messages listlengths 1 1 | ground_truth stringlengths 1 10 | dataset stringclasses 1 value | source null |
|---|---|---|---|
[
{
"content": "How many solutions does the equation 2(3|((3x + 2)/(1x + 3))|)^2 - 2 = 4(1|x + 1|) - 2 have for x in the interval [-10, 10]?",
"role": "user"
}
] | 2 | math | null |
[
{
"content": "Compute the rank of the given 5x5 matrix:\n[[12, -20, 11, 2, 11],\n [30, -17, 22, 5, 22],\n [-24, -8, -14, -4, -14],\n [-18, 27, -16, -3, -16],\n [24, -16, 18, 4, 18]]",
"role": "user"
}
] | 2 | math | null |
[
{
"content": "Let v(q) = 2*q - 8. Let d be v(5). Express the second largest root of 1920/11*r**3 - 2016/11*r**d + 702/11*r - 81/11 = 0 as n/m where n and m are coprime and calculate n + m.",
"role": "user"
}
] | 13 | math | null |
[
{
"content": "Calculate the rank of matrix A where A =\n[[1, -4, -9, 2, -23],\n [14, -10, -4, 19, 1],\n [18, -3, 8, 16, 25],\n [27, -16, -1, 35, 18],\n [-13, -17, -27, 7, -49]]",
"role": "user"
}
] | 3 | math | null |
[
{
"content": "What is the trace (sum of diagonal elements) when matrix A is multiplied by matrix B?\nA =\n[[-8, 7, 4, 0],\n [-7, 5, -3, 8],\n [4, 0, -2, 4],\n [2, 1, -4, -8],\n [7, -8, 1, -6]]\nB =\n[[-8, -2, -2, -2, 7],\n [-8, 6, -4, -6, 0],\n [5, 6, -7, -6, 7],\n [8, 0, 6, -1, -6]]",
"role": "user"
}
] | 198 | math | null |
[
{
"content": "let N be the greatest 3-digit positive integer with the property that both the number and the number formed by reversing its digits are divisible by 11. Let Q and R be the quotient and remainder, respectively, when N is divided by 100. Find Q + R.",
"role": "user"
}
] | 99 | math | null |
[
{
"content": "If 17472*z**4 - 4756 + 6154*z - 7352*z**3 - 9428*z**2 + 2124*z + 3796 - 2070*z = 0, what is n + m where n/m is the second largest root in simplified form?",
"role": "user"
}
] | 11 | math | null |
[
{
"content": "What is the second-largest prime factor of 3958696?",
"role": "user"
}
] | 223 | math | null |
[
{
"content": "Find the second-largest prime factor of 5431438.",
"role": "user"
}
] | 257 | math | null |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {k: 1, u: 1, j: 1, v: 1}, shuffle the letters in the word, what is the probability of exact 1 letter 'v' remains in the same position?\nIf the probability can be written as the form $\\fra... | 5 | math | null |
[
{
"content": "A 6-gon is colored so that in clockwise order, the vertices are colored as follows: vertex 0 is uncolored, vertex 1 is uncolored, vertex 2 is blue, vertex 3 is red, vertex 4 is red, vertex 5 is uncolored. How many valid colorings of the uncolored vertices exist such that the 6-gon can then be rota... | 2 | math | null |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {l: 6, v: 2}, shuffle the letters in the word, what is the probability of at least 1 letter 'v' remains in the same position?\nIf the probability can be written as the form $\\frac{m}{n}$,... | 37 | math | null |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {s: 2, i: 2, o: 2}, shuffle the letters in the word, what is the probability of no letter 'i' occupy any of their original positions?\nIf the probability can be written as the form $\\frac... | 23 | math | null |
[
{
"content": "Determine the number of intersection points between the functions f(x) = (1(1|(3(2x + 4)^2 - 5(2x + 4) + 3) - 1|) - 2)/(-2(1|(3(2x + 4)^2 - 5(2x + 4) + 3) - 1|) + 3) and g(x) = (3(-2|(-3x) - 3| - 3))/(-1(-2|(-3x) - 3| - 3) + 2) where -10 ≤ x ≤ 10.",
"role": "user"
}
] | 2 | math | null |
[
{
"content": "Let p be the smallest prime where n^7+-1=0 (mod p^3) has a solution, then find the minimal m for this p.",
"role": "user"
}
] | 1 | math | null |
[
{
