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... | v_{original} = \dfrac{p_{total}}{m_1+m_2+m_3} |
[
{
"content": "Let $f: (0, \\infty) \\to \\mathbb{R}$ be a continuous function. Determine whether $f$ maps any Cauchy sequence to a Cauchy sequence. Answer with 'True' or 'False'.",
"role": "user"
}
] | False |
[
{
"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 degrees |
[
{
"content": "Determine the norm \\( ||A|| \\) of an operator \\( A \\) that satisfies \\( AA = I \\) in a Hilbert space \\( H \\), where the norm is defined as \\( ||A|| = \\sup_{x \\in H} \\frac{|Ax|}{|x|} \\).",
"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... | 320000 |
[
{
"content": "For a positive integer $n$ with prime factorization $n = \\prod_{i=1}^r {p_i}^{\\alpha_i}$, determine the number of divisors of $n$ that contain exactly $k$ distinct prime factors, each with the corresponding multiplicity $\\alpha_i$. Provide your answer as a single integer.",
"role": "user"
... | \dbinom{r}{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... | 61.54% |
[
{
"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... | 2.308 |
[
{
"content": "Find the interval of convergence for the power series: $$\\sum_{n=1}^{\\infty} \\frac{\\cos(\\frac{1}{n})}{n^2}x^n$$",
"role": "user"
}
] | [-1, 1] |
[
{
"content": "Determine whether any function in $L^2(\\mathbb{R})$ that is continuous and vanishes at infinity can be approximated using functions of the form $p(x) e^{- \\alpha \\vert x \\vert}$, where $p(x)$ is a polynomial and $\\alpha > 0$. Provide a justification for your answer.",
"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... | 4.2e-3 m |
[
{
"content": "Given the functional equation $f(x)f(y) = f(x+y) + f(x-y)$ for any real $x$ and $y$, and the condition $f(1) = 1$, determine the period of the function $f(x)$. Provide your answer as a single number.",
"role": "user"
}
] | 6 |
[
{
"content": "As shown in the diagram, points \\( A, B, C \\) are on a sphere with a surface area of \\( 48 \\pi \\). Given that \\( AB = 2 \\cdot BC = 4 \\) and \\( \\angle ABC = 60^{\\circ} \\), and \\( O \\) is the center of the sphere, determine the angle between the line \\( OA \\) and the plane \\( ABC \\... | D |
[
{
"content": "Evaluate the limit: \\[ \\lim_{x \\to \\pi/6} \\frac{(2\\sin x + \\cos(6x))^2}{(6x - \\pi)\\sin(6x)} \\]",
"role": "user"
}
] | -\dfrac{1}{12} |
[
{
"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... | 11.44% |
[
{
"content": "Find the limit of the expected average gain of citizens as the number of citizens, $n$, goes to infinity, given that the gain from a policy is uniformly distributed on $[-1, 1]$ and the policy is implemented if more than half of the citizens vote for it. The expected gain is given by the formula:\... | 0 |
[
{
"content": "Given that $(a,n)=(b,n)=1$ and $(c,n)=d$, where $d$ divides $ab$, determine if $d=1$ is the only possible value for $d$. Assume $a, b, c, n \\in \\mathbb{N}$.",
"role": "user"
}
] | 1 |
[
{
"content": "Josh and Mike live 13 miles apart. Yesterday Josh started to ride his bicycle toward Mike's house. A little later Mike started to ride his bicycle toward Josh's house. When they met, Josh had ridden for twice the length of time as Mike and at four-fifths of Mike's rate. How many miles had Mike ri... | 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... | 1.014 mol |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 130 K |
[
{
"content": "Evaluate the limit: $$\\lim_{n\\to\\infty} \\left( \\frac{ g_n^{\\gamma}}{\\gamma^{g_n}} \\right)^{3n},$$ where $g_n$ and $\\gamma$ are defined as in the original question.",
"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... | 127.2 Pa |
[
{
"content": "Consider the set \\( S = \\{1, 2, 3, \\ldots, 2022\\} \\) and a permutation \\( A = \\{a_{1}, a_{2}, a_{3}, \\ldots, a_{2022}\\} \\) of \\( S \\). It is known that for any \\(1 \\leq n, m \\leq 2022\\), the sum \\( a_{n} + a_{m} \\) is divisible by the greatest common divisor (GCD) of \\( n \\) an... | 1 |
[
{
"content": "Determine whether the following statement is true or false: If $f \\in L_4([0,1])$, then $f \\in L_2([0,1])$ and $\\|f\\|_2 \\leq \\|f\\|_4$.",
"role": "user"
}
] | True |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 9.1% |
[
{
