$.",
"role": "user"
}
] | \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... | investing cash outflows |
[
{
"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... | 38M^{-2}s^{-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... | 2.465e-13 |
[
{
"content": "Evaluate the limit: \\[\\lim\\limits_{n\\to\\infty}\\frac{\\zeta(3,n)}{\\frac{1}{n}+\\frac{1}{3n^3}}\\] where \\(\\zeta(3,n)\\) is the generalized Riemann zeta function.",
"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... | $123,000 |
[
{
"content": "Suppose we have complex numbers $a_1, \\ldots, a_n$ and $c_1, \\ldots, c_n$ on the unit circle, with $c_i \\neq c_j$ for all $i, j \\in \\{1, \\ldots, n\\}$. If the sequence $a_1c_1^k + \\cdots + a_nc_n^k$ converges to $0$ as $k \\to \\infty$, can we conclude that $a_1, \\ldots, a_n$ are all $0$? ... | Yes |
[
{
"content": "The perimeter of a rectangle is 24 inches. What is the number of square inches in the maximum possible area for this rectangle?",
"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... | $45.54 |
[
{
"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... | Static |
[
{
"content": "Let $F$ be a field and $g$ a polynomial of degree $n$. Determine the length of the $F$-module $F[X]/\\langle g \\rangle$. Express your answer as a single integer.",
"role": "user"
}
] | 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... | 5.2% |
[
{
"content": "Determine whether there exists a block of 1000 consecutive positive integers that contains exactly five prime numbers.",
"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... | 0.915 m |
[
{
"content": "Let $A \\in M_3(\\mathbb{R})$ be a matrix such that $AA^T = A^TA = I$ and $\\det(A) = 1$. Prove that the characteristic polynomial $p_A(x)$ of $A$ satisfies $p_A(1) = 0$. ",
"role": "user"
}
] | 0 |
[
{
"content": "Determine whether there exist functions $f(x, t)$, where $t$ is a parameter, such that $f(x, t)$ is absolutely continuous in $x$ for each fixed $t$, but there does not exist an integrable function $B(t)$ satisfying $\\sup_{x} |f(x, t)| < B(t)$ almost everywhere. Provide a justification for your an... | 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... | sp3d |
[
{
"content": "Evaluate the limit: \\[ \\lim_{(x,y)\\to(0,0)} \\frac {e^{x+y^2}-1-\\sin \\left ( x + \\frac{y^2}{2} \\right )}{x^2+y^2} \\]",
"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... | 10^43 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... | 11.1% |
[
{
"content": "Determine the number of solutions to the equation \\[{(\\sqrt{3}\\sin x+\\cos x)}^{\\sqrt{\\sqrt{3}\\sin{2x}-\\cos{2x}+2}}=4.\\]",
"role": "user"
}
] | 1 |
[
{
"content": "In triangle \\( ABC \\), \\( AB = 33 \\), \\( AC = 21 \\), and \\( BC = m \\), where \\( m \\) is a positive integer. If point \\( D \\) is on \\( AB \\) and point \\( E \\) is on \\( AC \\) such that \\( AD = DE = EC = n \\), where \\( n \\) is a positive integer, determine the value of \\( m \\)... | 30 |
[
{
"content": "An integer-valued function $f$ is called tenuous if $f(x) + f(y) > y^2$ for all positive integers $x$ and $y.$ Let $g$ be a tenuous function such that $g(1) + g(2) + \\dots + g(20)$ is as small as possible. Compute the minimum possible value for $g(14).$",
"role": "user"
}
] | 136 |
[
{
"content": "Given a sequence of $N$ probability distributions $P$ over an alphabet $A$, calculate the probability that a string $S$ of length $N$, where the $i^{th}$ character is drawn from the $i^{th}$ probability distribution, contains a specific character repeated $T$ times consecutively. For example, if $... | 0.5 |
[
{
"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... | 4.591 |
[
{
