prompt list | ground_truth string |
|---|---|
[
{
"content": "Find the 6th derivative of the function \\( f(x)=\\frac{\\cos(5x^2)-1}{x^2} \\) evaluated at \\( x=0 \\). Use the Maclaurin series for \\( \\cos(5x^2) \\) to assist in your calculation.",
"role": "user"
}
] | 18750 |
[
{
"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... | 0.993 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... | 0.17 m/s |
[
{
"content": "Determine the norm of the operator $A$ in the space $\\ell^1$, where $A$ is defined by \\[ A(x_n)_n = \\left(\\sum_{k=0}^\\infty \\frac{a^k}{k!} x_{n+k} \\right)_n \\] for some constant $a > 0$. The norm of a sequence $(x_n)_n$ in $\\ell^1$ is given by \\[ \\|(x_n)_n\\| = \\sum_{n=1}^\\infty |x_n|... | e^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... | Amount invested in Stock C = $336,046.51
Amount invested in risk free asset = $128,953.49 |
[
{
"content": "Calculate the probability \\( P(Z > X + Y) \\) where \\( X, Y, Z \\sim U(0,1) \\) are independent random variables.",
"role": "user"
}
] | \dfrac{1}{6} |
[
{
"content": "Consider the operator \\( T: (C[-1, 1], \\|\\cdot\\|_\\infty) \\rightarrow \\mathbb{R} \\) defined by \\( Tf = \\int_{-1}^0 f(t)\\, dt - \\int_{0}^1 f(t)\\, dt \\). Prove that the norm of this operator is \\( \\|T\\| = 2 \\).",
"role": "user"
}
] | 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... | 10.86% |
[
{
"content": "Given the polynomial equation $x^4 - 2x^3 + 3x^2 - 4x + 2 = 0$ with distinct roots $a$, $b$, $c$, and $d$, find the value of $a^4 + b^4 + c^4 + d^4$. Express your answer as a single number.",
"role": "user"
}
] | 10 |
[
{
"content": "Evaluate the Fourier series \\(2 + 2\\sum_{k=1}^{\\infty} (-1)^k\\cos(kt)\\cdot\\frac{\\sin(2k)}{k}\\) at \\(t = \\pi-2\\).",
"role": "user"
}
] | \dfrac{\pi}{2} |
[
{
"content": "Suppose that $x$ is an integer that satisfies the following congruences: \\begin{align*}\n3+x &\\equiv 2^2 \\pmod{3^3} \\\\\n5+x &\\equiv 3^2 \\pmod{5^3} \\\\\n7+x &\\equiv 5^2 \\pmod{7^3}\n\\end{align*}What is the remainder when $x$ is divided by $105$?",
"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... | E = - \frac{4kqax}{{(a^2 - x^2)}^2} |
[
{
"content": "Let $A \\in M_{7}(\\mathbb{R})$ be a matrix that satisfies the polynomial $x(x-3)(x+5)$. Given that $\\operatorname{tr}(A) = -1$, determine the possible values of $\\operatorname{rank}(A)$. \\( \\boxed{} \\)",
"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... | 7.58 m/s |
[
{
"content": "Evaluate the limit \\( \\lim_{R\\to\\infty} \\int_{C_R} \\frac{e^{-iz}}{z^2} dz \\), where \\( C_R \\) is the semi-circle of radius \\( R \\) in the lower half-plane, centered at the origin and oriented clockwise, using a direct approach without Jordan's Lemma.",
"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... | $E=\pm V$ |
[
{
"content": "In the polynomial ring \\(\\mathbb{Z}_5[x]\\), determine all monic divisors of degree two for the polynomial \\(2x^3 + 2x^2 + 2x + 4\\).",
"role": "user"
}
] | x^2 + 2x + 3 |
[
{
"content": "Calculate \\((68! + 68^{86}) \\mod 75\\).",
"role": "user"
}
] | 49 |
[
{
"content": "Evaluate the integral \\( \\int_{[0,1]^n} \\mathbb{1}_{y_1 + y_2 + \\cdots + y_n \\leq 1} \\, dy_1 \\, dy_2 \\, \\cdots \\, dy_n \\) where the function is defined on the n-dimensional domain \\([0,1]^n\\).",
"role": "user"
}
] | \dfrac{1}{n!} |
[
{
"content": "Determine the value of \\( \\lim\\limits_{x\\to-\\infty} g(x) \\) for the function \\( g(x) = \\ln\\left(1 + \\frac{1}{x}\\right) - \\frac{1}{x+1} \\).",
"role": "user"
}
] | 0 |
[
{
