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... | 0.049 |
[
{
"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... | 3.385 |
[
{
"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... | $295,800.00 |
[
{
"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... | 190 patients or $17,100 |
[
{
"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... | $193,000 (unfavorable) |
[
{
"content": "Consider the probability simplex in $\\mathbb{R}^n$, where each point $p = (p_1, p_2, p_3, \\ldots, p_n)$ represents a distribution for a random variable $X$ taking one of $n$ values, with $\\mathbb{P}(X = a_i) = p_i$ and $a_j < a_k$ for $j < k$. Determine whether the region where $\\text{Var}(X) ... | 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... | 37.1 L |
[
{
"content": "Given the polynomial \\(p(x) = x^4 + ax^3 + bx^2 + cx + d\\) with conditions \\(p(1) = 10\\), \\(p(2) = 20\\), and \\(p(3) = 30\\), compute the value of \\(\\frac{p(12) + p(-8)}{10}\\).",
"role": "user"
}
] | 1984 |
[
{
"content": "Calculate the volume of the region $W$ in $\\\\mathbb{R}^3$ defined by $W=\\\\{ (x,y,z)\\\\in\\\\mathbb{R}^3 ∣ z≥2,\\\\, x^2+y^2≤6−z,\\\\, y≤x \\\\}$ using triple integration.",
"role": "user"
}
] | 4\pi |
[
{
"content": "Let \\( l = \\lim_{x \\rightarrow a}\\frac{x^x-a^x}{x-a} \\) and \\( m = \\lim_{x \\rightarrow a}\\frac{a^x-x^a}{x-a} \\) where \\( a > 0 \\). If \\( l = m \\), find the value of \\( a \\).",
"role": "user"
}
] | e^2 |
[
{
"content": "Are the roots of all polynomials with rational coefficients dense in the real numbers?",
"role": "user"
}
] | Yes |
[
{
"content": "For the sequence $u_n$, where $u_1 = 1$, $u_2 = 2$, and $u_{n+1} = 3u_n - u_{n-1}$, define $v_n$ as the sum $\\sum\\limits_{k=1}^{n} \\cot^{-1}(u_k)$. Given that $u_n = \\sqrt{5} \\cdot \\left({{\\left(\\frac{1+\\sqrt{5}}{2}\\right)}^{2n-1}}+{{\\left(\\frac{\\sqrt{5}-1}{2}\\right)}^{2n-1}}\\right)... | \dfrac{\pi}{2} |
[
{
"content": "Consider a sequence of tosses of a balanced die. Let \\(X_k\\) be the result of the \\(k\\)-th toss, and define \\(Y_n = \\max(X_1, X_2, \\ldots, X_n)\\). Determine the almost sure convergence of the sequence \\((Y_n)_{n \\geq 1}\\).",
"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... | $151,740,473.32 |
[
{
"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... | 7.96 mm |
[
{
"content": "Find the smallest positive integer \\( c \\) such that for any positive integer \\( n \\), the decimal representation of \\( c^n + 2014 \\) has all digits less than 5.",
"role": "user"
}
] | 10 |
[
{
"content": "In a convex quadrilateral, three of its vertices form a triangle such that the circumcenter of this triangle is located outside the triangle. Given this information, determine the value of angle $x$ in the quadrilateral.",
"role": "user"
}
] | 90^\circ |
[
{
"content": "Let \\( M = \\{ 1, 2, \\cdots, 19 \\} \\) and \\( A = \\{ a_{1}, a_{2}, \\cdots, a_{k} \\} \\subseteq M \\). Determine the smallest integer \\( k \\) such that for every \\( b \\in M \\), there exist elements \\( a_{i}, a_{j} \\in A \\) satisfying \\( b = a_{i} \\) or \\( b = a_{i} \\pm a_{j} \\).... | 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... | -22 kJ |
[
{
"content": "Determine whether the following statement is true or false: If \\( \\sum_{i=0}^\\infty a_{i_n} y^i \\rightarrow \\sum_{i=0}^\\infty a_{i} y^i \\) for all \\( y \\in [0,1] \\), does it imply that \\( a_{i_n} \\to_{n \\to \\infty} a_{i} \\) for all \\( i \\), given that \\( 0 \\leq a_i,a_{i_n} \\leq... | 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... | The speed of one ball is v1_f while the other is v2_f= - v1_f -1 m/s |
[
{
"content": "Determine the region within the domain \\(D = \\{(x, y) \\in \\mathbb{R}^2 \\mid x \\geq 1, y \\geq 1\\}\\) where the function \\(f(x, y) = \\begin{cases} \\frac{2x^2 - xy - y^2}{x^2 - y^2} & x \\neq y \\\\ \\frac{3}{2} & x = y \\end{cases}\\) is continuous.",
"role": "user"
}
] | D |
[
{
