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... | [H+] = 1.225e-9 M, [Na+] = 1.0e-2 M, [CN-] = 1.0e-2M |
[
{
"content": "Evaluate the limit \\( \\lim_{n \\to \\infty}\\left(1-\\dfrac{1}{\\eta^{x}} \\right)^n \\) for all real numbers \\(x\\), given that \\(\\eta > 0\\).",
"role": "user"
}
] | 0 |
[
{
"content": "Calculate the flow rate of the vector field \\( f(x,y,z) = \\left( \\frac{-x}{(x^2+y^2+z^2)^{\\frac{3}{2}}}, \\frac{-y}{(x^2+y^2+z^2)^{\\frac{3}{2}}}, \\frac{-z}{(x^2+y^2+z^2)^{\\frac{3}{2}}} \\right) \\) out of the surface \\( S \\), where \\( S = \\{(x,y,z) \\; | \\; x^2+y^2+z^2=1 \\} \\).",
... | -4\pi |
[
{
"content": "Given that $A$ and $P$ are $n \\times n$ matrices satisfying $A^2P = AP^2$, $A^3 = P^3$, and $A^2 + P^2$ is singular, find the value of $|A^4 + P^4|$. \\( \\text{(Express your answer as a single number.)} \\)",
"role": "user"
}
] | 0 |
[
{
"content": "Let \\( \\sigma \\) be an automorphism in \\( \\text{Aut}(\\mathbb{R}(t)/\\mathbb{R}) \\) such that \\( \\sigma(t) = -t \\). Determine the fixed field of \\( \\langle \\sigma \\rangle \\).",
"role": "user"
}
] | \mathbb{R}(t^2) |
[
{
"content": "Find all positive integer solutions \\((m, n, p)\\) to the Diophantine equation \\(5^m + n^2 = 3^p\\), given that \\((m, n, p) = (1, 2, 2)\\) is a solution and that 5 is a primitive root modulo \\(3^n\\) for all positive integers \\(n\\).",
"role": "user"
}
] | (1, 2, 2) |
[
{
"content": "Evaluate the limit: \\[ L = \\lim_{x \\to \\infty} x^2 \\times \\log \\left(x \\cot^{-1}x\\right) \\]",
"role": "user"
}
] | -\dfrac{1}{3} |
[
{
"content": "Evaluate the integral \\( \\int\\frac{2}{2+e^{ix}+\\frac{1}{e^{ix}}}dx \\) using the substitution \\( t = e^{ix} + 1 \\). Then, find the value of the integral when \\( x = \\frac{\\pi}{2} \\).",
"role": "user"
}
] | 1 |
[
{
"content": "Find the minimum value of the function \\( f(a, b, c) = \\frac{a}{\\sqrt{a^{2}+8bc}} + \\frac{b}{\\sqrt{b^{2}+8ac}} + \\frac{c}{\\sqrt{c^{2}+8ab}} \\) for all positive real numbers \\( a, b, c \\).",
"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... | 2.5 N |
[
{
"content": "Determine the number of integer solutions \\((a, n, p)\\) to the equation \\(a^p - a = n^p\\), where \\(p \\ge 0\\).",
"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... | \Delta m c^2=\frac{1}{2}m_0v^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... | The information search stage |
[
{
"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... | 45.12 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... | 0.5372849659 |
[
{
"content": "In a right triangle \\( \\triangle ABC \\) with \\( \\angle B = 90^\\circ \\), the median \\( AM \\) is drawn. If the measure of angle \\( \\angle AMB \\) is twice the measure of angle \\( \\angle A \\), calculate the ratio \\( \\frac{AM}{BC} \\).",
"role": "user"
}
] | \dfrac{3}{2} |
[
{
"content": "Let $G$ be a finite group and $x, y$ be distinct elements of $G$ with the same order. Is it possible to embed $G$ into a finite group $G_1$ such that $x$ and $y$ become conjugate in $G_1$?",
"role": "user"
}
] | Yes |
[
{
"content": "Determine the constant coefficient \\(m\\) such that the expression \\(a(b^2-c^2)+b(c^2-a^2)+c(a^2-b^2)\\) can be factorized as \\(m(a-b)(b-c)(c-a)\\).",
"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... | $980,910 |
[
{
"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... | 9.06 kg |
