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... | 71.1 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... | 692 |
[
{
"content": "Determine the whole number terms in the expansion of \\((\\sqrt[5]{11} + \\sqrt[11]{5})^{2015}\\).",
"role": "user"
}
] | 37 |
[
{
"content": "Evaluate the limit: \\[ \\lim_{n\\to\\infty} n^2 \\int_{0}^{1} \\frac{x\\sin{x}}{1+(nx)^3} \\, \\mathrm{d}x \\]",
"role": "user"
}
] | 0 |
[
{
"content": "Let $X$, $Y$, and $Z$ be independent normally distributed random variables with expected values $2$, $1$, and $0$, respectively, and each having a variance of $2$. Compute the probability $P(4X - 3Y > 5Z)$. Provide your answer to four decimal places.",
"role": "user"
}
] | 0.6915 |
[
{
"content": "Suppose $z$ is a complex number such that $z^2 = 24-32i$. Find $|z|$.",
"role": "user"
}
] | 2\sqrt{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... | 7.5uC |
[
{
"content": "Find the maximum three-digit positive integer \\( n \\) such that the sum of the first \\( n \\) positive integers is not a factor of the product of the first \\( n \\) positive integers.",
"role": "user"
}
] | 996 |
[
{
"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... | V(x) = \frac{\sigma}{2\epsilon_0} (\sqrt{x^2+R^2}-x) |
[
{
"content": "Calculate the sum \\( S \\) of the greatest integer values for the sequence:\n\\[\nS = \\left[\\frac{1}{1}\\right] + \\left[\\frac{2}{1}\\right] + \\left[\\frac{1}{2}\\right] + \\left[\\frac{2}{2}\\right] + \\left[\\frac{3}{2}\\right] + \\left[\\frac{4}{2}\\right] + \\left[\\frac{1}{3}\\right] + \... | 1078 |
[
{
"content": "Evaluate the limit \\( \\lim_{x\\rightarrow{\\infty}} \\frac{\\int_{0}^{1} (1+(xy)^{n})^{\\frac{1}{n}}dy}{x} \\) where \\( n\\geq 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... | 8.35% |
[
{
"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... | 0.174 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... | 1.88 |
[
{
"content": "A winter school hosted 40 girls, each having an even number of friends among the others. All the girls were initially paired such that each pair of roommates were friends. After a quarrel between two friends who were roommates, is it still possible to pair up all the girls again so that each pair ... | Yes |
[
{
"content": "Let $A$ be an $F$-algebra that is finite-dimensional over a field $F$. Is $A$ necessarily commutative?",
"role": "user"
}
] | No |
[
{
"content": "Consider the statement: Given a function $f: A \\rightarrow \\mathbb{R}$ such that \\( \\forall \\delta>0\\ (\\exists \\epsilon>0\\ (|x-y|<\\delta \\implies |f(x)-f(y)|<\\epsilon) ) \\). Does this statement hold for uniformly continuous functions defined on $A$? Provide a justification for your an... | Yes |
[
{
"content": "Determine the radius of convergence for the formal power series:\n\\[ f(x) = x\\sqrt{1} + x^2\\sqrt{2} + x^3\\sqrt{3} + \\cdots + x^n\\sqrt{n} + \\cdots \\]",
"role": "user"
}
] | 1 |
[
{
"content": "Find an irrational number $x$ such that $x^x$ is rational. Provide a specific example of such a number.",
"role": "user"
}
] | \sqrt{2}^{\sqrt{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... | 14.14% |
[
{
"content": "For a certain value of $k,$ the system\n\\begin{align*}\nx + ky + 3z &= 0, \\\\\n3x + ky - 2z &= 0, \\\\\n2x + 4y - 3z &= 0\n\\end{align*}has a solution where $x,$ $y,$ and $z$ are all nonzero. Find $\\frac{xz}{y^2}.$",
"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... | -2.821e5 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... | 25 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... | 96 ft/s |
[
{
"content": "Calculate the degree of the minimal polynomial over $L_2 = \\mathbb{Q}(\\sqrt[3]{2})$ with root $\\omega\\sqrt[3]{2}$, where $\\omega = e^\\frac{2\\pi i}{3}$. Determine the value of $[L_1L_2:L_2]$, where $L_1 = \\mathbb{Q}(\\omega\\sqrt[3]{2})$. Provide your answer as a single integer.",
"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... | 1.59 g |
[
{
"content": "You are at location \\((0,0)\\) and know the treasure is within 100 meters of you. Person A claims that they walked 108 meters to the treasure, with their distance calculated as \\(|x| + |y|\\). Person B claims they walked 105 meters to the treasure, with their distance calculated as \\(\\frac{|x|... | 4 |