"content": "Determine whether the sequence \\((x_n)_n\\) is convergent, given that \\(\\frac{2018}{x_n} = \\left(\\frac{x_{n+1}}{x_n}\\right)^{(n+1)/2}\\) for all \\(n \\geq 1\\).",
"role": "user"
}
] | 2018 |
[
{
"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 moles |
[
{
"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... | 2.21 |
[
{
"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... | Minimize the negative log likelihood: \mathcal{L}=-\sum_i \log\left(p_{\text{Kalman}}(x_i)\right) |
[
{
"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... | 0.67 g |
[
{
"content": "Find an expression for the value of the integral $I_p$ for any positive integer $p$, where $I_p$ is defined as\n\n$$I_p=\\lim_{n\\rightarrow \\infty } \\int ^{\\infty}_{0}\\dfrac{n\\sin \\left(\\frac {x}{n}\\right)}{\\left(1+\\frac {x}{n}\\right)^{n}}dx$$",
"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... | 1600 |
[
{
"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... | 1.39e-6 g |
[
{
"content": "In the alternating group \\(A_5\\), let \\(x\\) be an element of order 2 and \\(y\\) be an element of order 3 such that \\(\\langle x, y \\rangle = A_5\\). Is it necessary that the order of the product \\(xy\\) is 5?",
"role": "user"
}
] | Yes |
[
{
"content": "Find a quartic polynomial with integer coefficients whose roots are the primitive 12th roots of unity.",
"role": "user"
}
] | x^4 - x^2 + 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... | -$240,000 |
[
{
"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... | 116.3s |
[
{
"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... | 2.08 years |
[
{
"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... | 31.8 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... | 36 g |
[
{
"content": "Determine the value of $g(0,0)$ that makes the function $g(x,y) = [x]^y$ continuous at $(0,0)$, where $g: \\mathbb{R}^2 \\to \\mathbb{R}$.",
"role": "user"
}
] | 1 |
[
{
"content": "Suppose $H, G, K$ are abelian Hausdorff topological groups and $0 \\to H \\overset{\\alpha}{\\to} G \\overset{\\beta}{\\to} K \\to 0$ is an exact sequence of continuous homomorphisms. If $H$ and $K$ are compact, is $G$ necessarily compact as well?",
"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... | $102,650 U |
[
{
"content": "Determine the structure of the quotient ring \\( \\frac{\\mathbb{C}[u]}{u\\mathbb{C}[u]} \\), where \\( \\mathbb{C}[u] \\) is the algebra of polynomials with the indeterminate \\( u \\).",
"role": "user"
}
] | \mathbb{C} |
[
{
"content": "Determine the correct value of \\( S \\) in the recursive integral equation:\n\\[ S = \\frac{1}{\\int_1^2 \\frac{1}{\\int_1^2 \\frac{1}{\\int_1^2 \\ddots}}} \\]\nAssume that the variable of integration is either \\( x \\) or \\( S \\). Calculate \\( S \\) based on these assumptions and find the co... | 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... | 6596.31 N |
[
{
"content": "What is the minimum number of lines needed to divide a plane into regions such that no two points on a 9x9 grid lie in the same region?",
"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... | 4.85 M |
[
{
"content": "Evaluate the lambda calculus expression: $[[\\lambda f.\\lambda m. f(m - m^2))]([\\lambda n.3n])](4)$.",
"role": "user"
}
] | -36 |
[
{
"content": "Find the degree of the splitting field of the polynomial \\( p(x) = x^5 - 3x^3 + x^2 - 3 \\) over \\( \\mathbb{Q} \\).",
"role": "user"
}
] | 4 |
[
{
"content": "Calculate the derivative \\(\\frac{dT}{dt}\\), where \\(T\\) is the total kinetic energy of a fluid flow with velocity \\(\\underline{u}\\), pressure \\(p\\), and constant density \\(\\rho\\) within a closed region with a solid boundary. The fluid motion satisfies the Euler Equations: \\(u_t + (u ... | 0 |
[
{
"content": "Given the function $f(x+y) = f(x)f(y)$ for all $x$ and $y$, with $f(5) = 2$ and $f'(0) = 3$, find the value of $f'(5)$. ",
"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... | 2.7 m/s |
[
{
"content": "The cost to carpet a floor is directly proportional to the area. It costs $\\$$105 to carpet a floor that is $14\\times 5\n$ square feet. How much will it cost to carpet a floor that is $16\\times 13$ square feet? Express your answer in dollars.",
"role": "user"
}
] | 312 \text{ dollars} |
[
{
"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. Collect job cost information.
