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... | 3.53e-5 g/L |
[
{
"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... | 1:5 |
[
{
"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... | 168.84 |
[
{
"content": "Given the hazard function \\( \\phi(t) = 16t^3 \\), determine the survival function \\( \\mathcal{R}(t) \\).",
"role": "user"
}
] | e^{-4t^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... | 0.77% |
[
{
"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... | Year 1: Depreciation expense: $2,000, Accumulated Depreciation: $2,000, Book value: $3,000
Year 2: Depreciation expense: $1,200, Accumulated Depreciation: $3,200, Book value: $1,800
Year 3: Depreciation expense: $720, Accumulated Depreciation: $3,920, Book value: $1,080
Year 4: Depreciation expense: $432, Accumulated 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... | -0.156 |
[
{
"content": "Given that $a + b + c = 1$ with $a, b, c \\geq 0$, determine the maximum value of the expression \\[ \\frac{1}{a^2 - 4a + 9} + \\frac{1}{b^2 - 4b + 9} + \\frac{1}{c^2 - 4c + 9}. \\]",
"role": "user"
}
] | \dfrac{7}{18} |
[
{
"content": "Given a Lie algebra \\( \\mathfrak{g} \\) over \\( \\mathbb{R}^3 \\) spanned by the elements \\( X, Y, Z \\), with the relations \\([X,Y]=Y\\) and \\([X,Z]=Y+Z\\), determine the Lie bracket \\([X, [Z, Y]]\\).",
"role": "user"
}
] | 0 |
[
{
"content": "Evaluate the sum \\( \\frac{1}{g(1)} + \\frac{1}{g(3)} + \\frac{1}{g(5)} + \\ldots + \\frac{1}{g(999999)} \\), where \\( g(n) = (n^2 - 2n + 1)^{1/3} + (n^2 - 1)^{1/3} + (n^2 + 2n + 1)^{1/3} \\).",
"role": "user"
}
] | 50 |
[
{
"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... | 66 g |
[
{
"content": "Find \\[\\dfrac{3}{\\,\\,\\frac{6}{11}\\,\\,}.\\]",
"role": "user"
}
] | \frac{11}{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... | 0.198 mm |
[
{
"content": "Can a function composed of polynomial, rational, exponential, and logarithmic functions, excluding imaginary components, represent the entire sine function on a continuous interval greater than zero?",
"role": "user"
}
] | No |
[
{
"content": "Let $x, y, z > 0$ such that $x + y + z = 3$. Find the maximum value of the expression $S = \\sum_{cyc} \\frac{xy}{(x+2y)^2}$. Provide your answer as a single number.",
"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... | 1.565 H |
[
{
"content": "Consider a symmetric multisublinear continuous functional \\( S: V\\times\\cdots\\times V \\rightarrow \\mathbb{R} \\) that is positively homogeneous and subadditive in every component, satisfying certain additional assumptions. Let \\( T: U\\times\\cdots\\times U \\rightarrow \\mathbb{R} \\) be a... | Yes |
[
{
"content": "Provide an example of a countable set \\( S \\) such that the set of all limit points of \\( S \\), denoted \\( S' \\), is uncountable.",
"role": "user"
}
] | \mathbb{Q} |
[
{
"content": "Find the number of ways to arrange 6 people at three identical round tables such that each table is occupied.",
"role": "user"
}
] | 225 |
[
{
"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... | -6.79% |
[
{
"content": "Determine the number of real solutions to the equation \\( e^{2x} = 5x \\).",
"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... | -10 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... | 541.1408 |
[
{
"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... | 301.97 N |
[
{