"content": "Find the rank of the matrix:\n[[-31, 19, -12, 49, 29],\n [-22, 8, 28, 24, -18],\n [-32, -10, 64, 8, -80],\n [49, -16, 15, 8, 20],\n [-45, 3, 28, 6, -53]]",
"role": "user"
}
] | 4 | math | null |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {a: 1, s: 1, k: 2, w: 2}, shuffle the letters in the word, what is the probability of no letter 'a' occupy any of their original positions?\nIf the probability can be written as the form $... | 11 | math | null |
[
{
"content": "Define M to be the number of ordered triples of positive integers (a, b, c) where a, b, c <= 2^3 and 0a^2 + 0b^2 + 0c^2 = 0 (mod 2^2). Find the remainder of M when divided by 1000.",
"role": "user"
}
] | 512 | math | null |
[
{
"content": "Suppose you have a 6-gon, with vertices numbered 1 through 6 in counterclockwise order. Draw the diagonal from vertex 4 to vertex 2 and from vertex 1 to vertex 5. Then, rotate the entire setup, including the constructed diagonals, 5 vertices counterclockwise (so that vertex 1 ends up where vertex... | 6 | math | null |
[
{
"content": "How many solutions does the equation (-2(3|(4(-1x + 3)^2 + 2(-1x + 3) - 4) - 2| - 3) + 1)/(-1(3|(4(-1x + 3)^2 + 2(-1x + 3) - 4) - 2| - 3)) = 1sin(1π(-2|(-4x^2 + 2x + 4)| - 1) - 2) - 3 have for x in the interval [-10, 10]?",
"role": "user"
}
] | 4 | math | null |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {e: 1, d: 3, h: 3}, shuffle the letters in the word, what is the probability of no letter 'e' occupy any of their original positions?\nIf the probability can be written as the form $\\frac... | 13 | math | null |
[
{
"content": "Let r(d) be the first derivative of 1815/19*d**5 + 4 - 1296/19*d**2 + 3795/38*d**4 - 432/19*d - 767/19*d**3. For r(s) = 0, find the second largest root in simplified form n/m and return n + m.",
"role": "user"
}
] | 8 | math | null |
[
{
"content": "Circle D has center O and radius 2. OE = 6. Let W be the rotation of point E by angle pi/2 around point O. Point V is the midpoint of segment EO. Let A be the midpoint of segment OV. Let P be the inversion of point A in circle D. Let Z be the polar line of point W relative to circle D. Let L be th... | 4.14 | math | null |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {z: 5, c: 3}, shuffle the letters in the word, what is the probability of exact 3 letter 'c' remains in the same position?\nIf the probability can be written as the form $\\frac{m}{n}$, wh... | 57 | math | null |
[
{
"content": "Suppose you have a 6-gon, with vertices numbered 1 through 6 in counterclockwise order. Draw the diagonal from vertex 2 to vertex 4 and from vertex 5 to vertex 2. Then, rotate the entire setup, including the constructed diagonals, 2 vertices counterclockwise (so that vertex 1 ends up where vertex... | 7 | math | null |
[
{
"content": "Supposing you start in the bottom left (0, 0) cell of a 9x8 grid, what is minimum number of steps you can take to get to (6, 4), if your only valid moves are to move over 4 squares in one direction and over 3 squares in a perpendicular direction (at once)? (Assume you cannot move off the grid.)",
... | 6 | math | null |
[
{
"content": "Suppose you have a 10-gon, with vertices numbered 1 through 10 in counterclockwise order. Draw the diagonal from vertex 7 to vertex 5 and from vertex 7 to vertex 4. Then, rotate the entire setup, including the constructed diagonals, 4 vertices counterclockwise (so that vertex 1 ends up where vert... | 5 | math | null |
[
{
"content": "How many zeros does the function f(x) = -3sin(2π(2|(-5x + 4) - 3| + 2) - 1) + 1 have in the interval [-10, 10]?",
"role": "user"
}
] | 400 | math | null |
[
{
"content": "In a 6x4 grid, how many different paths are there from the bottom left (0, 0) to the top right (5, 3), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (0, 3), (5, 2), (4, 0), (4, 1), (1, 2)?",