[
{
"content": "Determine whether there exists a bijective differentiable function \\( f: \\mathbb{R^+} \\rightarrow \\mathbb{R^+} \\) whose derivative is not a continuous function.",
"role": "user"
}
] | Yes |
[
{
"content": "Determine whether any good tetrahedron can be placed inside any good parallelepiped.",
"role": "user"
}
] | No |
[
{
"content": "Find\n\\[\\sum_{n = 1}^\\infty \\frac{2^n}{1 + 2^n + 2^{n + 1} + 2^{2n + 1}}.\\]",
"role": "user"
}
] | \frac{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... | 29.2 |
[
{
"content": "Evaluate the integral \\( \\int_{-\\infty}^\\infty \\frac{\\sin(xt)}{1+t^2} \\, dt \\) using the residue theorem.",
"role": "user"
}
] | 0 |
[
{
"content": "Given that $x$ is real and $x^3+\\frac{1}{x^3}=52$, find $x+\\frac{1}{x}$.",
"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... | -3.5e-4 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... | 1013.4 J/kg K |
[
{
"content": "Evaluate the limit: \\[ \\lim_{n\\to\\infty}\\frac{(2n)!}{e^{n^{2}+2n}}. \\]",
"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... | 24.01 m |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | Stock X: $13,860, Stock Y: $8,140 |
[
{
"content": "Let \\( u(x,y) = x^3 + ax^2y + bxy^2 + 2y^3 \\) be a harmonic function, and \\( v(x,y) \\) be its harmonic conjugate. Given that \\( v(0,0) = 1 \\), find the value of \\(|a+b+v(1,1)|\\).",
"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... | $3,548.213 |
[
{
"content": "Find the minimum value of the expression\n\n$$\\left(a+\\frac{1}{a}\\right)\\left(a+\\frac{1}{b}\\right)+\\left(b+\\frac{1}{b}\\right)\\left(b+\\frac{1}{c}\\right)+\\left(c+\\frac{1}{c}\\right)\\left(c+\\frac{1}{a}\\right)$$\n\nsubject to the condition $a + b = c + 1$ and $a, b, c > 0$. ",
"ro... | 12 |
[
{
"content": "Suppose $\\langle z_n \\rangle_{n\\ge0}$ is a sequence of complex numbers such that $\\sum_{n=0}^\\infty z_n$ converges. Given that $f$ is an entire function such that $f(z_n)=n$, determine which of the following statements is true:\n\n(A) $f\\equiv 0$.\n\n(B) $f$ is unbounded.\n\n(C) No such $f$ ... | C |
[
{
"content": "Determine the supremum of the ratio $\\frac{m}{n}$, where $m$ is the sum of the divisors of a positive integer $n$. Provide your answer as a specific value or expression.",
"role": "user"
}
] | \infty |
[
{
"content": "Let \\( \\{a_n\\} \\) and \\( \\{b_n\\} \\) be two different arithmetic sequences such that \\((3n+1)a_n=(2n-1)b_n\\) for all positive integers \\(n\\). Define \\(A_n = a_1 + a_2 + \\ldots + a_n\\) and \\(B_n = b_1 + b_2 + \\ldots + b_n\\). Find the value of \\(\\frac{A_9}{B_6}\\).",
"role": "... | \dfrac{27}{23} |
[
{
"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... | pH=pK_a+log_10{([A^-])/([HA])} |
[
{
"content": "Evaluate the limit \\( L \\) using the ratio test for the series \\( \\sum_{n=1}^{\\infty}\\frac{(-1)^n}{(\\ln n)^n} \\). Determine \\( L \\) by calculating:\n\\[\nL = \\lim_{n\\to\\infty}\\left|\\frac{a_{n+1}}{a_n}\\right| = \\lim_{n\\to\\infty}\\left[\\frac{\\ln(n)}{\\ln(n+1)}\\right]^n\\frac{1}... | 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... | proscenium stage |
[
{
"content": "Let \\( P \\in \\mathbb{C}[X] \\) be a polynomial and \\( a \\in \\mathbb{C} \\) such that \\( P(a) \\neq 0 \\). Assume that \\( a \\) is a root of order \\( k \\) of \\( P - P(a) \\). Prove that for \\( \\rho > 0 \\) small enough, there exist \\( 2k \\) points on a circle centered at \\( a \\) wi... | 2k |
[
{
"content": "Find the maximum value of the function \\( F(x,y,z) = \\frac{x(1-x)y(1-y)z(1-z)}{1-(1-xy)z} \\) on the interval \\([0,1]\\times[0,1]\\times[0,1]\\).",
"role": "user"
}
] | 17 - 12\sqrt{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... | CuN12O17 |
[
{
"content": "Determine the values of the parameter \\(a\\) for which the equation \\(x^{4} - 40 x^{2} + 144 = a(x^{2} + 4x - 12)\\) has exactly three distinct solutions.",
"role": "user"
}
] | 48 |
[
{
