prompt list | ground_truth string |
|---|---|
[
{
"content": "Determine the correct form of a 0.99 confidence interval for \\( \\mu_i \\) given the model \\((x_1,y_1),\\ldots,(x_n,y_n)\\) with \\( n=23 \\), where \\( \\mu_i^* = \\frac{x_i+y_i}{2} \\) is the MLE estimator for \\( \\mu_i \\), and \\( \\sigma^* = \\frac{1}{4n}\\sum_{i=1}^{23}(x_i-y_i)^2 \\). Ch... | 2 |
[
{
"content": "In a random triangle where all pairs of angles have the same joint distribution, determine the correlation between two of the angles, assuming the variance of the angles is nonzero.",
"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... | 16.597 m |
[
{
"content": "Find the parameter $a$ such that the sequence defined by $x_0 = a$ and $x_{n+1} = x_n^2 - 4x_n + 6$ converges. What is the condition for convergence?",
"role": "user"
}
] | [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... | Event | Income Statement | Balance Sheet | Statement of Cash Flows
---|---|---|---
| Revenue - Expenses = Net Income | Assets = Liabilities + Stockholder's Equity | Cash |
| | Cash + Equipment - Accumulated Depreciation = Notes Payable + Interest Payable + Common Stock + Retained Earnings | |
1 | - = | $60,000 + - = + + $60,000 + | $60,000 FA |
2 | - = | -$40,000 + $40,000 - = + + + | -$40,000 IA|
3 | $72,000 - = $72,000 | $72,000 + - = + + + $72,000 | $72,000 OA |
4 | - $25,000 = -$25,000 | -$25,000 + - = + + + -$25,000 | -$25,000 OA |
5 | - $9,000= -$9,000 | + - $9,000 = + + + -$9,000 | NA |
Total | $72,000 - $34,000 = $38,000 | $67,000 + $40,000 - $9,000 = + + $60,000 + $38,000 | $67,000 NC | |
[
{
"content": "Suppose we have an orthonormal system $\\{ f_n \\}$ in $L^2(0,1)$ where $|f_n(x)| \\leq M$ almost everywhere for some $M > 0$. If the series $\\sum_{n = 1}^{\\infty} c_n f_n$ converges almost everywhere, does it follow that the sequence $\\{ c_n \\}$ must converge to zero? Answer yes or no.",
... | Yes |
[
{
"content": "Consider the curve \\(x^3+y^3=3axy\\) and the line \\(x+y+a=0\\). Using Bezout's theorem, determine the number of intersections between these curves and describe the nature of these intersections.",
"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... | $18,368.67 |
[
{
"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... | 20.00% |
[
{
"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... | 3.1 kN |
[
{
"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... | 2.88e-17 J, 180 eV |
[
{
"content": "Find the integer \\( n \\) such that \\( \\mathbb{Z}[i]/(-2+2i) \\cong \\mathbb{Z}/n\\mathbb{Z} \\).",
"role": "user"
}
] | 8 |
[
{
"content": "Determine the radius of convergence of the differential equation: $$(x^2-3)y''+6xy'+4y=0$$",
"role": "user"
}
] | \sqrt{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... | 3.53e8 molecules/cm^3 |
[
{
"content": "Consider a probability space $(\\Omega,\\mathcal{F},P)$ and a sequence of random vectors $(X_n)\\subseteq (\\mathbb{R}^k)^{\\Omega}$ that converges in probability to a vector $c\\in \\mathbb{R}^k$. Assume $c$ is an interior point of a compact subset $K$ of $\\mathbb{R}^k$. Given a sequence of meas... | 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... | 9.879e9 |
[
{