"role": "user"
}
] | 17 | math | null |
[
{
"content": "YS = 8. Circle J has center S and radius 12. Let D be the reflection of point S across point Y. Chord IK of circle J has length 1. Circle M passes through points K, I, and Y. Point N is the center of circle M. Let C be the midpoint of segment IK. Point R is the reflection of point C across segment... | 5.99 | math | null |
[
{
"content": "Form a word by randomly choosing 2 letters from the multiset {m: 2, z: 2, x: 1}. What is the expected number of occurrences of the pattern 'x.*z' in each word? Round your answer to 2 decimal places.",
"role": "user"
}
] | 0.1 | math | null |
[
{
"content": "Determine the rank of the following matrix:\n[[0, -5, -14, -23, 33],\n [-45, -4, -30, -4, 0],\n [-48, -3, -21, 0, -12],\n [11, 7, -6, 35, -25],\n [-48, -5, -18, -11, -3]]",
"role": "user"
}
] | 3 | math | null |
[
{
"content": "When randomly selecting 3 letters from the multiset {l: 1, b: 3} to form a word, what is the expected number of matches of the pattern 'l+l'? Round to 2 decimal places.",
"role": "user"
}
] | 0.0 | math | null |
[
{
"content": "Supposing you start in the bottom left (0, 0) cell of a 7x9 grid, what is minimum number of steps you can take to get to (7, 4), if your only valid moves are to move over 1 squares in one direction and over 6 squares in a perpendicular direction (at once)? (Assume you cannot move off the grid.)",
... | 9 | math | null |
[
{
"content": "Let a(v) be the first derivative of 2 + 63*v**3 + 1605/4*v**4 + 280*v**5 - 297/2*v**2 - 81*v. If a(b) = 0, what is n + m where n/m is the second largest root in simplified form?",
"role": "user"
}
] | 5 | math | null |
[
{
"content": "Suppose you have a 10-gon, with vertices numbered 1 through 10 in counterclockwise order. Draw the diagonal from vertex 7 to vertex 2, from vertex 2 to vertex 5, from vertex 4 to vertex 1, from vertex 7 to vertex 10, from vertex 10 to vertex 8, from vertex 8 to vertex 4, from vertex 6 to vertex 3,... | 6 | math | null |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {h: 2, d: 1, m: 1, t: 3}, shuffle the letters in the word, what is the probability of no letter 'm' occupy any of their original positions?\nIf the probability can be written as the form $... | 13 | math | null |
[
{
"content": "Determine the rank of the following matrix:\n[[-14, -10, -15, 6, 61],\n [-6, -13, -16, 3, 46],\n [15, 9, 6, -3, -37],\n [-31, -8, -3, 21, 35],\n [41, 0, 5, -30, -64]]",
"role": "user"
}
] | 4 | math | null |
[
{
"content": "Supposing you start in the bottom left (0, 0) cell of a 8x9 grid, what is minimum number of steps you can take to get to (8, 5), if your only valid moves are to move over 1 squares in one direction and over 6 squares in a perpendicular direction (at once)? (Assume you cannot move off the grid.)",
... | 7 | math | null |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {h: 5, s: 1, l: 2}, shuffle the letters in the word, what is the probability of no letter 'l' occupy any of their original positions?\nIf the probability can be written as the form $\\frac... | 47 | math | null |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {p: 1, r: 2, z: 2, a: 1}, shuffle the letters in the word, what is the probability of no letter 'z' occupy any of their original positions?\nIf the probability can be written as the form $... | 23 | math | null |
[
{
"content": "Calculate the greatest common factor of 5377482 and 1542024.",
"role": "user"
}
] | 6534 | math | null |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {j: 5, a: 2}, shuffle the letters in the word, what is the probability of no letter 'j' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}... | 22 | math | null |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {r: 4, b: 1}, shuffle the letters in the word, what is the probability of no letter 'b' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}... | 9 | math | null |