"content": "Determine the values of $p$ for which the series \\( \\sum_{n\\geq 0}\\left(\\sqrt{n+1}-\\sqrt{n}\\right)^{2p} \\) converges.",
"role": "user"
}
] | p > 1 |
[
{
"content": "Is there a group in which two elements have finite orders, but their product has an infinite order?",
"role": "user"
}
] | Yes |
[
{
"content": "Calculate the expected value of the absolute sum of two independent variables $x$ and $y$, each uniformly distributed between -1 and 1, i.e., $E(|x + y|)$.",
"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... | $4.61 per share |
[
{
"content": "Is it true that for the Lie algebra \\(\\mathfrak{gl}(n)\\), the trace of the commutator of any two elements is zero, i.e., \\(\\operatorname{Tr}([x, y]) = 0\\) for all \\(x, y \\in \\mathfrak{gl}(n)\\)?",
"role": "user"
}
] | True |
[
{
"content": "Evaluate the integral \\( \\int_C (z+\\bar{z})^3 \\, dz \\), where \\( C \\) is the unit circle in the complex plane.",
"role": "user"
}
] | 6\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... | 24.6Pa |
[
{
"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... | 0.358*10^-3 m |
[
{
"content": "Determine the limit of the sequence \\((x_n)_{n \\geq 0}\\) defined by the recurrence relations:\n\\[\\begin{cases}\nx_0 = 2017 \\\\\nx_{n+1} = x_n + e^{-2018x_n}\n\\end{cases}\\]\nfor every \\(n \\ge 0\\).",
"role": "user"
}
] | \infty |
[
{
"content": "Solve the differential equation for $y(x)$ given the boundary conditions:\n\n$$ y''-i(\\sin(x)y)'-i\\omega y-\\lvert y \\rvert^2y'=0 , \\quad y\\rvert_{x=\\pi}=0 \\quad y'\\rvert_{x=\\pi}=0 $$",
"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... | 11.43 cm or 38.56 cm |
[
{
"content": "Determine the maximum number of solutions that the equation \\(\\max \\{a_{1} x+b_{1}, \\ldots, a_{10} x+b_{10}\\} = 0\\) can have, given that \\(a_{1}, \\ldots, a_{10}, b_{1}, \\ldots, b_{10}\\) are real numbers and all \\(a_{i} \\neq 0\\).",
"role": "user"
}
] | 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... | $7100 |
[
{
"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... | 7.29e-10 |
[
{
"content": "Find the product of all solutions to the equation \\(x^{\\log_{10}x}=x(100+2^{\\sqrt{\\log_2(3)}}-3^{\\sqrt{\\log_3(2)}})\\).",
"role": "user"
}
] | 10 |
[
{
"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... | 9589 |
[
{
"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... | 8.301 |
[
{
"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... | 824094.95 V/m, downwards |
[
{
"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... | 2.52e-7 m |
[
{
"content": "Find the degree of the field extension \\(\\mathbb{Q}(\\sqrt[4]{11},\\sqrt[5]{11}):\\mathbb{Q}(\\sqrt[4]{11})\\).",
"role": "user"
}
] | 5 |
[
{
"content": "In triangle \\( ABC \\) with area \\( 7.8 \\), points \\( D \\) and \\( E \\) are on the extensions of \\( AC \\) and \\( AB \\) respectively in the same direction. Lines \\( BD \\) and \\( CE \\) intersect at point \\( P \\), and \\( BD = CE \\). If point \\( P \\) satisfies the equation \\( \\an... | AB = AC |
[
{
"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... | 3.97 L |
[
{
"content": "For a graph $G$ with $n \\geq 1$ vertices, determine the maximum number of vertices in its block-cutpoint graph $BC(G)$. Provide your answer as a single integer.",
"role": "user"
}
] | 2n - 3 |
[
{
"content": "Find the value of \\(x\\) such that \\(\\int_{0}^{x}\\{t\\}dt = \\int_{0}^{\\{x\\}}tdt\\), where \\(x > 0\\), \\(x \\notin \\mathbb{Z}\\), and \\(\\{x\\}\\) is the fractional part of \\(x\\).",
"role": "user"
}
] | (0,1) |
[
{
"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... | 1.343 atm |
