prompt list | ground_truth string |
|---|---|
[
{
"content": "Let the function \\( f(x) \\) be defined on \\(\\mathbf{R}\\). For any \\( x \\in \\mathbf{R} \\), the equations \\( f(1+4x)=f(3-2x) \\) and \\( f(2+3x)=-f(7-6x) \\) hold. Find the value of \\(\\sum_{k=1}^{100}[f(2k-1)+f(4k-2)]\\).",
"role": "user"
}
] | 0 |
[
{
"content": "Given the function \\( f(x)= \\sqrt{(x^2-2x+2)(-x^2+3x+10)}-\\sqrt{(-x^{2}+x-1)(x^{2}+x-6)} \\), where the domain is \\( D=[a,b+c] \\), find the value of \\( \\frac{a^3+b^3+c^3}{abc} \\).",
"role": "user"
}
] | 3 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 3.32e-13 |
[
{
"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... | 113,800 |
[
{
"content": "Let $p(x)$ be a cubic polynomial with integer coefficients such that $p(a) = b$, $p(b) = c$, and $p(c) = a$, where $a$, $b$, and $c$ are distinct integers. Determine the number of such polynomials.",
"role": "user"
}
] | 0 |
[
{
"content": "Find the maximum value of the product $xyz$ given that $x, y, z$ are integers and $x + y + z = 3n$, where $n$ is a constant integer.",
"role": "user"
}
] | n^3 |
[
{
"content": "Given a polynomial $Q(x)$ with real coefficients such that $Q(1) = 1$ and for all $x \\neq -7$ and $Q(x+1) \\neq 0$,\n\n$$ \\frac{Q(2x)}{Q(x+1)} = 8 - \\frac{56}{x+7}, $$\n\nfind the value of $Q(-1)$. \\( \\boxed{?} \\)",
"role": "user"
}
] | -\dfrac{5}{21} |
[
{
"content": "In a random walk on the 20 white faces of a truncated icosahedron (soccer ball), you move from one white face to an adjacent one at random with equal probability. Calculate the expected number of steps until you return to the starting white face.",
"role": "user"
}
] | 20 |
[
{
"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... | C6H7O6- |
[
{
"content": "Calculate the greatest common divisor (GCD) of the complex numbers $6-17i$ and $18+i$ in the ring of Gaussian integers $\\Bbb Z[i]$. Provide your answer in the form of a complex number.",
"role": "user"
}
] | 3 - 2i |
[
{
"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... | 0.95 mm |
[
{
"content": "Evaluate the double integral \\( \\iint_{[0,1]^2} f(x,y) \\mathrm{d}A \\) where the function \\( f(x,y) \\) is defined as follows: \\[ f(x,y) = \\begin{cases} e^{x^2}, & \\text{if } x > y \\\\ e^{y^2}, & \\text{if } y > x \\end{cases} \\]",
"role": "user"
}
] | e - 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... | 3.6e-7 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... | 4.89 m/s^2 |
[
{
"content": "Determine the number of isomorphism classes of real line bundles on the circle.",
"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... | 423.0 N |
[
{
"content": "Determine whether the derived set of irrational numbers, denoted as $A'$, is an empty set. Consider the properties of closure, interior, and boundary in your reasoning.",
"role": "user"
}
] | \mathbb{R} |
[
{
"content": "Find the 6-digit number such that when it is multiplied by 2, 3, 4, 5, and 6, the resulting numbers are permutations of the original number's digits.",
"role": "user"
}
] | 142857 |
[
{
"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... | 2.07 m/s at 23.79 degrees east of south |
[
{
"content": "Determine the 100th digit to the right of the decimal point in the decimal representation of \\((1 + \\sqrt{2})^{3000}\\).",
"role": "user"
}
] | 9 |
[
{
"content": "What is the length of the shortest path that traverses all edges in a complete graph with 14 vertices?",
"role": "user"
}
] | 98 |
[
{