[
{
"content": "Let y(n) be the first derivative of -13 - 792/13*n + 1089/13*n**2 + 4774/39*n**3 - 2695/13*n**4. For the polynomial y(s), find the second largest root in the form n/m where n and m are coprime integers. What is n + m?",
"role": "user"
}
] | 13 | math | null |
[
{
"content": "For the function f(x) = (3(-4(-1(1|x + 1| - 3) - 3)^2 - 4(-1(1|x + 1| - 3) - 3) + 3) - 1)/(1(-4(-1(1|x + 1| - 3) - 3)^2 - 4(-1(1|x + 1| - 3) - 3) + 3) - 2), find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.",
"role": "user"
}
] | 2 | math | null |
[
{
"content": "Compute the sum of all entries of the product matrix AB given:\nA =\n[[0, 7, -10, 3, -3],\n [-3, 1, 9, 7, 9],\n [-5, -7, 10, 10, 5],\n [-1, 8, 9, -9, -4],\n [-3, 5, 5, -3, -8]]\nB =\n[[2, -7, -9, -9, 8],\n [-2, -1, 4, 10, -1],\n [-10, 1, -4, -7, 5],\n [3, 4, -7, 6, 8],\n [6, -6, 7, 0, 1]]",
"r... | 79 | math | null |
[
{
"content": "Suppose you have a 14-gon, with vertices numbered 1 through 14 in counterclockwise order. Draw the diagonal from vertex 4 to vertex 12, from vertex 5 to vertex 3, from vertex 9 to vertex 5, from vertex 4 to vertex 6, from vertex 2 to vertex 7, from vertex 6 to vertex 12, and from vertex 3 to verte... | 2 | math | null |
[
{
"content": "If you add up all the x-coordinates where the functions f(x) = 1(3|((2x - 1)/(-1x + 3))| - 3) and g(x) = 2|((2x + 1)/(2x - 1)) - 2| - 1 meet in the interval [-10, 10] and round to the nearest integer, what do you get?",
"role": "user"
}
] | -5 | math | null |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {o: 3, z: 4}, shuffle the letters in the word, what is the probability of no letter 'z' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}... | 44 | math | null |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {i: 2, a: 4}, shuffle the letters in the word, what is the probability of exact 3 letter 'a' remains in the same position?\nIf the probability can be written as the form $\\frac{m}{n}$, wh... | 6 | math | null |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {x: 3, f: 2, j: 1}, shuffle the letters in the word, what is the probability of exact 2 letter 'x' remains in the same position?\nIf the probability can be written as the form $\\frac{m}{n... | 23 | math | null |
[
{
"content": "Calculate the rank of matrix A where A =\n[[18, 4, -15, -17, -7],\n [-18, 8, 2, 46, -15],\n [-16, 4, 41, 7, 16],\n [20, -2, -6, -29, 5],\n [-8, -60, -45, 25, 21]]",
"role": "user"
}
] | 4 | math | null |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {i: 3, m: 2}, shuffle the letters in the word, what is the probability of no letter 'm' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}... | 8 | math | null |
[
{
"content": "What is the rank of the matrix:\n[[-15, -12, -17, -8, -2],\n [12, -24, -5, 23, -31],\n [-18, 43, 52, -14, 21],\n [45, 8, -10, 11, 15],\n [21, 10, 14, 11, 1]]?",
"role": "user"
}
] | 3 | math | null |
[
{
"content": "What is the second-largest prime factor of 574603?",
"role": "user"
}
] | 71 | math | null |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 4(-3|x - 2| + 2) - 3 and g(x) = (2x - 2)/(2x + 1) from x = 1.6 to x = 2.4. Round to 1 decimal place.",
"role": "user"
}
] | 1.8 | math | null |
[
{
"content": "Suppose you have a 10-gon, with vertices numbered 1 through 10 in counterclockwise order. Draw the diagonal from vertex 7 to vertex 1, from vertex 2 to vertex 10, from vertex 8 to vertex 3, from vertex 5 to vertex 2, from vertex 1 to vertex 6, from vertex 8 to vertex 2, from vertex 5 to vertex 10,... | 4 | math | null |