"content": "Determine the length of the longest word that can be accepted by a deterministic finite automaton (DFA) with the following properties: it has 4 states and does not accept any word of length 8, 9, 10, 11, or 12.",
"role": "user"
}
] | 7 |
[
{
"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... | 47.4 L |
[
{
"content": "Given a random variable $X$ with the probability density function\n\\[\nf_{X}(x) = \\begin{cases} 1 &\\text{ if } 0 < x < 1 \\\\\n0 &\\text{ otherwise}\n\\end{cases}\n\\]\nand a random variable $Y$ with the conditional probability density function\n\\[\nf_{Y|X}(y|x) = \\begin{cases}\n1/x &\\text{ ... | -\ln(y) |
[
{
"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 the linear approximation of the implicit function \\(2xy - x^8 + y^2 = -2\\) at the point \\((-1, 1)\\) where the derivative \\(\\frac{\\mathrm dy}{\\mathrm dx}\\) is undefined.",
"role": "user"
}
] | x = -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... | $20.61 |
[
{
"content": "Find a word \\( \\mathbf{v} \\in \\mathcal{A}^{*} \\) such that the transducer \\( \\mathcal{T}^{\\prime} \\) can associate it with multiple different words.",
"role": "user"
}
] | 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... | 8670758 |
[
{
"content": "Determine the number of solutions to the system of equations: \\[\\begin{align*} x^2-y^2&=z, \\\\ y^2-z^2&=x, \\\\ z^2-x^2&=y. \\end{align*}\\]",
"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... | 1023.12 grams of Manganese (IV) Oxide |
[
{
"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... | Conflict |
[
{
"content": "Determine the values of $x$ for which the matrix \\( \\begin{bmatrix} 2 & x & 0 \\\\ x & 5 & 0 \\\\ 0 & 0 & x-1 \\end{bmatrix} \\) has two distinct repeated eigenvalues.",
"role": "user"
}
] | 2 |
[
{
"content": "Evaluate the integral \\( \\int_{{\\mathbb{R}_+}^2} (x^2 - y) e^{-x-y} \\, dy \\, dx \\).",
"role": "user"
}
] | 1 |
[
{
"content": "Evaluate the line integral of the vector field \\( \\boldsymbol{F}(x,y,z) = (3x^2y^{10}z^{10}, 10x^3y^9z^{10}, 10x^3y^{10}z^9) \\) along the straight line path from \\((0,0,0)\\) to \\((1,1,1)\\).",
"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... | $36.97 |
[
{
"content": "Evaluate the limit \\( \\lim_{n\\rightarrow \\infty}\\binom{2n}{n}^{\\frac{1}{n}} \\) without using the limit as a sum or Stirling's approximation.",
"role": "user"
}
] | 4 |
[
{
"content": "Find the line through the origin that is farthest from the points (1,1), (1,−1), and (−1,−1). Specifically, determine the line such that the sum of the square-distances between the points and their orthogonal projections onto the line is maximal.",
"role": "user"
}
] | y = -x |
[
{
"content": "Determine whether the following equality holds for a function $f \\in L^{1}(d\\mu)$ in a complete measure space $(X, \\Sigma, \\mu)$: \\[ \\int \\limits_{X} f\\chi_{\\{ f \\neq 0 \\} } \\,d\\mu = \\int \\limits_{X}f \\,d(\\chi_{\\{ f\\neq 0 \\} }\\,d\\mu). \\]",
"role": "user"
}
] | Yes |
[
{
"content": "Consider a scenario where \\( n \\) people each write their name on a card and place it in a box. Each person, one by one, draws a card from the box. If a person draws their own card, they put it back and draw again until they get a different card. After drawing a different card, they return their... | \dfrac{1}{31} |
[
{
"content": "Let $f(x)$ be a continuous and twice differentiable function such that $f(x), f'(x), f''(x)$ are all positive for all $x \\in [0, 7]$. If $f^{-1}(x)$ exists, determine the sign of the expression $f^{-1}(5) + 4f^{-1}(6) - 5f^{-1}(\\frac{29}{5})$. Provide your answer as positive, negative, or zero."... | negative |
[
{
"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... | 27.7 g of Cl2 |
[
{
"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... | 11.71 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... | 9.633 |
[
{
"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... | 4.69 |
[
{
"content": "Let \\( M = \\{1, 2, \\cdots, 17\\} \\). A pair of sets \\( \\{a, b\\} \\) and \\( \\{c, d\\} \\) is called a balanced pair if \\( a, b, c, d \\in M \\) are distinct numbers such that \\( a + b \\equiv c + d \\pmod{17} \\). Find the number of balanced pairs in the set \\( M \\).",