"content": "A particle starts at the origin $(0,0)$ on the Cartesian coordinate plane. Every second, it moves with equal probability to one of the eight nearest lattice points. A square is drawn with vertices at $(2, 2)$, $(-2, 2)$, $(-2, -2)$, and $(2, -2)$. The particle will eventually hit the square for th... | 39 |
[
{
"content": "Suppose $x_1, \\dots, x_n$ and $y_1, \\dots, y_n$ are independent random variables, each distributed as $N(0,1)$. Define $z_i = x_i y_i$ for each $i$. Are the random variables $z_1, \\dots, z_n$ independent from one another?",
"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... | Unassigned fund balance is $565,000 and budgetary fund balance is $45,000 |
[
{
"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... | $3,130.67 |
[
{
"content": "Determine the number of distinct real solutions to the equation \\( J(J(J(x))) = 0 \\), where the function \\( J(x) \\) is defined as follows:\n\\[ \nJ(x)=\\left\\{\\begin{array}{ll}\n4+x & \\text{ for } x \\leq -2, \\\\\n-x & \\text{ for }-2 < x \\leq 0, \\\\\nx & \\text{ for } x > 0.\n\\end{arra... | 4 |
[
{
"content": "Determine whether the differential equation $y' = t - y^2$ has solutions defined on some interval $(a, \\infty)$. Provide a justification for your answer.",
"role": "user"
}
] | Yes |
[
{
"content": "Evaluate the surface integral \\( \\int_{S}\\nabla\\times\\vec{F}\\cdot{\\rm d}\\vec{S} \\) where \\( \\vec{F}(x,y,z) = y^2\\vec{i} + 2xy\\vec{j} + xz^2\\vec{k} \\) and \\( S \\) is the surface of the paraboloid \\( z = x^2 + y^2 \\) bounded by the planes \\( x = 0, y = 0 \\), and \\( z = 1 \\) in... | \dfrac{2}{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... | 15 - 2Q |
[
{
"content": "Compute the covariance \\( \\text{Cov}(X, Y) \\) for the random variables \\( X \\) and \\( Y \\) with the joint probability density function given by:\n\\[\nf(x,y) = \\begin{cases}\n\\left(\\frac{2e^{-2x}}{x}\\right) & \\text{, $0 < y < x < ∞$} \\\\\n0 & \\text{, elsewhere}\n\\end{cases}\n\\]",
... | \dfrac{1}{8} |
[
{
"content": "Find the integer part of the expression \\(a + \\frac{9}{b}\\), where \\(a\\) and \\(b\\) are the integer and fractional parts, respectively, of the number \\(\\sqrt{76 - 42 \\sqrt{3}}\\).",
"role": "user"
}
] | 12 |
[
{
"content": "Construct a topological space $X$ such that the fundamental group $\\pi_1(X)$ is isomorphic to the group of integers under addition, and all higher homotopy groups of $X$ are trivial.",
"role": "user"
}
] | S^1 |
[
{
"content": "Calculate the Linear Minimum Mean Square Error (LMMSE) of $Y$ given $\\theta$, where $\\theta$ is uniformly distributed over $[0,\\pi]$ and $Y = \\cos(\\theta)$. Compute the covariance $\\text{Cov}(Y, \\theta)$ and verify the result. The expected answer is $-\\frac{2}{\\pi}$. Provide a detailed ca... | -\dfrac{2}{\pi} |
[
{
"content": "Determine the set of limit points of the set \\( A = \\left\\{ \\frac{\\sqrt{m} - \\sqrt{n}}{\\sqrt{m} + \\sqrt{n}} \\mid m, n \\in \\mathbb{N} \\right\\} \\).",
"role": "user"
}
] | [-1, 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... | 0.250 M |
[
{
"content": "Determine the rank of the linear operator on the vector space of real 3x3 matrices that maps a matrix X to AX - XA, where \\( A = \\begin{pmatrix} 1 & 0 & 0 \\\\ 0 & 1 & 0 \\\\ 0 & 0 & -1 \\end{pmatrix} \\).",