[
{
"content": "Suppose you have a 9-gon, with vertices numbered 1 through 9 in counterclockwise order. Draw the diagonal from vertex 6 to vertex 2 and from vertex 3 to vertex 7. Then, rotate the entire setup, including the constructed diagonals, 4 vertices counterclockwise (so that vertex 1 ends up where vertex... | 8 | math | null |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {g: 2, o: 3}, shuffle the letters in the word, what is the probability of no letter 'o' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}... | 7 | math | null |
[
{
"content": "If -928*m**2 - 360 - 178*m**4 + 573*m - 524*m**3 - 1067*m**4 + 3459*m**2 - 1455*m**4 - 136*m**3 = 0, what is n + m where n/m is the second largest root in simplified form?",
"role": "user"
}
] | 13 | math | null |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {b: 3, a: 3, w: 2}, shuffle the letters in the word, what is the probability of at least 1 letter 'a' remains in the same position?\nIf the probability can be written as the form $\\frac{m... | 43 | math | null |
[
{
"content": "What is the rank of the matrix:\n[[14, -22, 22, 26, -12],\n [-20, 30, -40, -35, 0],\n [-4, 10, 16, -13, 48],\n [16, -28, 8, 34, -48],\n [6, -8, 18, 9, 12]]?",
"role": "user"
}
] | 2 | math | null |
[
{
"content": "Let d(a) = -2008 + 1457*a - 54898*a**4 - 6433*a**3 + 12881*a**4 + 720*a + 20981*a**2. Let i(r) = 14006*r**4 + 2144*r**3 - 6993*r**2 - 726*r + 669. Let n(w) = -6*d(w) - 17*i(w). Suppose n(j) = 0. Express the second largest root as n/m where n and m are coprime and return n + m.",
"role": "user"... | 13 | math | null |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {y: 2, i: 2}, shuffle the letters in the word, what is the probability of no letter 'i' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}... | 3 | math | null |
[
{
"content": "Suppose you have a 6-gon, with vertices numbered 1 through 6 in counterclockwise order. Draw the diagonal from vertex 5 to vertex 3 and from vertex 5 to vertex 2. Then, rotate the entire setup, including the constructed diagonals, 4 vertices counterclockwise (so that vertex 1 ends up where vertex... | 6 | math | null |
[
{
"content": "Compute the rank of the given 5x5 matrix:\n[[12, -20, 11, 2, 11],\n [30, -17, 22, 5, 22],\n [-24, -8, -14, -4, -14],\n [-18, 27, -16, -3, -16],\n [24, -16, 18, 4, 18]]",
"role": "user"
}
] | 2 | math | null |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {k: 5, b: 2}, shuffle the letters in the word, what is the probability of at least 2 letter 'k' remains in the same position?\nIf the probability can be written as the form $\\frac{m}{n}$,... | 31 | math | null |
[
{
"content": "Suppose you have a 11-gon, with vertices numbered 1 through 11 in counterclockwise order. Draw the diagonal from vertex 7 to vertex 1, from vertex 7 to vertex 10, from vertex 4 to vertex 1, from vertex 10 to vertex 6, from vertex 8 to vertex 3, from vertex 3 to vertex 1, from vertex 8 to vertex 2,... | 0 | math | null |
[
{
"content": "Let n(c) be the second derivative of -243/2*c**2 + 11264/5*c**6 + 2*c + 8064/5*c**5 - 783/2*c**3 - 11 - 162*c**4. For the polynomial n(b), find the second largest root in the form n/m where n and m are coprime integers. What is n + m?",
"role": "user"
}
] | 13 | math | null |
[
{
"content": "Suppose you have a 8-gon, with vertices numbered 1 through 8 in counterclockwise order. Draw the diagonal from vertex 2 to vertex 5, from vertex 2 to vertex 6, from vertex 4 to vertex 2, from vertex 2 to vertex 8, from vertex 8 to vertex 5, from vertex 2 to vertex 7, and from vertex 3 to vertex 6.... | 3 | math | null |
[
{