[
{
"content": "Given two vector spaces $X$ and $Y$, suppose there exists a surjective map $f: X \\rightarrow Y$. If $M$ is a subspace of the kernel of $f$ ($M \\subset \\ker f$) and the quotient space $X/M$ is isomorphic to $Y$ under the induced map from $f$, prove or disprove that $M$ is equal to the kernel of ... | M = \ker f |
[
{
"content": "Compute the depth of the polynomial ring $k[x,y]$ with respect to the ideal $(x,y^2)$, denoted as $t_{(x,y^2)}(k[x,y])$, where $k$ is a field. The depth is defined as the supremum of natural numbers $r$ for which there exists a regular sequence $(x_i)_{i=1}^r$ in $(x,y^2)$. A regular sequence elem... | 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 sigma bonds and 1 pi bond |
[
{
"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... | 0.25 rad/s |
[
{
"content": "Find the area bounded by the curve \\( y = f(x) \\) from \\( x = 1 \\) to \\( x = 3 \\), given that \\( f(x) \\) satisfies the equation \\( \\int_0^1 (x - f(x)) f(x) \\, dx = \\frac{1}{12} \\).",
"role": "user"
}
] | 2 |
[
{
"content": "Determine the radius of convergence for the power series \\(\\sum_{n = 1}^{\\infty} \\frac{\\sqrt{n!}}{n} x^n\\).",
"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... | 221.3 rpm |
[
{
"content": "Given the equations \\(3^{\\log_a x} + 3x^{\\log_a 3} = 2\\) and \\(x = y^{-\\log_z a}\\), find the value of \\(y + z\\).",
"role": "user"
}
] | 5 |
[
{
"content": "In a right triangle \\( \\triangle ABC \\) with hypotenuse \\( AB = 6 \\), a line \\( BX \\) is drawn from vertex \\( B \\) to leg \\( AC \\) such that \\( AX = 3 \\). Then, a line \\( XY \\) is drawn to the hypotenuse, forming a right triangle, with \\( XY = 2 \\). Find the length of \\( BC \\)."... | 4 |
[
{
"content": "Suppose I have 6 shirts, 4 ties, and 3 pairs of pants. If an outfit requires a shirt and pants, and can either have a tie or not have a tie, how many outfits can I make?",
"role": "user"
}
] | 90 |
[
{
"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... | NO_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... | 4.7e-7 m |
[
{
"content": "In \\(\\triangle ABC\\), \\(\\angle ABC = 90^{\\circ}\\), and \\(BC = 8\\). Points \\(D\\) and \\(E\\) lie on \\(AB\\) and \\(AC\\) respectively, such that \\(CD = DE\\) and \\(\\angle DCB = \\angle EDA\\). If the area of \\(\\triangle EDC\\) is 50, find the length of \\(AB\\).",
"role": "user... | 56 |
[
{
"content": "Determine the number of ways to distribute 32 indistinguishable objects into five distinct bins labeled B1, B2, B3, B4, and B5 such that each of B1, B2, B3, and B4 contains an odd number of objects, and B5 contains an even number of objects, specifically x objects, where x is congruent to 2 modulo... | 1005 |
[
{
"content": "Calculate the limit \\(\\lim_{x \\to 0} \\left(\\frac{1 + \\sin x}{1 - \\cos x}\\right)^{\\frac{1}{x}}\\).",
"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... | Fe |
[
{
"content": "Evaluate the limit: \\[ \\lim_{x\\to0}\\frac{\\arcsin x-\\sin x}{x^3} \\] without using series expansion or L'Hospital's rule.",
"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... | 0.044 mol N_2 |
[
{
"content": "Find the minimum value of \\(x^3+y^3+z^3-3xyz\\) given that \\(x^2+y^2+z^2=1\\) and \\(x, y, z\\) are real numbers.",
"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... | 2.7 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... | $157,600 |