"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... | 1.26e-2 mol/L |
[
{
"content": "Let \\( \\{ X_\\alpha \\}_{\\alpha \\in \\Lambda} \\) be a collection of simply connected spaces. Prove or disprove that the fundamental group of the product space \\( \\prod_{\\alpha \\in \\Lambda} X_\\alpha \\) is trivial, i.e., \\( \\pi_1(\\prod_{\\alpha \\in \\Lambda} X_\\alpha) = 0 \\).",
... | \pi_1\left( \prod_{\alpha \in \Lambda} X_\alpha \right) = 0 |
[
{
"content": "Evaluate the integral \\( \\int_{-1}^{1} \\lvert f'(x) \\rvert \\, dx \\) where \\( f(x) = e^{x^2} \\).",
"role": "user"
}
] | 2(e - 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... | 4.765e-11 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... | $147,040.00 |
[
{
"content": "Are there any groups with exponential growth that have faithful Schreier graphs exhibiting polynomial growth?",
"role": "user"
}
] | Yes |
[
{
"content": "Consider the function \\( \\pi_{2n}(x)=\\text{card} \\{ p \\leq x : p, p+2n \\text{ are primes } \\} \\) for an arbitrary positive integer \\( n \\). Does it hold that \\( \\lim_{x \\to \\infty} \\frac{\\pi_{2n}(x)}{\\pi(x)} =0 \\)?",
"role": "user"
}
] | 0 |
[
{
"content": "Let \\( G \\) be the Galois group of a field with 27 elements over its subfield with 3 elements. Determine the number of orbits for the action of \\( G \\) on the field with 27 elements.",
"role": "user"
}
] | 11 |
[
{
"content": "Let $M$ be a connected $(d \\geq 2)$-dimensional smooth closed manifold. Does there exist a class $C^1$-diffeomorphism $\\phi$ from $M$ onto itself such that $(M,\\phi)$ is a topologically mixing discrete dynamical system?",
"role": "user"
}
] | Yes |
[
{
"content": "Determine the asymptotic growth rate of the function \\( f(x) = \\int_e^\\infty e^{-xt / \\log t} \\, dt \\) as \\( x \\to 0 \\). Specifically, find the value of \\( p \\) such that \\( f(x) \\approx \\frac{\\log^p(1/x)}{x} \\) for some \\( p > 0 \\).",
"role": "user"
}
] | 1 |
[
{
"content": "Calculate the limit: $$\\lim \\limits_{x \\to +\\infty}\\cos(x)\\left(\\ln\\left(\\sqrt{x-1}+2\\right)-\\ln\\left(\\sqrt{x+2}\\right)\\right)$$",
"role": "user"
}
] | 0 |
[
{
"content": "Find all functions \\( f: \\mathbb{N} \\to \\mathbb{N} \\) such that for all \\( m, n \\in \\mathbb{N} \\), the number \\( f^2(m) + f(n) \\) is a divisor of \\( (m^2 + n)^2 \\).",
"role": "user"
}
] | f(n) = n |
[
{
"content": "Find the limit: $$\\lim_{n\\to\\infty}\\left(\\frac{2}{1}\\cdot\\frac{4}{3}\\cdot\\dots\\frac{2n}{2n-1}\\right)^\\frac{1}{n}.$$",
"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... | $21,441.52 |
[
{
"content": "Evaluate the limit \\( \\lim_{n\\rightarrow\\infty}{\\int\\int}_{(0,\\infty)\\times (0,\\infty)} \\frac{\\sin^2(nxy)xy}{e^{(x^2+y^2)}}\\,dx\\,dy \\) using convergence theorems, such as Dominated Convergence.",
"role": "user"
}
] | \dfrac{1}{8} |
[
{
"content": "Evaluate the limit: \\[ \\lim_{x\\to 1} \\left( \\frac{1}{x-1} - \\frac{1}{\\ln(x)} \\right) \\] without using L'Hôpital's rule or Taylor series.",
"role": "user"
}
] | -\dfrac{1}{2} |
[
{
"content": "Compute the value of the integral \\( \\int_{0}^{2} \\sum_{n=1}^{\\infty} \\frac{g(5^{n}x)}{5^{n}} \\, dx \\), where \\( g(x) = \\min_{n \\in \\mathbb{Z}} |x - 2n| \\).",