"content": "A bag contains three coins: a fair coin, a biased coin (heads is thrice as likely as tails), and a two-headed coin. One coin is drawn at random and tossed $n$ times. Let $F$ and $B$ denote the events that the chosen coin is fair and biased, respectively. Assume each coin is equally likely to be dr... | \infty |
[
{
"content": "Determine the equation of the line \\( L \\) such that the graph of the function \\( y = x^4 - 4x^3 - 26x^2 \\) lies entirely on one side of this line and intersects it at exactly two points.",
"role": "user"
}
] | y = -60x - 225 |
[
{
"content": "Suppose that $\\alpha$ is inversely proportional to $\\beta$. If $\\alpha = 4$ when $\\beta = 9$, find $\\alpha$ when $\\beta = -72$.",
"role": "user"
}
] | -\frac{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... | 18.5 |
[
{
"content": "Calculate the value of the sum \\( \\sum_{k=0}^{49}(-1)^k\\binom{99}{2k} \\).",
"role": "user"
}
] | -2^{49} |
[
{
"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... | 1.24 |
[
{
"content": "Evaluate the integral: $$\\int_{-\\infty}^{\\infty} x^2 \\mathrm{e}^{-\\frac{1}{2}x^2} \\; \\mathrm{d}x$$",
"role": "user"
}
] | \sqrt{2\pi} |
[
{
"content": "Evaluate the limit: \\[ \\lim_{n\\to\\infty} \\frac{(3n)! \\, e^n}{(2n)!\\,n^n\\,8^n} \\]",
"role": "user"
}
] | 0 |
[
{
"content": "Determine the gradient of the function \\( f(x,y) = \\begin{cases} \\frac{xy}{\\sqrt{x^2+y^2}}, & x^2+y^2 \\neq 0 \\\\ 0, & x=y=0 \\end{cases} \\) at the point \\((0,0)\\).",
"role": "user"
}
] | (0,0) |
[
{
"content": "Let $f: \\mathbb{R} \\to [0,1]$ be a Lipschitz continuous function with $f(0) = 0$. Assume there does not exist $\\delta > 0$ such that $f(x) = 0$ for all $x \\in [0, \\delta]$. Determine whether there must exist a strictly decreasing sequence $x_n \\to 0$ such that $f(x_n) > 0$ and $f'(x_n) > 0$.... | Yes |
[
{
"content": "Evaluate the line integral \\( \\int_{C}{z\\,\\mathrm dx+x\\,\\mathrm dy-y\\,\\mathrm dz} \\) where \\( C \\) is the path defined by \\( \\gamma(t)=(t^2, 1-t, t) \\) for \\( t \\in [-1,1] \\).",
"role": "user"
}
] | -\dfrac{4}{3} |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 0.32 m |
[
{
"content": "Consider the function field \\( \\mathbb{F}_2(t) \\) over \\( \\mathbb{F}_2 \\). Let \\( \\mathbb{F}_2(t)(\\alpha) \\) be an extension of degree 4 of \\( \\mathbb{F}_2(t) \\), where the minimal polynomial of \\( \\alpha \\) over \\( \\mathbb{F}_2(t) \\) is given by:\n\\[\n\\alpha^4 + a\\alpha^2 + ... | No |
[
{
"content": "Evaluate the limit: $$\\lim_{n\\to\\infty} \\left[\\frac{n(n+1)(n+2)\\dots(n+r)}{n^{r+1}} - 1\\right]$$ where $r$ is a finite positive integer.",
"role": "user"
}
] | 0 |
[
{
"content": "Let $g$ be a real continuous function satisfying $g(1)=1$ and for each natural number $n$:\n\n$$(n+1)^2\\int_{x}^{x+\\frac{1}{n+1}} g(t)\\;\\text{d}t = ng(x) + 1$$\n\nFind the value of $g(1001)$. \\(\\boxed{\\text{Your answer here}}\\)",
"role": "user"
}
] | 1 |
[
{
"content": "What is the value of the arithmetic series $28 + 30 + 32 + \\cdots + 86$?",
"role": "user"
}
] | 1710 |
[
{
"content": "Let $a,$ $b,$ and $c$ be nonnegative real numbers such that $a + b + c = 1.$ Find the maximum value of\n\\[a + \\sqrt{ab} + \\sqrt[3]{abc}.\\]",
"role": "user"
}
] | \frac{4}{3} |
[
{
"content": "Evaluate the limit: \\[ \\lim_{x \\to -0.5^{-}} \\left\\lfloor\\frac{1}{x} \\left\\lfloor \\frac{-1}{x} \\right\\rfloor\\right\\rfloor \\]",
"role": "user"
}
] | -2 |
[
{
"content": "Find an integer solution to the quadratic congruence equation \\(x^2 \\equiv 7 \\pmod{787}\\), where \\(1 \\leq x \\leq 786\\).",
"role": "user"
}
] | 105 |
[
{
"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... | 17.03 s |