"role": "use... | 476 |
[
{
"content": "Given the following information:\n\n1. The annual number of claims for a policyholder follows a binomial distribution with probability function: \\( p(x \\mid q) = {2\\choose x}q^{x}(1-q)^{2-x} \\), where \\( x = 0, 1, 2 \\).\n2. The prior distribution is \\( \\pi(q) = 4q^{3} \\), where \\( 0 < q ... | \dfrac{4}{3} |
[
{
"content": "If $N \\unlhd G$, and $M,K \\leq G$ such that $M \\unlhd K$, does it imply that $MN \\unlhd KN$? Justify your answer.",
"role": "user"
}
] | Yes |
[
{
"content": "Determine all functions \\( f: \\mathbb{R} \\to \\mathbb{R} \\) that satisfy the following conditions: \\( f(x-y) = f(x) - f(y) \\), \\( f(x+1) = f(x) + 2 \\), and \\( f\\left(\\frac{x+y}{2}\\right) = \\frac{f(x) + f(y)}{2} \\).",
"role": "user"
}
] | 2x |
[
{
"content": "Let \\( n > 1 \\) and for \\( 1 \\leq k \\leq n \\), let \\( p_k = p_k(a_1, a_2, \\ldots, a_n) \\) be the sum of the products of all possible combinations of \\( k \\) of the numbers \\( a_1, a_2, \\ldots, a_n \\). Furthermore, let \\( P = P(a_1, a_2, \\ldots, a_n) \\) be the sum of all \\( p_k \\... | 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... | floorlog(b,n) = (\mu. k < n) [ b^k \le n \land b^{k+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... | 1.14e-19 J |
[
{
"content": "Consider a sequence $(a_i)_{i=1}^\\infty$ defined by $a_0 = 0$ and $a_{k+1} = a_k + \\frac{1}{d+a_k}$ for each $k \\geq 0$, where $d > 0$ is a fixed real number. Determine whether this sequence diverges to infinity as $k \\to \\infty$. Provide a justification for your answer.",
"role": "user"
... | \infty |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | $113,333 |
[
{
"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... | 50 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... | 7.53% |
[
{
"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(NH_4)_2S(aq) + 2AlPO_4(aq) -> Al_2S_3(s) + 2(NH_4)_3PO_4(aq) |
[
{
"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... | $2,547,166.31 |
[
{
"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... | 2460 |
[
{
"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... | Black holes |
[
{
"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... | -20.5 J/K |
[
{
"content": "Determine whether the following statement is true or false: If $(x_n)$ is a real sequence with $\\lim \\sup (x_{n+1}-x_n)=+\\infty$, then $\\lim \\frac{n}{x_n}=0$.",
"role": "user"
}
] | False |
[
{
"content": "Does every function in the space of Absolutely Converging Fourier Series, $A(\\mathbb{T})$, also belong to the space of Continuous Functions, $C(\\mathbb{T})$? In other words, does the absolute convergence of a Fourier series imply that the limit function coincides with the original function?",
... | Yes |
[
{
"content": "Evaluate \\( \\frac{x}{yz} + \\frac{y}{xz} + \\frac{z}{xy} \\) given that \\( x + y + z = 4 \\), \\( xyz = -60 \\), and \\( xy + xz + yz = -17 \\).",
"role": "user"
}
] | -\dfrac{5}{6} |
[
{
"content": "Consider an entire function $f$. Determine the value of $\\inf_{z\\in\\mathbb{C}}|f(z)|$.",
"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... | 10.63 |
[
{
"content": "Determine the spectrum of the operator defined by multiplication by $x$ on $L^2([0,1])$. Is the spectrum $\\sigma(T) = [0,1]$?",
"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... | 0.0353 |
[
{
"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... | 6e3 J |
[
{
"content": "Given the sequences \\(a_n=\\int_0^1 (1-x^2)^n \\,dx\\) and \\(b_n=\\int_0^1 (1-x^3)^n \\,dx\\) where \\(n \\in \\mathbb{N}\\), find the limit:\n\\[ \\lim_{n\\to \\infty}(10\\sqrt[n]{a_n}+5\\sqrt[n]{b_n}). \\]",
"role": "user"
}
] | 15 |
[
{
"content": "Determine the number of elements in the intersection of the sets \\(A\\) and \\(B\\), where:\n\n\\[ A=\\left\\{\\frac{3 n-4}{5 n-3}: n \\in \\mathbb{Z}\\right\\} \\quad \\text{and} \\quad B=\\left\\{\\frac{4 k-3}{7 k-6}: k \\in \\mathbb{Z}\\right\\}. \\]",