"content": "At the beginning of my bike ride I feel good, so I can travel 20 miles per hour. Later, I get tired and travel only 12 miles per hour. If I travel a total of 122 miles in a total time of 8 hours, for how many hours did I feel good? Express your answer as a common fraction.",
"role": "... | \frac{13}{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... | 11.843 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... | 0.53 second |
[
{
"content": "Find the probability distribution of the sum \\( \\Phi = \\Phi_1 + \\Phi_2 \\), where \\( \\Phi_1 \\) and \\( \\Phi_2 \\) are independent circular uniform random variables on the interval \\([0, 2\\pi]\\).",
"role": "user"
}
] | \frac{1}{2\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... | 79,000 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... | Land 500
Cash 500 |
[
{
"content": "Determine the nature of the entire function $f$ given that \\( \\int_{|z|=1}\\frac{f(z)}{((k+1)z-1)^n}dz=0 \\) for any natural number $k$ and for all positive integers $n$. What can be concluded about $f$?",
"role": "user"
}
] | f(z) = 0 |
[
{
"content": "Determine the degree of the intermediate field $L$ over $\\mathbb{Q}$, where $L$ is an intermediate field of $\\mathbb{Q}(\\alpha^{16})$ such that $\\alpha^4 \\in L$, given that $\\alpha$ is a root of the polynomial $x^{16} - 3$. Provide your answer as an integer.",
"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... | 3.47e8 |
[
{
"content": "Show that the random variable \\( \\frac{N_n}{n \\ln n} \\) converges in probability to 1, where \\( N_n \\) is the number of cards you need to buy to collect a complete set of \\( n \\) baseball cards, with each card being randomly chosen one at a time.",
"role": "user"
}
] | 1 |
[
{
"content": "Determine whether the following statement is true or false: \"If $R$ is a field, then $R[x]$ is an Euclidean Domain (ED).\"",
"role": "user"
}
] | A |
[
{
"content": "Find a dominating function for the sequence of functions \\(f_n(y) = \\frac{n}{(1+y)^n(ny)^\\frac{1}{n}}\\) and use the Dominated Convergence Theorem to evaluate the limit:\n\\[\\lim_{n\\to\\infty}\\int_0^\\infty \\frac{n}{(1+y)^n(ny)^\\frac{1}{n}}dy\\]",
"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... | $30.63 |
[
{
"content": "Evaluate the limit: $$\\lim\\limits_{x\\to0}\\frac{\\log_{\\sin^2x}\\cos x}{\\log_{\\sin^2{\\frac x2}}\\cos\\frac x2}$$",
"role": "user"
}
] | 4 |
[
{
"content": "Solve the Diophantine equation \\(m^3 - 5m + 10 = 2^n\\) for all integer pairs \\((m, n)\\).",
"role": "user"
}
] | (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... | 4.42e-7 m |
[
{
"content": "Find all values of \\( x \\) such that among the four numbers \\( a = x - \\sqrt{2} \\), \\( b = x - \\frac{1}{x} \\), \\( c = x + \\frac{1}{x} \\), and \\( d = x^{2} + 2 \\sqrt{2} \\), exactly one is not an integer.",
"role": "user"
}
] | -1 + \sqrt{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... | 5.3 * 10^(-23) g |
[
{
"content": "Find the smallest known value of $C$ such that there are infinitely many prime pairs differing by $C$. Provide your answer as a single number.",
"role": "user"
}
] | 246 |
[
{
"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... | 5.237 m |
[
{
"content": "Calculate the number of unique sequences of 6 objects, each of which can be in one of 4 states, where sequences that are mirror images of each other are considered equivalent. For example, the sequences 111112 and 211111 are equivalent, as are 123123 and 321321. What is the total number of such un... | 2080 |
[
{
"content": "Let $f:[0,1]\\rightarrow [0,1]$ be a continuous function such that $f(0)=f(1)$. Define the set \\( A = \\{ (t,s) \\in [0,1] \\times [0,1] \\mid t \\neq s \\text{ and } f(t)=f(s) \\} \\). Determine the number of elements in the set $A$. \\( \\text{(Express your answer as a number or state if it is ... | \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... | 548.6 BTU/s |
[
{
"content": "A game of Plinko is played by dropping a ball at the top-middle of a set of pegs. Each time the ball hits a peg, it has a $\\frac{1}{2}$ probability of deflecting either to the left or to the right. What is the probability that the ball lands in the middle slot as shown in the diagram (the red lin... | \frac{35}{128} |
[
{