"role": "user"
}
] | \dfrac{1}{4} |
[
{
"content": "Determine if the sequence of functions \\( f_n(x) = \\frac{x^n}{1-x} \\) converges uniformly on the interval \\((0, 0.5)\\).",
"role": "user"
}
] | Yes |
[
{
"content": "Evaluate the limit: $$ \\lim_{x \\rightarrow 0} \\frac{\\ln \\left( \\frac{\\sin x \\cdot e^{\\frac{x}{x+1}} - x}{x \\cdot \\sin x} \\right)}{\\arctan x} $$",
"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... | 3.75 |
[
{
"content": "Evaluate the integral \\( \\int_0^{2\\pi} \\frac{dx}{\\sin^6x+\\cos^6x} \\).",
"role": "user"
}
] | 4\pi |
[
{
"content": "Given thirty sets \\( A_1, A_2, \\ldots, A_{30} \\), each containing five elements, and \\( n \\) sets \\( B_1, B_2, \\ldots, B_n \\), each containing three elements, such that \\( \\bigcup_{i=1}^{30} A_i = \\bigcup_{j=1}^{n} B_j = S \\). Every element in \\( S \\) belongs to exactly 10 of the \\(... | 45 |
[
{
"content": "Solve the differential equation \\( \\frac{\\mathrm{d}^2 x}{\\mathrm{d}t^2} + \\left(\\frac{\\mathrm{d}x}{\\mathrm{d}t}\\right)^2 = 0 \\) with the initial conditions \\( x(0) = 0 \\) and \\( \\frac{\\mathrm{d}x}{\\mathrm{d}t}(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... | 0.9509 |
[
{
"content": "Evaluate the limit \\( \\lim_{x\\to\\infty}\\left(\\frac{\\max\\{f(x),g(x)\\}}{\\min\\{f^4(x),g^4(x)\\}}\\right) \\) given that \\( \\lim_{x\\to\\infty}f(x)=\\lim_{x\\to\\infty}g(x)=\\infty \\).",
"role": "user"
}
] | 0 |
[
{
"content": "Let \\( f(x) \\) be a continuous function on \\([0, 1]\\) satisfying the following conditions:\n\n1. \\( f(1) = 0 \\)\n2. \\( \\int_0^1 [f'(x)]^2 \\, \\mathrm{d}x = 7 \\)\n3. \\( \\int_0^{1} x^2f(x) \\, \\mathrm{d}x = \\dfrac{1}{3} \\)\n\nFind the value of \\( \\int_0^{1} f(x) \\, \\mathrm{d}x \\)... | \dfrac{7}{5} |
[
{
"content": "The American Mathematics College is holding its orientation for incoming freshmen. The incoming freshman class contains fewer than $500$ people. When the freshmen are told to line up in columns of $23$, $22$ people are in the last column. When the freshmen are told to line up in columns of $21$, $... | 413 |
[
{
"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... | 26.0 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... | 6.43e-3% |
[
{
"content": "The area of a square equals the square of a length of the side of the square. The perimeter of a square equals the sum of the lengths of all four sides. The sum of the areas of two squares is 65, while the difference in their areas is 33. Find the sum of their perimeters.",
"role": "user"
}... | 44 |
[
{
"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... | $12.1875 per hour |
[
{
"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... | 2.91 |
[
{
"content": "Find the radius of convergence of the series \\( \\sum_{n=1}^{\\infty}\\frac{(-1)^n}{n}z^{n(n+1)} \\).",
"role": "user"
}
] | 1 |
[
{
"content": "Evaluate the integral: $$\\int_{-\\pi/2}^{\\pi/2} \\frac{\\sin^{2014}x}{\\sin^{2014}x+\\cos^{2014}x} \\, dx$$",
"role": "user"
}
] | \dfrac{\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... | Iodine |
[
{