[
{
"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... | 146.26 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... | {eq}h=\frac{v}{g}(v+gt\pm\sqrt(v^2 +2gvT){/eq} |
[
{
"content": "Suppose the random variable X has a moment generating function given by \\( M(t) = \\frac{e^{at}}{1-bt^2} \\) for \\(-1 < t < 1\\). Given that the mean and variance of X are 3 and 2, respectively, find the value of \\(a + b\\).",
"role": "user"
}
] | 4 |
[
{
"content": "Let $\\mathbb{F}$ be $\\mathbb{Z}_7$. Consider the matrix $A=\\begin{bmatrix} 2 & 5\\\\ 5 & 3 \\end{bmatrix} \\in M_{2\\times 2}(\\mathbb{F})$. Define the subspace $W=\\{B \\in M_{2\\times 2}(\\mathbb{F}) \\mid (AB)^t = AB\\}$. Find a basis and the dimension of the subspace $W$. \\(\\text{Note: } ... | 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... | 6.76 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... | 4.25 |
[
{
"content": "Determine whether the following statement is true or false: Let $f$ be a non-negative function continuous on $[0, \\infty)$ and differentiable on $(0, \\infty)$ such that $f(0)=0$ and $f'(x) \\le f(x)$ for all $x \\in (0, \\infty)$. Then $f \\equiv 0$. Provide a justification for your answer.",
... | True |
[
{
"content": "Determine the limit of the sequence \\( S_n = \\left(n\\prod_{k=2}^{n-1} k^{2^{n-k}}\\right)^{2^{-n}} \\) as \\( n \\to \\infty \\).",
"role": "user"
}
] | 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... | $73,000 |
[
{
"content": "Evaluate the limit \\( \\lim_{x \\to 0} [x - x^2\\ln(1+\\frac{1}{x})] \\) using the Taylor series expansion of the function \\( f(x) = x^2 \\ln(1+\\frac{1}{x}) \\).",
"role": "user"
}
] | 0 |
[
{
"content": "Determine the maximum possible value of \\(|a|+|b|+|c|\\) for a quadratic polynomial \\(ax^2+bx+c\\) with real coefficients that satisfies the inequality \\(|ax^2+bx+c| \\leq 2\\) for \\(0\\leq x\\leq 1\\).",
"role": "user"
}
] | 34 |
[
{
"content": "Given a transitive countable model $M$ of $ZFC + \\mathbb{V} = \\mathbb{L}$, suppose we add a single Cohen generic $G$ to obtain $M[G]$. If $A \\in M[G]$ is also Cohen generic over $\\mathbb{L}$ and $M[A] \\neq M[G]$, determine whether there exists a Cohen generic $G'$ over $M[A]$ such that $M[A][... | Yes |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | $13.10 |
[
{
"content": "The quadratic equation \\(x^2 - 3ax + b = 0\\) does not have distinct real roots. Find the least possible value of \\(\\frac{b}{a-2}\\), given that \\(a > 2\\).",
"role": "user"
}
] | 18 |
[
{
"content": "If $\\tau_{1}$ and $\\tau_{2}$ are two topologies on a set $\\Omega$ such that $\\tau_{1}$ is weaker than $\\tau_{2}$ (i.e. $\\tau_{1}\\subset\\tau_{2}$) and $\\tau_{1}$ is metrizable, is $\\tau_{2}$ also necessarily metrizable? Answer with 'Yes' or 'No'.",
"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... | Dec. 31, 2007: $70,000
Dec. 31, 2008: $84,000
Dec. 31, 2009: $60,448
Dec. 31, 2010: $66,667 |
[
{
"content": "Evaluate the sum: \\[ S_{2016} = \\sum_{k=1}^{2016}\\left(\\sum_{n=k}^{2016}\\frac{1}{n}\\right)^2 + \\sum_{k=1}^{2016}\\frac{1}{k} \\]",
"role": "user"
}
] | 4032 |
[
{
"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... | Nitrogen |
[
{
"content": "Find the value of $a + b$ if the equations $x^2 + y^2 - 12x - 6y - 4 = 0$ and $x^2 + y^2 - 4x - 12y - k = 0$ have simultaneous real solutions $(x, y)$ if and only if $a \\leq k \\leq b$.",
"role": "user"
}
] | 68 |
[
{
"content": "Determine whether two dense sets in a metric space can have an empty intersection, even if they are not both open.",