"content": "Compute the Lebesgue integral \\( \\int_{[1, \\infty)} \\frac{1}{x^2} \\, d\\mu \\).",
"role": "user"
}
] | 1 |
[
{
"content": "A 3x3 square table can have each of its cells painted in one of three colors: black, white, or red. How many distinct colorings of the table are there if rotations of the table are considered equivalent?",
"role": "user"
}
] | 4995 |
[
{
"content": "Evaluate the limit: $$ \\lim_{n\\to\\infty}\\left(\\frac{(n!)^3}{(3n)!}\\right)^{1/n} $$",
"role": "user"
}
] | \dfrac{1}{27} |
[
{
"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... | SO_3^{2 -} + 2Fe^{3 + } + 2OH^- \to SO_4^{2 -} + 2Fe^{2 + } + H_2O |
[
{
"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... | 10.83m |
[
{
"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-bromopent-3-en-1-ol |
[
{
"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... | 11.4% |
[
{
"content": "Evaluate the limit: $$\\lim_{x\\to-\\infty} \\left(\\frac{3x+5}{3x-1}\\right)^{3x-2}$$",
"role": "user"
}
] | e^6 |
[
{
"content": "Given three complex numbers $z$, $w$, and $u$ with $|z|=1$, $|w|=2$, and $|u|=3$, find the maximum value of $|z-u|$ subject to the condition $|z+w+u|=|z+w-2u|$. Express your answer as a single number.",
"role": "user"
}
] | \sqrt{13} |
[
{
"content": "Evaluate the integral \\( \\int_0^{2\\pi} \\frac{x \\cos x}{2 - \\cos^2 x} \\, dx \\).",
"role": "user"
}
] | 0 |
[
{
"content": "Determine the radius of convergence for the series \\( \\sum_{n=1}^\\infty \\left(1+\\frac{1}{2}+\\frac{1}{3}+\\cdots+\\frac{1}{n} \\right)x^n \\).",
"role": "user"
}
] | 1 |
[
{
"content": "Evaluate the limit: $$\\lim_{|(x,y,z)|\\to+\\infty}(x^4+y^2+z^2-x+3y-z).$$",
"role": "user"
}
] | +\infty |
[
{
"content": "Find the Taylor series expansion of \\( \\frac{x^3-2x}{(x+2)^2} \\) at \\( x=0 \\). Also, determine its radius of convergence.",
"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... | 75% |
[
{
"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... | 80t-16t^2 |
[
{
"content": "Find the integer $n$ such that $n$ divides $2^n + 2$ and $100 < n < 1000$. What is the value of $n$?",
"role": "user"
}
] | 946 |
[
{
"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... | $2,194,500 |
[
{
"content": "For all positive $x$, if a function $f(x)$ satisfies $f(x) \\geq e^x$, determine whether it must also hold that $f'(x) \\geq f(x)$. Justify your answer.",
"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... | Stockholders' Equity
Contributed Capital:
Common stock (13,000 shares * $1 par) $13,000
Additional paid-in capital on common stock $156,000
Preferred stock (11,500 shares * $10 par) $115,000
Additional paid-in capital on preferred stock $149,500
Total contributed capital $433,500
Retained earnings $31,000
Total stockholders' equity $464,500 |
[
{
"content": "Determine whether the sequence \\(a_N=\\int_1^N x^{-a}e^{ix} \\, dx\\) is bounded for a fixed constant \\(0<a\\le 1\\).",
"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... | 12 carats |
[
{
"content": "A biased coin has a probability of 0.70 of landing on heads. If the first flip results in tails, what is the expected number of additional flips required until the number of heads equals the number of tails?",
"role": "user"
}
] | \dfrac{5}{2} |
[
{
"content": "Let X be a real normed space with finitely many non-zero terms, equipped with the supremum norm. Consider the linear operator \\( T: X \\to X \\) defined by \\( T(x_1, x_2, x_3, \\ldots) = (x_1, \\frac{x_2}{4}, \\frac{x_3}{9}, \\ldots) \\). Determine which of the following statements is true:\n\n1... | 1 |
[
{
"content": "For an odd prime $p$, determine if it is possible to partition the set $\\{1,2,\\dots,p-1\\}$ into pairs $(a,b)$ such that the difference $a-b$ modulo $p$ is unique for each pair. Provide a justification for your answer.",
"role": "user"
}
] | Yes |
[
{
"content": "Compute $f''(0)$ given that $f'''(x)$ is continuous everywhere, and the limit \\(\\lim_{x \\to 0}(1+x+\\frac{f(x)}{x})^{1/x}=e^3\\) holds. Use Taylor's theorem and the given limit to derive the expression for $f''(0)$. Provide your answer in the form of a single number.",
"role": "user"
}
] | 4 |
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