[
{
"content": "Determine the sign of the expression \\( S_n + T_n - \\frac{1}{2} \\), where \\( S_n = \\frac{1}{n}\\sum_{k=1}^n \\left(\\frac{k}{n}\\right)^3 \\) and \\( T_n = \\frac{1}{n}\\sum_{k=1}^n \\left(\\frac{k-1}{n}\\right)^3 \\).",
"role": "user"
}
] | + |
[
{
"content": "Evaluate the limit without using L'Hopital's rule: $$\\lim_{x\\to0}\\frac{(1+2x)^{\\frac{1}{4}} - (1-2x)^{\\frac{1}{4}}}{x((1+2x)^{\\frac{1}{8}} + (1-2x)^{\\frac{1}{8}})}$$",
"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... | The Fed would implement a contractionary monetary policy by increasing the discount rate, increasing the reserve requirements, selling government securities, and increasing the interest on reserves. |
[
{
"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... | -420.825 K |
[
{
"content": "An archipelago consists of \\( N \\geq 7 \\) islands. Each pair of islands is connected by at most one bridge. No more than 5 bridges lead from each island, and among any 7 islands, there are always two islands connected by a bridge. What is the maximum possible value of \\( N \\)?",
"role": "... | 36 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | Debit Bond Payable $160,000
Debit Loss on Retirement of Bonds $3,050
Credit Discount on Bonds Payable $2,050
Credit Cash $161,000 |
[
{
"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... | 665.21 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... | 9.56% |
[
{
"content": "Determine the winding number of the circle defined by \\( r(t) = 1 + 2e^{2it} \\) for \\( t \\in [0, 2\\pi] \\) around the point \\( z = 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... | 9.3 W/m^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... | 0.0191 |
[
{
"content": "Determine whether the kernel of $G_{\\alpha}$ acting on $\\Omega - \\alpha$, denoted as $K$, is equal to the kernel of $G$ acting on $\\Omega$. Verify the following proof: Given that $k \\in K$, $k$ maps every $\\beta$ in $G_{\\alpha}$ to itself, implying it fixes all elements in $\\Omega$. Thus, ... | K |
[
{
"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... | Current Liabilities:
1. Notes Payable (due May 1, 2018) - $20,000
2. Accounts Payable - $157,000
3. FICA Taxes Payable - $7,800
4. Sales Tax Payable - $1,700
5. Unearned Rent Revenue - $240,000
6. Interest Payable - $40,000
7. Income Tax Payable - $3,500
Total Current Liabilities: $470,000
Long-Term Liabilities:
1. No... |
[
{
"content": "Determine the number of positive integers \\( n \\) less than or equal to 1988 for which the function \\( f(n) = n \\), where the function \\( f \\) is defined on the positive integers by:\n\\[ f(1) = 1, \\quad f(3) = 3, \\]\n\\[ f(2n) = f(n), \\]\n\\[ f(4n + 1) = 2f(2n + 1) - f(n), \\]\n\\[ f(4n ... | 92 |
[
{
"content": "Let \\( f: \\mathbf{N}^{+} \\rightarrow \\mathbf{N}^{+} \\) be a function such that for any \\( m, n \\in \\mathbf{N}^{+} \\), \\( f(m+n) \\geqslant f(m) + f(n) \\). Additionally, it is given that \\( f(2) = 0 \\), \\( f(3) > 0 \\), and \\( f(9999) = 3333 \\). Find \\( f(1997) \\).",
"role": "... | 665 |
[
{
"content": "Let \\( g(a) = \\int_{0}^{\\pi/2} |\\sin 2x - a\\cos x| \\, dx \\) for \\( a \\in [0, 1] \\). If \\( L \\) and \\( M \\) are the minimum and maximum values of \\( g(a) \\) for all \\( a \\in [0, 1] \\), find the value of \\( L + M \\).",
"role": "user"
}
] | \dfrac{3}{2} |
[
{
"content": "Evaluate the limit: $$\\lim_{n \\to \\infty} \\tan ^{-1}\\left(\\frac{1}{n^2}\\right)\\, \\log(n!)$$",
"role": "user"
}
] | 0 |