2. Calculate total direct materials costs.
3. Compute total direct labor costs.
4. Apply manufacturing overhead.
5. Calculate total job costs by summing steps 2, 3, and 4.
6. Calculate the COGM by adding total costs for all completed jobs during the period. |
[
{
"content": "Suppose that \\(\\{a_t\\}\\) is a sequence of real numbers satisfying \\( \\lim_{n\\to\\infty}\\frac{1}{n}\\sum_{t=1}^na_t=L<\\infty. \\) Determine whether the sequence \\(\\{a_t\\}\\) is necessarily bounded.",
"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... | 2.02 |
[
{
"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... | 9.0 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... | 0.81m/s and -3.02m/s or -2.68m/s and 2.8m/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... | 8.77 percent |
[
{
"content": "Determine the greatest positive integer $m$ such that $3^m$ divides the product of all differences $(c-d)$, where $c$ and $d$ are integers satisfying $1 \\le c < d \\le 15$. \\( \\boxed{m} \\)",
"role": "user"
}
] | 36 |
[
{
"content": "Find the number of solutions in positive integers to the equation \\(x_1 + x_2 + x_3 + x_4 = 19\\) subject to the conditions \\(x_2 \\neq 2x_3\\) and \\(x_1 \\neq x_2\\).",
"role": "user"
}
] | 702 |
[
{
"content": "Consider the operator \\( T: L^2([0,1]) \\to L^2([0,1]) \\) defined by \\( Tf(t) = \\int_0^t f(s) \\, ds \\). Find \\( \\alpha < 1 \\) such that \\( ||T|| \\leq \\alpha \\).",
"role": "user"
}
] | \dfrac{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... | 10Na(s) + 2NaNO_3(aq) -> 6Na_2O(aq) + N_2(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... | $908,400 |
[
{
"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... | 4203.4 g/mol |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 71.43 |
[
{
"content": "Evaluate the expression \\( \\frac {(x + \\frac{1}{x})^6 - (x^6 + \\frac{1}{x^6}) - 2} {(x + \\frac{1}{x})^3 - (x^3 + \\frac{1}{x^3})} \\) and determine its minimum value.",
"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... | 9.49 |
[
{
"content": "Determine whether there exist natural numbers \\(m, n, k\\) such that \\(m, n, k \\ge 1\\), \\(m \\neq n \\neq k \\neq m\\), and \\[ \\frac{1}{2m+1} + \\frac{1}{2n+1} = \\frac{2}{2k+1}. \\]",
"role": "user"
}
] | Yes |
[
{
"content": "Richard is cycling at a speed of \\( v \\) km/h when he checks his cycle computer, which shows a time \\( t \\) hours to reach home. He cycles at this speed for 40 minutes, then slows down by 1 km/h. The computer still shows \\( t \\) hours to reach home. After cycling at this new speed for 45 min... | 54 |
[
{
"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... | $212,800 |
[
{
"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... | 1/3 |
[
{
"content": "Given a group homomorphism $\\varphi:G\\to H$, if $U$ is a subgroup of $G$ and $\\varphi(U)$ is a characteristic subgroup of $H$, is $\\varphi(U)$ necessarily a normal subgroup of $H$? Justify your answer.",
"role": "user"
}
] | Yes |
[
{
"content": "Evaluate the limit: $$\\lim\\limits_{(x, y) \\to (0, 0)} \\dfrac{xy^4}{x^4+y^4}$$",
"role": "user"
}
] | 0 |
[
{
"content": "Calculate the sum of the Fourier series for the 2π-periodic function \\(f(x)=e^{x}\\) at \\(x=4\\), given that the function is defined for \\(|x|\\le \\pi\\) and its Fourier series is \\[f(x)=\\frac{e^{\\pi}-e^{-\\pi}}{2\\pi} + \\frac{e^{\\pi}}{\\pi}\\sum_{n=-\\infty}^\\infty \\frac{(-1)^{n}}{1+n^... | e^{4 - 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... | Flexible Budget
Flexible Budget Actual Variance
Units Manufactured 20,000 units 20,000 units 0
Direct Material 460,000 489,300 29,300 U
Direct Labor 120,000 127,900 7,900 U
Variable Production Overhead 137,000 170,000 33,000 U
Depreciation 28,000 28,000 0
Supervisory Salaries 41,000 42,100 ... |
[
{
"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... | rdrd\theta |
[
{
"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... | 0.145m |
[
{
"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. Calculate the present value of the note payable based on the discounted market rate of interest.