[
{
"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... | $278.88 |
[
{
"content": "In a supermarket, waiting times at a cashier counter are exponentially distributed with a parameter of 0.1 minutes. If 100 customers visit the counter in a day, approximate the probability that at least 50 of them will wait for more than 10 minutes. Use the Central Limit Theorem for your approxima... | 0.0031 |
[
{
"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... | 3.2e+4 Pa |
[
{
"content": "How many positive two-digit integers have an odd number of positive factors?",
"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... | 136900 |
[
{
"content": "Evaluate the limit: \\[ \\lim_{n \\to \\infty} \\left(\\frac{n^3+n+4}{n^3+2n^2}\\right)^{n^2} \\]",
"role": "user"
}
] | 0 |
[
{
"content": "Find the minimum value of $x^2 + y^2 + z^2$ subject to the conditions $xyz = 1$ and $x, y, z > 0$.",
"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... | 76400 |
[
{
"content": "In a metric space $(X, d)$, let $B_d(x, r)$ be the open ball centered at $x$ with radius $r$. Given that $G_1$ is an open dense subset of $X$ and $B_d(x, r) \\cap G_1$ is non-empty, with $x_1 \\in B_d(x, r) \\cap G_1$, determine if there exists a positive radius $r_2 > 0$ such that $B_d(x_1, r_2) ... | 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... | 5.78 m/s |
[
{
"content": "Let \\( f : [1, ∞) \\to \\mathbb{R} \\) be a real-valued function such that \\( f(1) = 1 \\) and for all \\( x \\in [1, ∞) \\), \\( f'(x) = \\frac{1}{x^2 + f(x)^2} \\). Determine \\( \\lim_{x \\to \\infty} f(x) \\). Choose the correct option:\n\n(a) The limit exists and is equal to zero.\n(b) The ... | C |
[
{
"content": "Determine the number of elements of order \\( p \\) in the general linear group \\( \\text{GL}(2, \\mathbb{Z}_p) \\).",
"role": "user"
}
] | p^2 - 1 |
[
{
"content": "Does every open cover of \\(\\mathbb{R}\\) have a countable subcover?",
"role": "user"
}
] | Yes |
[
{
"content": "Let \\( F: \\mathbb{R}^3 \\rightarrow \\mathbb{R}^3 \\) be a linear transformation such that \\( F(0,0,1) = (2,-1,\\alpha) \\). The vectors \\( (1,0,-1) \\) and \\( (0,1,0) \\) are eigenvectors of \\( F \\) with associated eigenvalues \\( 3 \\) and \\( -9 \\) respectively. Determine the value of \... | -4 |
[
{
"content": "Calculate the sum \\( \\sum_{n=1}^{2015} \\phi(n) \\cdot \\left\\lfloor \\frac{2015}{n} \\right\\rfloor \\), where \\( \\phi(n) \\) is the Euler phi function and \\( \\lfloor x \\rfloor \\) is the floor function.",
"role": "user"
}
] | 2031120 |
[
{
"content": "Show that the function \\( f(x) = \\sum_{i=1}^n \\prod_{j \\ne i} \\frac{x-a_j}{a_i-a_j} = 1 \\) for \\( n > 1 \\) without simplifying the expression. Consider the following form:\n\\[\n\\begin{align}\n\\frac{(x − a_2)(x − a_3)\\cdots(x − a_n)}{(a_1 − a_2)(a_1 − a_3)\\cdots(a_1 − a_n)} &+ \\frac... | 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... | 136.8 V |
[
{
"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... | 865000 |
[
{
"content": "Let \\( S \\) be a non-empty set with a binary operation such that:\n1. The operation is associative.\n2. If \\( ab = ac \\), then \\( b = c \\).\n3. If \\( ba = ca \\), then \\( b = c \\).\n4. For each element in \\( S \\), the set of its powers is finite.\n\nIs \\( S \\) necessarily a group?",