"content": "In quadrilateral \\(ABCD\\), the diagonals intersect at point \\(M\\) with an angle \\(\\alpha\\) between them. Let \\(O_{1}, O_{2}, O_{3}, O_{4}\\) be the centers of the circumcircles of triangles \\(ABM, BCM, CDM,\\) and \\(DAM\\), respectively. Find the ratio of the areas of quadrilateral \\(AB... | 2 \sin^2 \alpha |
[
{
"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... | 122.4 m |
[
{
"content": "Calculate the determinant of the following \\(2n \\times 2n\\) matrix \\(A\\):\n\\[\nA=\\left( \\begin{array}{ccccccc}\na & 0 & 0 & \\ldots & 0 & 0 & b \\\\\n0 & a & 0 & \\ldots & 0 & b & 0 \\\\\n0 & 0 & a & \\ldots & b & 0 & 0 \\\\\n\\vdots & \\vdots & \\vdots & \\ddots & \\vdots & \\vdots & \\vd... | (a^2 - b^2)^n |
[
{
"content": "Determine whether the contour integral \\( \\oint_C f(z)dz \\) can be zero if the function \\( f(z) \\) is not holomorphic at an interior point of the contour \\( C \\).",
"role": "user"
}
] | Yes |
[
{
"content": "Determine the value of \\( \\limsup_{n \\to \\infty}(n!|a_n|)^{1/n} \\) for an entire function \\( f(z) \\) that satisfies \\( |f(z)| \\le e^{(2\\pi M+\\epsilon)|z|} \\) for any \\( \\epsilon > 0 \\).",
"role": "user"
}
] | 2\pi M |
[
{
"content": "Determine whether the following statement is true: For distinct odd primes \\(p\\) and \\(q\\), \\((pq,(p-1)(q-1)) =1\\) if and only if \\((pq,\\operatorname{lcm}(p-1,q-1))=1\\).",
"role": "user"
}
] | True |
[
{
"content": "Simplify\n\\[\\frac{3 + 5i}{3 - 5i} + \\frac{3 - 5i}{3 + 5i}.\\]",
"role": "user"
}
] | -\frac{16}{17} |
[
{
"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... | 4.8*10^{-12} 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... | 2984268 N |
[
{
"content": "Is a characteristic 0 field that is complete with a discrete valuation always non-Archimedean?",
"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... | 1.2e+18 units |
[
{
"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... | E propto ([I_(anode)])/([I_(cathode)]) |
[
{
"content": "Evaluate the limit using the Squeeze Theorem: $$\\lim_{n\\to \\infty}\\dfrac{\\sum\\limits_{k=3}^n k\\sin\\dfrac{2\\pi}{k}}{n^2}$$",
"role": "user"
}
] | 0 |
[
{
"content": "Use Rouche's Theorem to find the number of zeros of the function \\( h(z) = z^5 + \\cos(z) \\) inside the circle \\( |z| = 2 \\).",
"role": "user"
}
] | 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... | -5.14 N |
[
{
"content": "Simplify the expression: \\[ \\sqrt[3]{a+\\frac{a+8}{3}\\sqrt{\\frac{a-1}{3}}}+\\sqrt[3]{a-\\frac{a+8}{3}\\sqrt{\\frac{a-1}{3}}} \\]",
"role": "user"
}
] | 2 |
[
{
"content": "Differentiate the function \\( f(x) = x^T A x \\) with respect to \\( x \\), where \\( A \\) is a symmetric matrix. Express the result in terms of \\( x \\) and \\( A \\).",
"role": "user"
}
] | 2Ax |
[
{
"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... | 0.033 V |
[
{
"content": "In a complete graph with 5 vertices, labeled \\( \\{1, 2, 3, 4, 5\\} \\), how many Hamiltonian cycles include both the edges \\( \\{1, 2\\} \\) and \\( \\{3, 4\\} \\)? Assume that a Hamiltonian cycle is defined solely by the collection of edges it contains, without regard to orientation or startin... | 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... | ln(Q) = \beta_0 + \beta_1ln(Y) + \beta_2 ln(N) + \epsilon |
[
{
"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... | $18.96 |
[
{
"content": "Given a martingale $M_t$ with $M_0=0$ and $E[M_t^2]<\\infty$, where the quadratic variation of $M_t$ is $[M]_t = \\ln(1+t)$, calculate $\\limsup_{t\\to\\infty} \\frac{M_t}{\\sqrt{t}}$. Provide your answer as a single value.",
"role": "user"
}
] | 0 |
[
{