"content": "Evaluate the integral \\( \\int_0^{2\\pi} \\ln(2 R \\sin(\\frac{\\theta}{2})) \\, d\\theta \\) using contour integration, where \\( R > 0 \\).",
"role": "user"
}
] | 2\pi \ln R |
[
{
"content": "Let \\(\\mathbf{A}\\) be an \\(s \\times r\\) block matrix and \\(\\mathbf{B}\\) be an \\(r \\times q\\) block matrix over a ring, where each entry \\(A_{ij}\\) and \\(B_{ij}\\) is a sub-matrix. If the block matrix multiplication \\(\\sum_{k=1}^{r} \\left[\\begin{array}{ccc} A_{1k}B_{k1} & A_{1k}B... | 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... | 1462 kPa |
[
{
"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. Compare the after-tax cost of debt with the cost of other financing sources like equity. Borrowing is favored if the former is less than the latter.
2. If existing debt exists, increasing debt proportion can raise the cost of equity, potentially offsetting the lower cost of debt and not reducing the overall weighted average cost of capital.
3. Increasing debt can increase return on equity for shareholders.
4. Increased debt elevates financial leverage and risk due to interest payments. |
[
{
"content": "A person claims that 7 times their birth year, when divided by 13, leaves a remainder of 11, and 13 times their birth year, when divided by 11, leaves a remainder of 7. Determine how old this person will be in the year 1954.",
"role": "user"
}
] | 86 |
[
{
"content": "Is it always true that for every blocking flow $f$ in an acyclic directed graph $G=(V,E)$ with source $s \\in V$ and sink $t \\in V$, the value of $f$ satisfies $\\text{value}(f) \\geq \\frac{c}{n}$, where $c$ is the value of a maximum $s$-$t$-flow and $n=|V|$?",
"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... | 15.5 g/mol |
[
{
"content": "Evaluate the sum \\( S = \\cos 45^{\\circ} + i \\cos 135^{\\circ} + \\cdots + i^{n} \\cos (45 + 90n)^{\\circ} + \\cdots + i^{40} \\cos 3645^{\\circ} \\). Choose the correct answer from the following options:\n\n(A) \\(\\frac{\\sqrt{2}}{2}\\).\n(B) \\(-10 \\sqrt{2} i\\).\n(C) \\(\\frac{21 \\sqrt{2}... | 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... | 4 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... | 29 m/s |
[
{
"content": "Let $X$ be a compact metric space and $(\\Omega, F, P)$ a probability space. If $f: \\Omega \\rightarrow X$ is an $F$-measurable function, and $(\\Omega, F', P')$ is the completion of $(\\Omega, F, P)$, does there exist an $F'$-measurable function $g$ such that $g=f$ almost everywhere?",
"role... | 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... | $8.39 |
[
{
"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... | $2,171.52 |
[
{
"content": "Express as a common fraction: $\\cfrac{ \\frac{2}{5}+\\frac{3}{4} }{ \\frac{4}{9}+\\frac{1}{6}}$.",
"role": "user"
}
] | \frac{207}{110} |
[
{
"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... | 1.90e-6 |
[
{
"content": "Calculate the outward flux of the vector field \\( \\mathbf{v} = \\begin{pmatrix} x^2yz \\\\ xy^2z \\\\ z \\end{pmatrix} \\) through the surface \\( M \\) defined by \\( M = \\{ (x,y,z) \\in \\mathbb{R}^3 : x^2 + y^2 = z, \\; 0 \\leq z \\leq 1 \\} \\) using Gauss's theorem.",
"role": "user"
... | -\dfrac{\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... | Lmax = 22.6mH, Lmin = 3.69mH |