... | 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... | 1580 g/L |
[
{
"content": "Find the maximum value of the function \\( f(x) = \\int^{x}_{0} \\sqrt{(x^2-x)^2+y^4}~dy \\) for \\( 0 \\leq x \\leq 1 \\).",
"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... | 7.86% |
[
{
"content": "What is the value of the Hausdorff measure \\(\\mathcal{H}^2\\) for the unit cube \\(A = \\{(x,y,z) \\in \\mathbb{R}^3: x \\in [0,1], y \\in [0,1], z \\in [0,1]\\}\\) in \\(\\mathbb{R}^3\\)? Justify your answer.",
"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... | 1.88e-12 T |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 105,767.58 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... | Period|Loan balance|Periodic Payment (EMI)|Interest|Principle Payment|Remaining Loan
0|527259.81|
1|527259.81|5665.96|4393.83|1272.13|525987.68
2|525987.68|5665.96|4383.23|1282.73|524704.95 |
[
{
"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... | A: 67,500, B: 52,500, C: 45,000, D: 15,000 |
[
{
"content": "Determine if the series expansion \\( \\frac{1}{1-\\frac{x^2}{n^2\\pi^2}} = 1 + \\left(\\frac{x^2}{n^2\\pi^2}\\right) + \\left(\\frac{x^2}{n^2\\pi^2}\\right)^2 + \\left(\\frac{x^2}{n^2\\pi^2}\\right)^3 + \\cdots \\) is valid for \\(|x| < \\pi\\). Justify your answer.",
"role": "user"
}
] | Yes |
[
{
"content": "How many subsets of the set $\\{1,2,3,4,5\\}$ contain the number 5?",
"role": "user"
}
] | 16 |
[
{
"content": "Calculate the expected value of the square of the distance between two randomly chosen points in a unit square. Let $D$ denote the distance between the points. Find $E[D^2]$. ",
"role": "user"
}
] | \dfrac{1}{3} |
[
{
"content": "Solve the recursive equation $2x^{2x^{2x^{..}}}=4$ for $x$.",
"role": "user"
}
] | \sqrt[4]{2} |
[
{
"content": "Given that $f(x) f(1/x) = f(x) + f(1/x)$ for a continuous function $f$, and $f(2) > 1$, find the value of $f(1)$. \n\nExpress your answer as a number in the form \\( \\boxed{\\text{number}} \\).",
"role": "user"
}
] | 2 |
[
{
"content": "Consider a Poisson process $N_t$ with $\\\\langle N \\\\rangle_t = N_t$, and a continuous process of finite variation $X_t$ with $\\\\langle X \\\\rangle_t = 0$. Determine if the quadratic covariation $\\\\langle X, N \\\\rangle_t = 0$ is true.",
"role": "user"
}
] | 0 |
[
{
"content": "In the tetrahedron \\( D-ABC \\), \\( DA \\) is perpendicular to the plane \\( ABC \\), and \\( \\triangle ABC \\) is an equilateral triangle with side length 2. Given that the tangent of the dihedral angle \\( A-BD-C \\) is 2, find the volume \\( V \\) of the tetrahedron \\( D-ABC \\).",
"rol... | 2 |
[
{
"content": "Given a set where \\(|I_{r}| \\leq O(r^{2})\\) and \\(|I_{r}| \\geq \\rho^{r}\\) with \\(\\rho = 1 + \\epsilon\\), prove that there exists a threshold \\(r^* = f(\\rho)\\) such that the inequality \\(\\rho^r \\leq O(r^2)\\) holds for all \\(r = 0, 1, 2, \\ldots, r^*-1\\), but not for any \\(r \\ge... | 1466 |
[
{
"content": "Determine the rank of the $n \\times n$ matrix $A$ with coefficients $a_{i,j} = \\frac{1}{i+j}$. Consider the context of linear independence and positive definiteness in your solution.",
"role": "user"
}
] | n |
[
{
"content": "Consider the equation \\(z^4 - 6z + 3 = 0\\). Determine how many of its complex solutions satisfy the condition \\(1 < |z| < 2\\).",
"role": "user"
}
] | 3 |
[
{