"role": "user"
}
] | Yes |
[
{
"content": "Several circles are drawn connected by segments. Kostya chooses a natural number \\( n \\) and places different natural numbers in the circles such that:\n\n1. If the numbers \\( a \\) and \\( b \\) are not connected by a segment, then \\( a + b \\) is coprime with \\( n \\).\n2. If they are conne... | 3 |
[
{
"content": "Determine whether there exists a continuous, strictly increasing function \\( f: [0, \\infty) \\to [0, \\infty) \\) with \\( f(0) = 0 \\) such that \\( \\tilde{d} = f \\circ d \\) is not a metric, where \\( (X, d) \\) is \\( \\mathbb{R} \\) with the standard metric.",
"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... | $3,200.00 |
[
{
"content": "Express the size $m$ of a plane graph in terms of its order $n$ and an exterior boundary $k$-cycle, given that all interior regions have a triangular boundary and $k \\geq 3$. Provide the expression for $m$.",
"role": "user"
}
] | 3n - k - 3 |
[
{
"content": "Evaluate the limit: \\[ \\lim_{n\\to\\infty}\\left(\\frac{n-1}{n+1}\\right)^n \\] and show that it equals \\( \\frac{1}{e^2} \\).",
"role": "user"
}
] | \dfrac{1}{e^2} |
[
{
"content": "In a geometric progression \\( \\{b_n\\} \\) with \\( b_n > 0 \\), the sum of the terms from \\( b_6 \\) to \\( b_{2018} \\) is 6, and the sum of these terms with alternating signs, \\( b_6 - b_7 + b_8 - \\ldots - b_{2017} + b_{2018} \\), is 3. Calculate the sum of the squares of these terms: \\( ... | 18 |
[
{
"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... | 8.37628866e-5 m |
[
{
"content": "Determine if the Riemann-Lebesgue Lemma can be applied to the integral \\( \\int_{-\\pi}^{\\pi}\\frac{\\sin(nt)\\cos^2(t/2)}{\\sin(t/2)}dt \\) to conclude that it converges to 0 as \\( n \\to \\infty \\).",
"role": "user"
}
] | 0 |
[
{
"content": "Given a finite poset \\((P, <)\\) with \\(n\\) elements chosen uniformly at random, determine a good upper bound on the expected height of \\((P, <)\\). The height of a poset is defined as the length of the longest maximal chain within it.",
"role": "user"
}
] | 3 |
[
{
"content": "In a group of 10 chickens, 9 are real and each weighs 2kg, while 1 is a false chicken that weighs either 1kg or 3kg, each with a probability of \\(\\frac{1}{2}\\). A machine randomly selects each chicken with a probability of \\(\\frac{1}{2}\\) for weighing, and after weighing, all chickens are re... | \dfrac{3}{5} |
[
{
"content": "Determine the range of the real number \\( a > 0 \\) such that the function \\( f(x) = \\sqrt{x^2 + 1} - ax \\) is monotonic on the interval \\((0, +\\infty)\\).",
"role": "user"
}
] | [1, +\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... | 33 days |
[
{
"content": "Evaluate the limit: $$\\lim_{n \\rightarrow \\infty}\\left[\\prod_{k=1}^{n}\\left(1+\\frac{(k+1)^{n}}{n^{n+1}}\\right)\\right]$$",
"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... | $346,500 |
[
{
"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... | 0.019 |
[
{
"content": "Determine the range of values for \\( m \\) such that the inequality \\(-3<\\frac{x^2+mx-2}{x^2-x+1}>2\\) holds true.",
"role": "user"
}
] | (-1, 2) |
[
{
"content": "Is the following statement true for a discrete random variable $X$ with $X \\ge 0$ and a new random variable $Y = X |_{X>0}$? The $n^{th}$ moment of $Y$ is given by:\n\\[E(Y^n) = \\frac{E(X^n)}{1-P(X=0)}\\]",
"role": "user"
}
] | True |
[
{
"content": "You have 4 unit vectors in 3D space, and you know all 6 angles between them. If you add another unit vector to this set, how many additional angles are needed to uniquely identify this new vector?",