"content": "Solve the equation: \\(2^{x+3} + 3^{x-5} = 2^{3x-7} + 3^{2x-10}\\) for \\(x\\).",
"role": "user"
}
] | 5 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 2.04 |
[
{
"content": "Let $f$ be a continuous function on $\\mathbb{R}$ such that $f(0) = f(2)$. Determine whether the following statement is true or false: There exists $\\alpha \\in [0, 1]$ such that $f(\\alpha) = f(\\alpha + 1)$. Provide your answer as either \"True\" or \"False\".",
"role": "user"
}
] | True |
[
{
"content": "Jeff decides to play with a Magic 8 Ball. Each time he asks it a question, it has a 2/5 chance of giving him a positive answer. If he asks it 5 questions, what is the probability that it gives him exactly 2 positive answers?",
"role": "user"
}
] | \frac{216}{625} |
[
{
"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... | 499.856 km / h |
[
{
"content": "Assume two random variables X and Y are exponentially distributed with rates p and q, respectively. Given that the random variable X - Y is distributed like X' - Y', where X' and Y' are independent exponential random variables with rates p and q, does it follow that X and Y are independent?",
... | Yes |
[
{
"content": "Determine whether the set \\( S = \\{(x,y,z) \\in \\mathbb{R}^3 \\mid \\sin(xy) \\geq 1/2\\} \\) is open or closed in \\( \\mathbb{R}^3 \\).",
"role": "user"
}
] | closed |
[
{
"content": "Find the limit: $$\\lim_{x \\to\\infty}\\frac{2^{2^x}}{x^{x^2}}$$.",
"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... | 0.145 kg |
[
{
"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 Performance Report
| | Actual Results | Flexible Budget | Variance | Flexible Budget Sales Volume Variance | Static Budget |
|---|---|---|---|---|---|
| Units | 7,200 | 7,200 | 0 | 300 U | 7,500 |
| Sales Revenue | $737,000 | $720,000 | $17,000 F | $30,000 U | $750,000 |
| Variable Expenses | $483,000... |
[
{
"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... | 12.96% |
[
{
"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... | $56,000 Favorable |
[
{
"content": "Determine whether the polynomial \\((x_1 + x_2 + \\cdots + x_n)^n\\) can be expressed as a sum of nonnegative terms for any positive integer \\(n\\) using the Bricks Throwing Method.",
"role": "user"
}
] | Yes |
[
{
"content": "Calculate the variance of the expression $2X - 3Y + Z - 5$, where $X, Y,$ and $Z$ are uniformly distributed on the set $\\{(x,y,z) \\in \\{0,3\\}^3: x + y + z \\text{ is even}\\}$.",
"role": "user"
}
] | \dfrac{63}{2} |
[
{
"content": "Compute the value of \\(2^{2^{23}} \\pmod{100}\\) efficiently.",
"role": "user"
}
] | 56 |
[
{
"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... | 490 g FeCl_3 |
[
{
"content": "Let $f$ be a polynomial function on $\\mathbb{R}$ such that $f(2x) = f'(x)f''(x)$. Determine the value of $f(3)$. \\( \\boxed{?} \\)",
"role": "user"
}
] | 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... | product cost, direct materials |
[
{
"content": "Is there a simple $C^*$ algebra $A$, not isomorphic to $M_2(\\mathbb{C})$, such that for every commutator element $x = ab - ba$, $x^2$ is a scalar element?",
"role": "user"
}
] | \mathbb{C} |
[
{
"content": "Calculate the arc length of the curve defined by the parametric equations \\( x = 3.5(2 \\cos t - \\cos 2t) \\) and \\( y = 3.5(2 \\sin t - \\sin 2t) \\) for \\( 0 \\leq t \\leq \\frac{\\pi}{2} \\).",
"role": "user"
}
] | 28 - 14\sqrt{2} |
[
{