"content": "Let $T$ be a linear transformation on a vector space with an inner product. If $T$ is diagonalizable and $W$ is an invariant subspace under $T$, is the restriction of $T$ to $W$ diagonalizable?",
"role": "user"
}
] | Yes |
[
{
"content": "Evaluate \\( \\lim_{n \\to \\infty} \\int_0^n \\frac{dx}{1 + n^2 \\cos^2 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... | 0.39 |
[
{
"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... | 6.4 N |
[
{
"content": "Consider a real-valued function $g$ that is integrable on the interval $[a, b]$. If $g$ is non-zero on a subset of $[a, b]$ with positive measure, does it follow that \\( \\int_a^b |g(x)| \\, dx > 0 \\)? Answer 'yes' or 'no' and justify 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... | -701.44 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^n |
[
{
"content": "Determine whether the inequality \\( \\prod\\limits_{i=1}^n\\left(3 + \\dfrac{1}{3i}\\right) < \\left(3 + \\dfrac{1}{n}\\right)^n \\) holds for all positive integers \\( n \\).",
"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... | 2500 W |
[
{
"content": "Evaluate the integral \\( \\int{4x^2+y^2} \\, dA \\) using the change of variables \\( y+2x=u, \\; y-2x=v \\) with the limits \\( 0<u<2, \\; -2<v<0 \\) and the Jacobian \\( \\frac{1}{4} \\).",
"role": "user"
}
] | \dfrac{4}{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... | -4.07e5 m/s^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... | $3.75M |
[
{
"content": "For how many different digits $n$ is the three-digit number $14n$ divisible by $n$?\n\nNote: $14n$ refers to a three-digit number with the unit digit of $n,$ not the product of $14$ and $n.$",
"role": "user"
}
] | 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... | 157 cm |
[
{
"content": "Is it possible for a matrix $A$ with eigenvalue $\\lambda$ that for some positive integer $n$, the inequality \\( \\text{dim}(N((A-\\lambda I)^{n+1})) - \\text{dim}(N((A-\\lambda I)^{n})) > 1 \\) holds? Justify your answer.",
"role": "user"
}
] | Yes |
[
{
"content": "Expand the following product: $\\frac{2}{5}\\left(\\frac{5}{x} + 10x^2\\right)$.",
"role": "user"
}
] | \frac{2}{x} + 4x^2 |
[
{
"content": "Is it true that two birational projective nonsingular curves have the same genus?",
"role": "user"
}
] | Yes |
[
{
"content": "Given the ciphertexts \\((c_1, c_2, c_3) = (13, 19, 3)\\) and the corresponding plaintexts \\((m_1, m_2, m_3) = (5, 10, 23)\\), determine the modulus \\( p \\) used in the affine cipher.",
"role": "user"
}
] | 79 |
[
{
"content": "Determine whether the series \\( \\sum_{n=0}^\\infty \\frac{\\sin(2n+1)}{2n+1} \\) converges, and if so, find its sum.",
"role": "user"
}
] | \dfrac{\pi}{4} |
[
{
"content": "Evaluate the limit \\( \\lim_{n\\rightarrow \\infty} \\int_{\\mathbb{R}^2} e^{-(x^2+y^2)^n} \\, dx \\, dy \\).",
"role": "user"
}
] | \pi |
[
{
"content": "Calculate the triple integral \\( \\iiint_{x^2+y^2+z^2\\leq z} \\sqrt{x^2+y^2+z^2} \\, dx \\, dy \\, dz \\) using spherical coordinates. Determine the correct limits for \\( \\rho \\), \\( \\phi \\), and \\( \\theta \\) to evaluate the integral.",
"role": "user"
}
] | \dfrac{\pi}{10} |
[
{
"content": "Evaluate the limit: \\( \\lim_{x\\to 0^{+}}e^{x^{x^x}\\ln x} \\).",
"role": "user"
}
] | 1 |
[
{
"content": "Is the topological space \\((\\mathbb{R}, \\tau)\\) normal for every topology \\(\\tau\\) on \\(\\mathbb{R}\\)?",
"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... | 3.24 * 10^-3 T.m^2 |
[
{
"content": "Evaluate the iterated integral: $$\\int_0^4\\int_x^4\\int_0^y\\frac{6}{1 + 48z - z^3}\\, dz\\, dy\\, dx$$.",
"role": "user"
}
] | \ln 129 |
[
{
"content": "Find the last four digits of \\(7^{65}\\).",
"role": "user"
}
] | 8807 |
[
{