"role": "user"
}
] | 8 |
[
{
"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... | 367 W |
[
{
"content": "A ball falls from rest at a height $H$ and rebounds with a coefficient of restitution $e = 0.8$. After 5 bounces, the ball is damaged, and the coefficient of restitution changes to $g$. Determine the possible range of values for $g$ such that the total distance traveled by the ball is more than $4... | [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... | For 4000 Machine Hours:
Sales: $40,000
Indirect Labor: $20,000
Indirect Materials: $10,000
Maintenance: $2,000
Utilities: $1,200
Contribution: $6,800
Supervision: $1,200
Insurance: $400
Property Taxes: $600
Depreciation: $1,800
Net Income: $2,800
For 6000 Machine Hours:
Sales: $60,000
Indirect Labor: $30,000
Indirect ... |
[
{
"content": "Find all real continuous functions \\( f \\) such that for all \\( x \\neq 0 \\), the following equation holds:\n\\[ f(x+1) = f(x) + f\\left(\\frac{1}{x}\\right) \\]",
"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... | 1.45e-10 C |
[
{
"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... | 3.797 m/s |
[
{
"content": "Given that $[A,B] = AB - BA = B$, calculate the expression $e^{iA}Be^{-iA}$.",
"role": "user"
}
] | e^{i} B |
[
{
"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... | 3.23m |
[
{
"content": "Show that the sequence \\(a_n = \\left(\\frac{n^2+8n-1}{n^2-4n-5}\\right)^n\\) converges to \\(e^{12}\\).",
"role": "user"
}
] | e^{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... | 3180 N/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... | pH=1/2(pK_a-loga) |
[
{
"content": "Find the limit of the series \\( \\sum^{\\infty}_{n=0} \\frac {(-1)^n 2^{-n} x^{2n+1}} {n!} \\) where \\( x \\in \\mathbb{R} \\).",
"role": "user"
}
] | x e^{-x^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... | 1.5e14 m^(-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... | $515950 |
[
{
"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}\rm 6H^{+}(aq)+2PO_{4}^{3-}(aq) + 3Ba^{2+}(aq)+6OH^{-}(aq) \to Ba_3(PO_4)_2(s) + 6H_2O(l) {/eq} or {eq}\rm H^{+}(aq)+OH^{-}(aq) \to H_2O(l) {/eq} |
[
{
"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... | 82.65 cm |
[
{
"content": "Determine whether a finite set of points can have exactly 100 points at a distance of 1 from each point in the set. Provide a justification for your answer.",
"role": "user"
}
] | Yes |
[
{
"content": "In triangle \\( \\triangle ABC \\), where \\( BC = 5 \\), \\( AC = 4 \\), and \\( \\cos(A-B) = \\frac{7}{8} \\), find the value of \\( \\cos C \\).",
"role": "user"
}
] | \dfrac{11}{16} |
[
{
"content": "Find the area enclosed by the curve given by the parametric equations \\( x = \\cos^3(t) \\) and \\( y = \\sin^3(t) \\) for \\( t \\in [0, 2\\pi] \\). Use the formula \\(-\\int_C y \\, dx\\) to compute the area.",
"role": "user"
}
] | \dfrac{3\pi}{8} |
[
{
"content": "Evaluate the limit \\(\\lim_{x \\to 0}{\\frac{1-\\sqrt{\\cos x}}{1-\\cos \\sqrt{x}}}.\\)",
"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... | 61.0 lb |
[
{
"content": "Let $g$ be a locally integrable function. If $\\int_a^b g(t)\\,dt=0$ for every $a,b$, can we conclude that $g$ is zero almost everywhere? 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... | 0.14% |
[
{
"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... | 1.12 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... | 18000 m/s |
[
{
"content": "Determine the radius of convergence for the power series:\n\n$$\\sum_{n=1}^\\infty \\frac{(n+1)^n}{n^{2n}} z^n$$",
"role": "user"
}
] | \infty |
[
{
"content": "A hotel packed breakfast for each of three guests. Each breakfast should have consisted of three types of rolls, one each of nut, cheese, and fruit rolls. The preparer wrapped each of the nine rolls and once wrapped, the rolls were indistinguishable from one another. She then randomly put three ro... | 79 |
[
{
"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... | 43.94% |
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