"content": "Suppose you have a 9-gon, with vertices numbered 1 through 9 in counterclockwise order. Draw the diagonal from vertex 1 to vertex 8, from vertex 3 to vertex 1, and from vertex 9 to vertex 6. Then, rotate the entire setup, including the constructed diagonals, 7 vertices counterclockwise (so that v... | 9 | math | null |
[
{
"content": "Determine the number of intersection points between the functions f(x) = 3(3|((-1(-5x^2 + 4x - 4) + 1)/(1(-5x^2 + 4x - 4) - 2))| - 1) and g(x) = 1|(-1(-1x - 4)^2 + 2(-1x - 4) + 4) - 3| - 1 where -10 ≤ x ≤ 10.",
"role": "user"
}
] | 2 | math | null |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {z: 1, k: 5}, shuffle the letters in the word, what is the probability of no letter 'z' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}... | 11 | math | null |
[
{
"content": "Suppose you have a 12-gon, with vertices numbered 1 through 12 in counterclockwise order. Draw the diagonal from vertex 8 to vertex 5, from vertex 10 to vertex 8, from vertex 6 to vertex 3, from vertex 7 to vertex 9, from vertex 9 to vertex 4, from vertex 9 to vertex 11, from vertex 4 to vertex 12... | 3 | math | null |
[
{
"content": "Compute the rank of the given 4x4 matrix:\n[[10, -7, 7, 26],\n [18, -17, 11, 10],\n [-8, 9, -18, -6],\n [-16, 13, -4, -20]]",
"role": "user"
}
] | 3 | math | null |
[
{
"content": "Let R be the circle with center B and radius 7. F has center K and radius 9 and is externally tangent to circle R. Let C be the inversion of point B in circle F. Let H be the rotation of point C by angle pi/12 around point K. Let W be the midpoint of segment CH. Point P is the midpoint of segment ... | 1.32 | math | null |
[
{
"content": "Calculate the greatest common divisor of 16533205 and 4485.",
"role": "user"
}
] | 1495 | math | null |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {p: 2, h: 2, i: 1, v: 1}, shuffle the letters in the word, what is the probability of at least 1 letter 'h' remains in the same position?\nIf the probability can be written as the form $\\... | 4 | math | null |
[
{
"content": "Let p be the smallest prime number for which there exists a positive integer n where n^2+(2) is a multiple of p^3, and n^2+(2) is also a multiple of p^4. Find the largest positive integer m such that m^2+(2) is a multiple of p^3.",
"role": "user"
}
] | 59 | math | null |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -3|(2e^(1x)) - 2| - 1 and g(x) = 1x^2 + 4x - 3 between the vertical lines x = -2.6 and x = 0.2. Round to 1 decimal place.",
"role": "user"
}
] | 3.0 | math | null |
[
{
"content": "Let z be 227700/368*80/78. For the polynomial -270/13 - 2610/13*i - z*i**2 - 8470/13*i**3, find the second largest root in the form n/m where n and m are coprime integers. What is n + m?",
"role": "user"
}
] | 4 | math | null |
[
{
"content": "Let I be the circle with center O and radius 5. R has center M and radius 1 and is externally tangent to circle I. Let N be the inversion of point M in circle I. Let C be the polar line of point N relative to circle I. Let D be the reflection of line C through point O. Point E lies on line D at di... | 24.0 | math | null |
[
{
"content": "A 6-gon is colored so that in clockwise order, the vertices are colored as follows: vertex 0 is uncolored, vertex 1 is red, vertex 2 is uncolored, vertex 3 is red, vertex 4 is uncolored, vertex 5 is red. How many valid colorings of the uncolored vertices exist such that the 6-gon can then be rotat... | 8 | math | null |
[
{