"content": "Find all polynomials \\( Q(x) \\) with real coefficients such that \\( |Q(x)| \\leq \\sum_{r=0}^{\\infty} |\\cos (x)|^{r} \\) for all \\( x \\in \\mathbb{R} \\).",
"role": "user"
}
] | Q(x) = c |
[
{
"content": "If $X$ is a dense subspace of a complete metric space $Y$, is $Y$ necessarily the completion of $X$? Provide a justification for your answer.",
"role": "user"
}
] | Yes |
[
{
"content": "Suppose we have two positive integers $x$ and $y$ such that $$x \\bmod p \\leqslant y \\bmod p$$ for every prime number $p$. Does it follow that $x = y$? Answer yes or no.",
"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... | $1,660.55 |
[
{
"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... | 3.25 |
[
{
"content": "Given the equation \\( \\frac{3-\\tan^2\\frac{\\pi}{7}}{1-\\tan^2\\frac{\\pi}{7}}=\\alpha \\cos\\frac{\\pi}{7} \\), where \\( \\alpha \\) is a natural number, find the value of \\( \\alpha \\).",
"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... | 3.51% |
[
{
"content": "Evaluate the contour integral \\(\\int_{\\gamma}\\frac{z^3-2}{z(4z^2+9)}\\) where \\(\\gamma\\) is the negatively oriented circular contour of radius \\(\\frac{1}{2}\\) about the point \\(-1\\).",
"role": "user"
}
] | 0 |
[
{
"content": "Let $X = Y = \\Bbb{N}$, where $\\Bbb{N}$ is the set of natural numbers. Define $f: X \\to Y$ by $f(x) = 2x$ and define $g: Y \\to X$ by $g(y) = 3y$. Let $W = \\bigcup_{n=0}^\\infty (g(fg))^n(Y - D)$, where $D = f(X)$. $W$ is a subset of $X$. Find an element of $X$ that is not in $W$.",
"role":... | 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... | 0.035 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... | 705.95 kg |
[
{
"content": "Evaluate the Lebesgue integral of the function \\( f(x) = \\begin{cases} 1 & x \\in C \\cap \\mathbb{Q} \\\\\\ 2 & x \\in C \\cap (\\mathbb{R} \\setminus \\mathbb{Q}) \\\\\\ 3 & x \\in [0, 1] \\setminus C \\end{cases} \\), where \\( C \\) is the Cantor ternary set.",
"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... | 1.99 L |
[
{
"content": "Use the Laplace transform to solve the differential equation \\(xy''+(1-x)y'+my=0\\). Choose the correct solution from the following options:\n\n(a) \\(y=\\frac{e^t}{k!} \\frac{d^k}{dt^k}(t^{-k}e^{-t})\\)\n\n(b) \\(y=\\frac{e^t}{k} \\frac{d^k}{dt^k}(t^k e^{-t})\\)\n\n(c) \\(y=\\frac{e^t}{k!} \\fra... | C |
[
{
"content": "Given a distribution $P$ and a set of distributions $Q$ such that each $Q$ is at most $d$ distance from $P$ in terms of Total Variation Distance, determine the maximum distance between $P$ and the convex combination $S$ of all such distributions $Q$. Assume the Total Variation Distance is used as ... | 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... | HClO2 |
[
{
"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... | 684 days |
[
{
"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... | 10.87% |
[
{
"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... | Parilo Company
Journal Entries
Date|Particulars|Debit ($)|Credit ($)
---|---|---|---
May 1, 2016|6% bonds|158,400|
|Cash||158,400
Nov. 1, 2016|Cash|4,752|
|Interest on bonds||4,752
Nov. 1, 2016|Cash|45,030|
|Loss on sale of bonds|2,370|
|6% bonds||47,400
Dec. 31, 2016|Accrued interest on bonds|1,110|
|Interest on bo... |
[
{
"content": "Determine whether there exists a differentiable function \\( f : \\mathbb{R} \\to \\mathbb{R} \\) such that \\( |f(x) - f(y)| < 1 \\) for all \\( x, y \\in \\mathbb{R} \\), but \\( |f'(x)| \\) is not necessarily less than or equal to 1 for all \\( x \\in \\mathbb{R} \\).",
"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... | 0.3827 |
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