"content": "Let \\( \\alpha \\) and \\( \\beta \\) be any two interior angles of a triangle. Determine the range of the real number \\( a \\) such that the inequality \\[ \\cos \\sqrt{\\alpha} + \\cos \\sqrt{\\beta} > a + \\cos \\sqrt{\\alpha \\beta} \\] holds for some \\( \\alpha \\) and \\( \\beta \\).",
... | (-\infty, 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... | 2.91e+08 V |
[
{
"content": "Given a smooth manifold $M$ and points $p \\in M$, consider two vectors $v_p, w_p \\in T_p M$. If for all smooth maps $f: M \\to \\mathbb{R}$, the differential satisfies $(f_*)_p(v_p) = (f_*)_p(w_p)$, where $(f_*)_p: T_pM \\to T_{f(p)}\\mathbb{R}\\cong \\mathbb{R}$, determine whether we can conclu... | 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... | 35.99% |
[
{
"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... | 307228.36 |
[
{
"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... | $65,355.35 |
[
{
"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... | $21,000 |
[
{
"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... | 535.17 |
[
{
"content": "A 19-digit binary string contains all possible 4-digit binary strings exactly once. If this string starts with 1111, what are the last four digits?",
"role": "user"
}
] | 0111 |
[
{
"content": "Find the least non-residue of the product $41 \\times 42 \\times \\ldots \\times 54$ modulo $19$. Given that $41 \\equiv 3 \\pmod{19}$ and $54 \\equiv 16 \\pmod{19}$, simplify the expression using the factorial representation $\\frac{54!}{40!}$.",
"role": "user"
}
] | 14 |
[
{
"content": "Among all non-negative real numbers $a, b, c, d, e, f, g$ such that $a + b + c + d + e + f + g = 1$, determine the minimum possible value of $M = \\max \\{a+b+c, b+c+d, c+d+e, d+e+f, e+f+g\\}$.",
"role": "user"
}
] | \dfrac{1}{3} |
[
{
"content": "Calculate the sum of the series \\( \\sum_{k=1}^\\infty kx^k \\) using term-by-term differentiation, where \\( x=\\frac{5}{6} \\).",
"role": "user"
}
] | 30 |
[
{
"content": "Find the value of \\( \\arctan(\\cosh u) \\) as \\( u \\to -\\infty \\).",
"role": "user"
}
] | \dfrac{\pi}{2} |
[
{
"content": "The line described by\n\\[\\begin{pmatrix} 2 \\\\ -1 \\\\ 3 \\end{pmatrix} + t \\begin{pmatrix} k \\\\ 2 \\\\ 1 \\end{pmatrix}\\]is perpendicular to the line described by\n\\[\\begin{pmatrix} 2 \\\\ -1 \\\\ 1 \\end{pmatrix} + u \\begin{pmatrix} 2 \\\\ 1 \\\\ 2 \\end{pmatrix}\\]and passes through t... | -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... | HgS < Fe(OH)_3 < PbS < Mn(OH)_2 < BaSO_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... | 0.4772 Btu/R |
[
{
"content": "Evaluate the integral: \\[ \\int_0^4 \\frac{\\ln x}{\\sqrt{4x-x^2}} \\,\\mathrm{d}x \\]",
"role": "user"
}
] | 0 |
[
{
"content": "Three uncoordinated aliens launch a 3-day attack on 4 galaxies. Each day, each of the three aliens chooses a galaxy uniformly at random from the remaining galaxies and destroys it. They make their choice simultaneously and independently, so two aliens could destroy the same galaxy. If the probabil... | 1151 |
[
{
"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... | 66.82 |
[
{
"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... | 40.0 L |
[
{
"content": "Is it possible to construct a deterministic finite automaton (DFA) for any positive integer $k$, such that when the DFA reads a binary number from the least significant bit, it determines whether the number is divisible by $k$?",
"role": "user"
}
] | Yes |
[
{