2. Multiply the present value by the market value of the note to calculate interest income.
3. Record the calculated interest income by crediting interest income and debiting property, goods, or services. |
[
{
"content": "How many four-digit positive integers have at least one digit that is a 2 or a 3?",
"role": "user"
}
] | 5416 |
[
{
"content": "Evaluate the integral \\( \\int_{1}^{2}\\frac{e^{1/x}}{x^2}\\,dx \\).",
"role": "user"
}
] | e - \sqrt{e} |
[
{
"content": "Determine the values of \\( y \\) for which the polynomial \\( f(x) = -x^3 + 3x - y \\) has three distinct real roots.",
"role": "user"
}
] | (-2, 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... | PP: 0.1410
Pp: 0.4690
pp: 0.3900 |
[
{
"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... | 4e-5 V |
[
{
"content": "Two years ago there were 20 trailer homes on Elm Street with an average age of 18 years. At that time, a group of brand new trailer homes was then added to Elm Street. Today, the average age of all the trailer homes on Elm Street is 14 years. How many new trailer homes were added two years ago?",
... | 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... | 487.57 g |
[
{
"content": "Evaluate the improper integral \\(\\displaystyle\\int_{a}^{b} \\frac{1}{\\sqrt{(x-a)(b-x)}}dx\\) using the substitution \\(t=\\frac{x-a}{b-a}\\).",
"role": "user"
}
] | \pi |
[
{
"content": "Is it possible to find all solutions to a third-order linear inhomogeneous differential equation given four linearly independent solutions?",
"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... | 580.7L |
[
{
"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... | import java.util.Scanner;public class MinMax{public static void main( String[] args ){Scanner keyboard = new Scanner(System.in);double[] arr = new double[5];for (int i = 0; i < 5; i++){System.out.println("Please provide value " + (i + 1) + ": ");arr[i] = keyboard.nextDouble();}double min, max;min = arr[0];max = arr[0];... |
[
{
"content": "Determine the range of positive values of \\( x \\) for which the series \\( \\sum_{n=0}^{\\infty}\\frac{1}{1+x^{n}} \\) is both convergent and uniformly convergent.",
"role": "user"
}
] | (1, \infty) |
[
{
"content": "Find the covariance \\( \\text{Cov}(X, Y) \\) for the joint probability density function \\( f(x, y) = e^{-y} \\), where \\( 0 \\leq x \\leq y \\) and the conditional expectation \\( E[Y|X] = x + 1 \\).",
"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... | -5.6035 T/s |
[
{
"content": "Calculate the expected number of Bernoulli trials required to achieve a streak of 10 consecutive successes, given that the probability of success for each trial is 0.2.",
"role": "user"
}
] | 12207030 |
[
{
"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... | 48.18 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... | 0.41r |
[
{
"content": "Find the remainder when \\((x-1)^{2013}\\) is divided by \\(x^2-2x+2\\).",
"role": "user"
}
] | x - 1 |
[
{
"content": "Let \\( f:\\mathbb{R}^+\\to \\mathbb{R}^+ \\) be a function such that for all \\( x,y \\in \\mathbb{R}^+\\), \\( f(x)f(y)=f(xy)+f\\left(\\frac{x}{y}\\right) \\), where \\( \\mathbb{R}^+ \\) represents the positive real numbers. Given that \\( f(2)=3 \\), compute the last two digits of \\( f\\left(... | 47 |
[
{
"content": "A set of distinct positive integers has a sum of 1987. Determine the maximum possible value of the expression \\(3n + k\\), where \\(n\\) is the total number of integers in the set and \\(k\\) is the number of odd integers in the set.",
"role": "user"
}
] | 221 |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.