[
{
"content": "The sequence \\(a_n\\) is defined such that \\(a_n\\) and \\(a_{n+1}\\) are the roots of the quadratic equation \\(x^2 - c_n x + \\frac{1}{3^n} = 0\\), with the initial condition \\(a_1 = 2\\). Determine the value of \\(\\sum_{n=1}^{\\infty} c_n\\).",
"role": "user"
}
] | \dfrac{9}{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... | 294 N |
[
{
"content": "Consider a polynomial $P(x,y)$ with real coefficients. Assume that $P(\\kappa_{1}, \\kappa_{2})$ is an intrinsically invariant quantity for all surfaces in $\\mathbb{R}^{3}$, meaning it is invariant under isometries of surfaces. Is it true that $P(x,y)$ must be of the form $P(x,y)=F(xy)$ for some ... | Yes |
[
{
"content": "Determine the distribution of the random variable \\( Z = \\frac{\\bar{X} - \\bar{Y}}{\\sigma \\sqrt{\\frac{n+k}{nk}}} \\), where \\( \\bar{X} \\) and \\( \\bar{Y} \\) are the sample means of independent observations \\( x_1, \\ldots, x_n \\) and \\( y_1, \\ldots, y_k \\) from a normal distributio... | N(0, 1) |
[
{
"content": "Determine all functions \\( f: \\mathbb{R} \\rightarrow \\mathbb{R} \\) that satisfy the equation \\( f(f(f(x) + f(y))) = f(x) + y \\) for all real numbers \\( x \\) and \\( y \\).",
"role": "user"
}
] | f(x) = 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... | v=f^{-1}(m)=c\sqrt{1-\frac{m^2_0}{m^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... | 0.1736 radian |
[
{
"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... | An increase in employment does not always lead to an equivalent decrease in unemployment because the labor force participation rate can also change. For example, if the number of employed people increases by 5 from 95 to 100, but the number of unemployed people increases by 5 from 5 to 10 because more people enter the ... |
[
{
"content": "Consider a symmetric random walk starting at $0$. Let $T_x$ denote the first time the walk visits $x$. For $a, b > 0$, determine the expected value of $\\mathsf{E}(\\min(T_a, T_{-b}))$. Use a technique similar to conditioning on the first step, as done in calculating $P(T_a < T_{-b})$. You may als... | ab |
[
{
"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 degrees |
[
{
"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... | 0.5454 |
[
{
"content": "Find the sum of the six distinct prime factors of the positive integer given by the expression \\[ \\sum_{i=0}^{9} \\left(i+(-9)^i\\right)8^{9-i} \\binom{9}{i}\\].",
"role": "user"
}
] | 835 |
[
{
"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... | 9.59 m |
[
{
"content": "Find a basis for the field $F = \\mathbb{Z}_5[x]/(x^3-x^2-1)$ over $\\mathbb{Z}_5$. Express your answer in terms of the element $u = [x]$. ",
"role": "user"
}
] | \{1, u, u^2\} |
[
{
"content": "Let $M$ be a smooth connected manifold with boundary. Is the interior of $M$ also connected, assuming $M$ is second-countable and Hausdorff?",
"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... | 626 V |
[
{
"content": "Determine whether it is possible to construct a closed subset of the interval $[0,1]$ that has no interior points and a Lebesgue measure less than 1.",
"role": "user"
}
] | Yes |
[
{
"content": "Find the remainder when \\(25^{105}\\) is divided by \\(527\\).",
"role": "user"
}
] | 280 |
[
{
"content": "Cities $A$, $B$, $C$, $D$, and $E$ are connected by roads $\\widetilde{AB}$, $\\widetilde{AD}$, $\\widetilde{AE}$, $\\widetilde{BC}$, $\\widetilde{BD}$, $\\widetilde{CD}$, and $\\widetilde{DE}$. How many different routes are there from $A$ to $B$ that use each road exactly once? (Such a route will... | 16 |