"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... | theta = \tan^{-1} (4H/R) |
[
{
"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... | $959.04 |
[
{
"content": "Let $n$ be a positive integer. Jadzia writes all integers from $1$ to $2n-1$ on a board, coloring each integer either blue or red. A pair of numbers $i, j \\in \\{1, 2, 3, \\ldots, 2n-1\\}$, where $i \\leq j$, is called \\textit{good} if the number of blue numbers among $i, i+1, \\ldots, j$ is odd... | n^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... | $120,000 |
[
{
"content": "Determine the greatest negative value of \\( x - y \\) for all pairs \\((x, y)\\) that satisfy the equation:\n\\[\n(\\sin x + \\sin y)(\\cos x - \\cos y) = \\frac{1}{2} + \\sin(x - y) \\cos(x + y)\n\\]",
"role": "user"
}
] | -\dfrac{\pi}{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... | Pronghorn Company\nBalance Sheet\nAs of December 31, 2019\n\nAssets\nCurrent Assets:\nCash $2,400\nDebt investments (short-term) $3,900\nAccounts receivable $2,200\nInventory $1,700\nPrepaid insurance $720\nTotal Current Assets $10,920\n\nNon-Current Assets:\nStock investments (long-term) $300\nEquipment $11,900\nLess: Accumulated depreciation-equipment $5,800\nNet Equipment $6,100\nTotal Non-Current Assets $6,400\n\nTotal Assets $17,320\n\nLiabilities and Stockholders' Equity\nCurrent Liabilities:\nAccounts payable $1,800\nNotes payable (due in 2020) $400\nTotal Current Liabilities $2,200\n\nLong-term Liabilities:\nNotes payable (due after 2020) $500\nLong-term debt $1,000\nTotal Long-term Liabilities $1,500\n\nTotal Liabilities $3,700\n\nStockholders' Equity:\nCommon stock $9,620\nRetained earnings $4,000\nTotal Stockholders' Equity $13,620\n\nTotal Liabilities and Stockholders' Equity $17,320 |
[
{
"content": "Let $u: \\mathbb{R} \\rightarrow (-\\infty, +\\infty]$ be a convex function that admits a point of minimum. Define the mollified function:\n\n$$(\\varphi_\\epsilon * u)(x) = \\int_{\\mathbb{R}^n} \\varphi_\\epsilon(y) u(x-y) \\, dy,$$\n\nwhere $\\varphi_{\\epsilon}$ is the standard mollifier. Intr... | 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... | x = exp((U_bar - y)/2) |
[
{
"content": "Find the remainder when \\(15^{40}\\) is divided by 1309.",
"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... | 22.5 m |
[
{
"content": "In triangle $ABC,$ $M$ is the midpoint of $\\overline{BC},$ $AB = 12,$ and $AC = 16.$ Let $E$ be on $\\overline{AC},$ and $F$ be on $\\overline{AB},$ and let $G$ be the intersection of $\\overline{EF}$ and $\\overline{AM}.$ If $AE = 2AF,$ then find $\\frac{EG}{GF}.$\n\n[asy]\nunitsize(0.3 cm);\n... | \frac{3}{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... | C5H14N2 |
[
{
"content": "Determine the values of \\(\\alpha \\in \\mathbb{R}\\) for which the integral \\(\\int_{\\mathbb{R}^2} \\frac{\\sin(x^2+y^2)}{(x^2+y^2+1)^\\alpha} \\, dx\\,dy\\) converges.",
"role": "user"
}
] | \alpha > 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... | 10.1 |
[
{
"content": "Find a function $f \\in L^p(\\mathbb{R})$ such that for a given non-negative function $g \\in L^1(\\mathbb{R})$, the convolution $f * g = ||g||_1 \\cdot f$, where $*$ denotes convolution.",
"role": "user"
}
] | 0 |
[
{
"content": "Given the sequence \\(\\{a_{n}\\}\\) with the first term 2, and the condition \\(6 S_{n} = 3 a_{n+1} + 4^{n} - 1\\), determine the maximum value of \\(S_{n}\\).",
"role": "user"
}
] | 10 |
[
{
"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... | 21.9 m/s |
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