[
{
"content": "Determine the order of the pole at \\(z=\\infty\\) in the Laurent expansion of \\(\\frac{z^2}{(z^2-1)^{\\frac{1}{2}}}\\) in terms of \\(z\\).",
"role": "user"
}
] | 1 |
[
{
"content": "Determine whether the sequence of fractional parts \\( \\{\\log_{10}(n!)\\}_n \\) is dense in the interval \\([0,1]\\).",
"role": "user"
}
] | Yes |
[
{
"content": "Given a call graph $G = (V, E)$ where each vertex $v \\in V$ represents a phone number and each edge $\\{v, w\\} \\in E$ indicates a call between $v$ and $w$, a set $S \\subseteq V$ of authorized seeds with $|S| = 300$ is monitored. Calls can be investigated for vertices within a distance of 3 hop... | 297030300 |
[
{
"content": "Compute the integral \\( \\int_{-\\infty}^{+\\infty} 2^{-4^t}(1-2^{-4^t})\\,dt \\).",
"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... | 1.95e4 N/C |
[
{
"content": "A certain organism begins as three cells. Each cell splits and becomes two cells at the end of two days. At the end of another two days, every cell of the organism splits and becomes two cells. This process lasts for a total of 8 days, and no cells die during this time. How many cells are there at... | 48 |
[
{
"content": "Consider the parabola given by the equation \\( y^2 = 2px \\). At a point \\( A \\) on the parabola, a tangent line \\( L_1 \\) is drawn, intersecting the x-axis at point \\( B \\). From point \\( A \\), a line \\( L_2 \\) is drawn perpendicular to the x-axis, intersecting the parabola again at po... | y^2 = -2px |
[
{
"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... | $89,199.9 |
[
{
"content": "Evaluate the integral \\( \\int_{\\pi/4}^{\\pi/2}{(2\\csc(x))^{17}dx} \\) and determine which of the following expressions it is equal to:\n\n(a) \\( \\int_0^{\\ln(1+\\sqrt{2})}{2(e^u+e^{-u})^{16}du} \\)\n\n(b) \\( \\int_0^{\\ln(1+\\sqrt{2})}{2(e^u+e^{-u})^{17}du} \\)\n\n(c) \\( \\int_0^{\\ln(1+\\... | 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... | 14.61% |
[
{
"content": "Suppose $f$ is a continuous function on the boundary of a disc $D \\subset \\mathbb{C}$, and it satisfies the condition \\(\\int_{\\partial D} f(\\zeta) \\zeta^k d\\zeta = 0\\) for all non-negative integers \\(k\\). Determine if it is possible to extend $f$ to be a holomorphic function within $D$.... | 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... | 84.6 g |
[
{
"content": "For what value of \\( k > 1 \\) is the integral \\( \\int_k^{k^2} \\frac{1}{x} \\log\\frac{x-1}{32} \\, \\mathrm{d}x \\) minimal?",
"role": "user"
}
] | 3 |
[
{
"content": "Evaluate the limit: $$\\lim_{x\\to 14} \\left(\\left(x^2-30\\cdot x+225\\right)^\\frac{1}{x^2-29\\cdot x +210}\\right)$$",
"role": "user"
}
] | e^2 |
[
{
"content": "Let $X$ and $Y$ be independent random variables with the probability distribution function $P(n) = 3^{-n}$ for $n = 1, 2, 3, \\ldots$. Calculate $P(X \\geq 3Y)$. \\( \\boxed{?} \\)",
"role": "user"
}
] | \dfrac{3}{160} |
[
{
"content": "Evaluate \\(\\int\\int (x-y-z) \\, dS\\), where \\(S\\) is the boundary of the unit ball \\(B\\). Explain how symmetry helps in solving this problem.",
"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... | 5.616% |
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