[
{
"content": "Let \\( f:[0,1]\\rightarrow \\mathbb{R} \\) be a continuous function such that \\( f(0)=2016 \\). Evaluate the limit:\n\\[ \\lim_{n\\to \\infty}\\int_{0}^{1}f(x^n)dx. \\]",
"role": "user"
}
] | 2016 |
[
{
"content": "Let $G$ be a simple graph where each vertex has exactly 36 neighbors. For any two vertices $X$ and $Y$, if $X$ is a neighbor of $Y$, there are exactly 18 other vertices that are neighbors to both $X$ and $Y$. If $X$ is not a neighbor of $Y$, there are exactly 4 other vertices that are neighbors to... | 190 |
[
{
"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... | $172.18 |
[
{
"content": "At the World Meteorological Conference, each participant announced the average monthly temperature in their hometown in turn. All other participants recorded the product of the temperatures in their own city and the announced city. A total of 36 positive and 36 negative numbers were recorded. What... | 3 |
[
{
"content": "Two circles of radius 2 are centered at $(2,0)$ and at $(0,2)$. What is the area of the intersection of the interiors of the two circles? Express your answer in fully expanded form in terms of $\\pi$.",
"role": "user"
}
] | 2\pi-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... | 21 seconds |
[
{
"content": "Given the sequence of inequalities:\n\n$$(x_1 - 4x_2 + 3x_3 )\\geqslant0$$\n$$(x_2 - 4x_3 + 3x_4 )\\geqslant0$$\n$$\\vdots$$\n$$(x_{100} - 4x_1 + 3x_2 )\\geqslant0$$\n\nand the condition $x_{50} = 2$, determine the value of $x_{51}$. \\(\\boxed{\\text{Answer}}\\)",
"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... | Unemployment rate = (Number of Unemployed / Labor Force) * 100, where Labor Force = Unemployed + Employed |
[
{
"content": "Given that \\( \\int_{0}^{\\infty} \\left(\\frac{\\sin x}{x}\\right)^3 \\, dx = A \\), find the value of \\( k \\) such that \\( \\int_{0}^{\\infty} \\frac{x - \\sin x}{x^3} \\, dx = kA \\).",
"role": "user"
}
] | \dfrac{2}{3} |
[
{
"content": "Find the Fourier transform of the product $f(x)\\delta(x)$, where $f(x)$ is a continuous function and $\\delta(x)$ is the Dirac delta function.",
"role": "user"
}
] | \dfrac{f(0)}{\sqrt{2\pi}} |
[
{
"content": "Find a set $K$ such that $\\text{span}(K)$ is the vector space of all polynomials $p(x)$ in $\\mathbb{R}[x]$ that satisfy the condition $p(x) = p(x-2)$. Provide the set $K$.",
"role": "user"
}
] | \{1\} |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 0.15 m |
[
{
"content": "For real numbers \\(a\\) and \\(b\\) satisfying the equation \\(a^{2} + 4b^{2} = 4\\), determine the maximum value of the expression \\(3a^{5}b - 40a^{3}b^{3} + 48ab^{5}\\).",
"role": "user"
}
] | 16 |
[
{
"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... | 2.82 L |
[
{
"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... | January: $559,650
February: $407,750 |
[
{
"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... | 0.178 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... | 70 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... | 1.00*10^4 rad/s |
[
{
"content": "Determine if the curve given by the equation \\(x^3 + y^3 = 3xy\\) has an asymptote of the form \\(x + y = k\\). If it does, find the value of \\(k\\).",
"role": "user"
}
] | -1 |
[
{
"content": "A square has a diagonal of length $10\\sqrt{2}$ centimeters. What is the number of square centimeters in the area of the square?",
"role": "user"
}
] | 100 |
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