"content": "Evaluate the line integral \\( \\int_C y \\, dx + z^2 \\, dy + x \\, dz \\) over the curve \\( C \\), which is the intersection of the surfaces \\( z = \\sqrt{x^2 + y^2} \\) and \\( z = 6 - (x^2 + y^2) \\).",
"role": "user"
}
] | -4\pi |
[
{
"content": "Given the sequence \\((a_{n})\\) defined by the recurrence relation \\(a_{n+1}=\\frac{1}{2}(a_{n}+\\frac{3}{a_{n}})\\), which converges to \\(\\sqrt{3}\\), determine the rate of convergence of the sequence.",
"role": "user"
}
] | quadratic |
[
{
"content": "Determine whether the pointwise minimum of two Riemann integrable functions is always Riemann integrable. 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... | 21 m/s |
[
{
"content": "Evaluate the second derivative \\( f''\\left(\\frac{8}{\\pi x}\\right) \\) at \\( x = 2 \\) for the function \\( f(x) \\) defined by the integral \\( \\int \\sec^{-1}[-\\sin^2x]dx = f(x) + c \\), where \\([y]\\) denotes the greatest integer function.",
"role": "user"
}
] | 0 |
[
{
"content": "Determine the points at which the function \\( f: \\mathbb{R} \\to \\mathbb{R} \\), defined as \\[ f(x) = \\begin{cases} x & \\text{if } x \\notin \\mathbb{Q} \\\\ \\frac{m}{2n+1} & \\text{if } x = \\frac{m}{n}, \\ m\\in \\mathbb{Z}, n \\in \\mathbb{N}, \\text{ and } m \\text{ and } n \\text{ are ... | 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... | 1.3715 L |
[
{
"content": "Evaluate the limit: $$\\lim_{x\\to\\infty} x^{7/2} \\left[\\sqrt{x+1}+\\sqrt{x-1}-2\\sqrt{x}\\left(1-\\frac1{8x^2}\\right)\\right] $$",
"role": "user"
}
] | -\dfrac{5}{64} |
[
{
"content": "Given a sheaf $F$ on a topological space $X$ and an open subset $U \\subseteq X$, let $F|_U$ denote the restricted sheaf of $F$ to $U$. For any point $y \\in U$, is it true that the stalk $F_y$ is equal to the stalk $(F|_U)_y$?",
"role": "user"
}
] | Yes |
[
{
"content": "Convert the point $(\\rho,\\theta,\\phi) = \\left( 3, \\frac{5 \\pi}{12}, 0 \\right)$ in spherical coordinates to rectangular coordinates.",
"role": "user"
}
] | (0,0,3) |
[
{
"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... | 2.86% |
[
{
"content": "Given the function defined implicitly by the equation \\(3\\sin(x^2yz) - 3x + 2y^2 + e^{yz} = 0\\) near the point \\((1,1,0)\\), find the maximum value of the directional derivative of \\(z\\) at the point \\((1,1)\\).",
"role": "user"
}
] | \dfrac{5}{4} |
[
{
"content": "Determine whether the following statement is true or false: In every bipartite graph, there exists a vertex cover of size at most half the number of vertices in the graph.",
"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... | Beginning Inventory + Purchases |
[
{
"content": "In quadrilateral $ABCD$, $\\angle B$ is a right angle, diagonal $\\overline{AC}$ is perpendicular to $\\overline{CD}$, $AB=18$, $BC=21$, and $CD=14$. Find the perimeter of $ABCD$.",
"role": "user"
}
] | 84 |
[
{
"content": "Given a normed linear space $X$ over a field $K$, an arbitrary indexing set $I$, a family of elements $\\{f_\\alpha: \\alpha \\in I\\} \\subset X$, and a family of scalars $\\{c_\\alpha: \\alpha \\in I\\} \\subset K$, determine if there exists exactly one bounded linear functional $f' \\in X'$ suc... | Yes |
[
{
"content": "Simplify the expression \\( \\sum_{k=0}^n\\binom{n}{k}(-1)^k\\left(\\sum_{j=0}^k\\binom{k}{j}3^j\\right) \\).",
"role": "user"
}
] | (-3)^n |
[
{
"content": "Find an upper bound for the number of solutions \\( N_{\\sqrt{2}}(1) \\) to the inequality \\( \\left \\lvert \\sqrt{2} - \\frac{p}{q} \\right \\rvert < \\frac{1}{q^{3}} \\) for \\( \\sqrt{2} \\) with \\( \\epsilon=1 \\).",