"content": "What is the area of the portion of the circle defined by $x^2-12x+y^2=28$ that lies above the $x$-axis and to the right of the line $y=6-x$?",
"role": "user"
}
] | 24 \pi |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 24.787 |
[
{
"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... | Common Stock: $250,000
Retained Earnings: $229,000
Accumulated OCI: $24,700
Total Stockholders' Equity: $503,700 |
[
{
"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... | 41.03 grams |
[
{
"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 m |
[
{
"content": "Find a non-zero function $f(x)$ such that $f(2x) = f'(x) \\cdot f''(x)$.",
"role": "user"
}
] | e^x |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | $72,890 |
[
{
"content": "Evaluate the limit: $$\\lim_{x\\to-\\infty}\\left|\\frac{x-3}{x+1}\\right|^{\\sqrt{x^2+2x}}$$",
"role": "user"
}
] | e^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... | $1,718,061.67 |
[
{
"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... | b, c, d, e |
[
{
"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... | 68.19 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... | the virus has to create a DNA intermediate, the viral genome needs to encode for RNA-dependent RNA polymerase, and the virus needs to have its own RNA-dependent RNA polymerase |
[
{
"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... | $87,100 |
[
{
"content": "Determine the box-counting dimension (Minkowski Dimension) of the set \\( S = \\left\\{ \\frac{1}{n^2} \\mid n \\in \\mathbb{Z}^+ \\right\\} \\).",
"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... | 25 mi/h |
[
{
"content": "Let $X_1, X_2, \\dots$ be independent Bernoulli random variables, where $X_i \\sim \\text{Binomial}(1, p_i)$. Define the sequence of random variables $$Y_n = \\frac{1}{n} \\sum_{i=1}^n (X_i - p_i).$$ Prove, using Chebyshev's inequality, that the sequence $Y_1, Y_2, \\dots$ converges stochastically... | 0 |
[
{
"content": "In triangle $ABC$, $AB = 5$, $BC = 4$, and $CA = 3$.\n\n[asy]\ndefaultpen(1);\n\npair C=(0,0), A = (0,3), B = (4,0);\ndraw(A--B--C--cycle);\n\nlabel(\"\\(A\\)\",A,N);\nlabel(\"\\(B\\)\",B,E);\nlabel(\"\\(C\\)\",C,SW);\n[/asy]\n\nPoint $P$ is randomly selected inside triangle $ABC$. What is the pr... | \frac{1}{2} |
[
{
"content": "Determine the number of distinct ways to color a 3x4 rectangle using exactly 6 of each of two colors, considering that two colorings are equivalent if they can be obtained from each other by permuting rows or by cyclically permuting columns.",
"role": "user"
}
] | 48 |
[
{
"content": "Evaluate the integral \\( \\int_{-\\infty}^{\\infty}\\frac{x^2 \\cos(x)}{(x^2+1)^2}dx \\) using the method of residues.",
"role": "user"
}
] | 0 |
[
{
"content": "Evaluate the limit \\( \\lim _{n\\rightarrow \\infty }\\dfrac {n^b}{2^{\\sqrt{\\ln(n)}}} \\) where \\( b \\) is a positive integer.",
"role": "user"
}
] | \infty |
[
{
"content": "Determine the order of the center of the group $G = \\{e, x, x^2, x^3, y, xy, x^2y, x^3y\\}$, where $O(x)=4$, $O(y)=2$, and $xy=yx^3$. Express your answer as an integer.",
"role": "user"
}
] | 2 |
[
{
"content": "Determine whether the following statement is true or false: In a Hausdorff topological space, the complement of a singleton set is dense if and only if the singleton is not an isolated point.",
"role": "user"
}
] | A |
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