"content": "Let XK = 1. Let P be the midpoint of segment XK. Let C be the rotation of point X by angle pi/3 around point P. Line T is the angle bisector of angle CKX. Let D be the circle with center P passing through point K. Point R is the reflection of point C across line T. Circle E is the reflection of ci... | 0.66 | math | null |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {q: 2, r: 1, l: 1, m: 2}, shuffle the letters in the word, what is the probability of no letter 'r' occupy any of their original positions?\nIf the probability can be written as the form $... | 11 | math | null |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {v: 1, c: 4, n: 1}, shuffle the letters in the word, what is the probability of no letter 'n' occupy any of their original positions?\nIf the probability can be written as the form $\\frac... | 11 | math | null |
[
{
"content": "Determine the number of intersection points between the functions f(x) = 5(2sin(1πx + 2) - 2) + 3 and g(x) = (-1x - 3)/(3x) where -10 ≤ x ≤ 10.",
"role": "user"
}
] | 19 | math | null |
[
{
"content": "Suppose 48 = 8*n + 16*n. Express the second largest root of 28662*q**4 + 810*q + 8827*q**4 + 324 - 309*q**4 - 6768*q**n - 9594*q**3 = 0 as n/m where n and m are coprime and calculate n + m.",
"role": "user"
}
] | 13 | math | null |
[
{
"content": "Let IO = 5. Let Y be the rotation of point I by angle pi/12 around point O. S is placed 6 units away from O. Let Q be the angle bisector of angle SOI. Point Z is the reflection of point S across line Q. Let A be the rotation of point I by angle pi/3 around point Z. Point U is the reflection of poi... | 1.02 | math | null |
[
{
"content": "There are 3 houses, numbered 1 to 3 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:\n - Each person has a unique name: `Peter`, `Eric`, `Arnold`\n - Each person has a uniq... | 2 | math | null |
[
{
"content": "Supposing you start in the bottom left (0, 0) cell of a 6x5 grid, what is minimum number of steps you can take to get to (2, 5), if your only valid moves are to move over 4 squares in one direction and over 1 squares in a perpendicular direction (at once)? (Assume you cannot move off the grid.)",
... | 7 | math | null |
[
{
"content": "Find the total number of local minima and maxima for f(x) = -2e^(1(1|((-3(1x^2 + 2x - 4) - 2)/(1(1x^2 + 2x - 4) + 2)) - 2|)) - 2 where -10 ≤ x ≤ 10.",
"role": "user"
}
] | 5 | math | null |
[
{
"content": "There are 2 houses, numbered 1 to 2 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:\n - Each person has a unique name: `Eric`, `Arnold`\n - Each person has a unique level ... | 0 | math | null |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {n: 3, q: 3}, shuffle the letters in the word, what is the probability of exact 2 letter 'n' remains in the same position?\nIf the probability can be written as the form $\\frac{m}{n}$, wh... | 23 | math | null |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-30, -20, -9, -17, 0],\n [-20, 17, 22, -9, -21],\n [-24, -4, 4, -14, -4],\n [-36, 6, 18, -30, 18],\n [6, 2, 1, -8, 38]]",
"role": "user"
}
] | 3 | math | null |
[
{
"content": "Suppose 2083*w**2 - 2950*w**2 + 166*w - 174*w**3 - 970*w**3 + 120 = 0. Express the second largest root as n/m where n and m are coprime and return n + m.",
"role": "user"
}
] | 7 | math | null |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-5, -9, 7, 2],\n [8, 12, 11, -9],\n [-10, 7, -6, 12],\n [-12, 4, -3, 11]]",
"role": "user"
}
] | 378 | math | null |
[
{
"content": "Supposing you start in the bottom left (0, 0) cell of a 6x9 grid, what is minimum number of steps you can take to get to (6, 5), if your only valid moves are to move over 2 squares in one direction and over 3 squares in a perpendicular direction (at once)? (Assume you cannot move off the grid.)",
... | 5 | math | null |
[
{
"content": "There are 4 houses, numbered 1 to 4 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:\n - Each person has a unique name: `Arnold`, `Eric`, `Peter`, `Alice`\n - Each person h... | 3 | math | null |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.