"role": "user"
}
] | 3 |
[
{
"content": "Given real matrices $A_{n\\times n}$ and $B_{n\\times n}$, determine whether there exists a matrix $C_{n\\times n}$ such that $AA^{T} + BB^{T} = CC^{T}$, given that $AA^{T} + BB^{T}$ is not positive definite.",
"role": "user"
}
] | Yes |
[
{
"content": "Let $A^*:D(A^*)\\subset Y^*\\to X^*$ be the adjoint of $A:D(A)\\subset X\\to Y$. Determine whether there always exists an $x'\\in X^*$ such that $y'(Ax)=x'(x)$ for all $x\\in D(A)$, given $y'\\in D(A^*)$. Provide a justification for your answer.",
"role": "user"
}
] | Yes |
[
{
"content": "Evaluate the limit: $$\\lim_{x \\to 1} \\left(\\frac{23}{1-x^{23}}-\\frac{11}{1-x^{11}} \\right)$$",
"role": "user"
}
] | 6 |
[
{
"content": "Given two graphs $G_1$ and $G_2$ with vertex chromatic numbers 5 and 7, respectively, and an edge between vertices 7 and 8 in both graphs, determine the vertex chromatic number of the graph $G$ formed by taking the union of the edge sets of $G_1$ and $G_2$. Provide your answer as a single number."... | 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... | -1.2757 |
[
{
"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... | 10.9 |
[
{
"content": "How many different $4\\times 4$ arrays whose entries are all 1's and -1's have the property that the sum of the entries in each row is 0 and the sum of the entries in each column is 0?",
"role": "user"
}
] | 90 |
[
{
"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... | 50683.20 |
[
{
"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... | Q = C + 0.75 |
[
{
"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... | Q FC VC TC AFC AVC ATC MC
0 $200 0 $200 - - - -
10 $200 $50 $250 $20 $5 $25 $50
20 $200 $100 $300 $10 $5 $15 $50
30 $200 $160 $360 $6.67 $5.33 $12 $60
40 $200 $480 $680 $5 $12 $17 $320
50 $200 $1250 $1450 $4 $25 $29 $770
60 $200 $2020 $2220 $3.33 $33.67 $37 $770 |
[
{
"content": "Calculate the mass of a half disc of radius \\( R \\) centered at the origin \\((0,0)\\), with \\( y>0 \\) and density given by \\( \\rho = \\frac{\\rho_0 y}{\\sqrt{x^2+y^2}} \\) for \\( y>0 \\), where \\( \\rho_0 \\) is a constant with units of \\( \\text{kg.m}^{-3} \\).",
"role": "user"
}
... | \rho_0 R^2 |
[
{
"content": "For a function $u \\in L^p(\\Omega)$ with $p > 1$, determine if there exists a positive constant $k$ such that \\( \\int_{\\{x \\in \\Omega : u(x) > k\\}} |u(x)|^p \\, dx < 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... | Common Stock 99,000
Retained Earnings 100,000
Total Stockholders' Equity 199,000 |
[
{
"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... | 0.113 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... | 487.92 nm |
[
{
"content": "Find all real values of $x$ that satisfy $\\frac{1}{x+1} + \\frac{3}{x+7} \\ge \\frac23.$ (Give your answer in interval notation.)",
"role": "user"
}
] | (-7, -4] \cup (-1, 2] |
[
{
"content": "In a 4-dimensional space divided into 16 regions about the origin, what is the maximal number of these regions that a plane can intersect? For reference, in a 3-dimensional space divided into 8 regions, a plane can intersect up to 7 of these regions.",
"role": "user"
}
] | 11 |
[
{
"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... | 1.41*10^{-4} N/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... | 8.97 |
[
{
"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=sqrt(2qV/m) |
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