instruction_seed stringlengths 5 2.9k | response_seed stringlengths 3 9.55k | input stringclasses 1
value | _source stringclasses 1
value |
|---|---|---|---|
What is (3/(-7))/((-5433)/50708)?\n | 4\n | ibivibiv/math_instruct | |
What are the prime factors of -40 + 46 - (-1 - 21226)?\n | 17, 1249\n | ibivibiv/math_instruct | |
What is the derivative of h**2*v + 7710369*h**2 - 4*h*v - 521844*v wrt v?\n | h**2 - 4*h - 521844\n | ibivibiv/math_instruct | |
Three letters picked without replacement from {y: 3, e: 2, x: 1, s: 1, k: 4}. Give prob of picking 2 e and 1 y.\n | 1/55\n | ibivibiv/math_instruct | |
Solve 2*s - 10*b = -40, -48*s - 5*b = -44*s + 30 for s.\n | -10\n | ibivibiv/math_instruct | |
Factor 4*j**2 - 7424*j + 3444736.\n | 4*(j - 928)**2\n | ibivibiv/math_instruct | |
Suppose -77*m - 182 = -78*m - 2*j, m - 4*j = 152. Let v = m + -167. What is the greatest common factor of 185 and v?\n | 5\n | ibivibiv/math_instruct | |
Let d(h) = h**2 - 2*h + 2. Let y(t) = -t**2 + 7*t + 3. Let l be y(7). Let s(m) be the second derivative of m**3/6 - m**2/2 - 21*m + 2. What is l*s(o) + d(o)?\n | o**2 + o - 1\n | ibivibiv/math_instruct | |
Solve 0 = -117*t + 220*t - 119*t - 288 for t.\n | -18\n | ibivibiv/math_instruct | |
What is the second biggest value in -3, -0.2, 2, -1, -3051/7?\n | -0.2\n | ibivibiv/math_instruct | |
Does 5 divide 4206810?\n | True\n | ibivibiv/math_instruct | |
Express (71*j - 54 + 54)*(-4*j + 3*j + 2*j) in the form t*j**2 + o + a*j and give t.\n | 71\n | ibivibiv/math_instruct | |
What is 0.867489 decades in months?\n | 104.09868\n | ibivibiv/math_instruct | |
Expand -99*g + 248 - 248 + (1 + 0 + 0)*(0*g - 2*g + g) - g + g - g + 3*g + 0*g - 5*g.\n | -103*g\n | ibivibiv/math_instruct | |
Let t(x) be the third derivative of 25*x**2 + 1/24*x**6 + 0*x + 7/12*x**5 - 5/24*x**4 - 35/6*x**3 + 2. Suppose t(h) = 0. What is h?\n | -7, -1, 1\n | ibivibiv/math_instruct | |
-2198620 - -81\n | -2198539\n | ibivibiv/math_instruct | |
Multiply 1894 and -0.9.\n | -1704.6\n | ibivibiv/math_instruct | |
Suppose 2*i - 22 = 3*m, -3*m - 22 = -2*i + 2*m. Differentiate -41 - 7*t - 14 + i*t - 9*t with respect to t.\n | -5\n | ibivibiv/math_instruct | |
Evaluate (-26)/(-39)*(-6)/4.\n | -1\n | ibivibiv/math_instruct | |
Let r(q) = 43*q. Let g(v) = -33*v**2. What is g(r(m))?\n | -61017*m**2\n | ibivibiv/math_instruct | |
Is 1709/(48/(-360)*3/(-2)) prime?\n | False\n | ibivibiv/math_instruct | |
Suppose 0 = -4*b + 8, -b - 2*b + 6 = 3*r. Suppose 8*p - 3*p - 180 = r. Let g = 1 + p. Calculate the remainder when g is divided by 19.\n | 18\n | ibivibiv/math_instruct | |
Suppose l - 56 + 20 = 0. Suppose a - 2*a = -l. What is the tens digit of a?\n | 3\n | ibivibiv/math_instruct | |
Suppose -d - 15 = 2*v + 2*v, -v = -2*d + 15. Let k = d + 43. Is k a multiple of 17?\n | False\n | ibivibiv/math_instruct | |
Let h = 0.04 - 0.34. Let m = -13 - -18. Which is the second biggest value? (a) h (b) -1/6 (c) m\n | b\n | ibivibiv/math_instruct | |
b"What is the xth term of -688, -739, -818, -919, -1036, -1163, -1294, -1423?\n" | x**3 - 20*x**2 + 2*x - 671\n | ibivibiv/math_instruct | |
Is -24 less than or equal to 0.102?\n | True\n | ibivibiv/math_instruct | |
Let c be 3/1 + 3/3. Suppose -5*j + 3 = c*n - 33, -n = j - 8. Solve -4*u + 12 + n = 0 for u.\n | 4\n | ibivibiv/math_instruct | |
Let j = -6 - -7. Let t be (2 - (5 + -2))/2. Let n = 149/465 - 41/186. Which is the third smallest value? (a) j (b) n (c) t\n | a\n | ibivibiv/math_instruct | |
Is 2176914809 a prime number?\n | True\n | ibivibiv/math_instruct | |
Put 2/17, 4, 2/23 in decreasing order.\n | 4, 2/17, 2/23\n | ibivibiv/math_instruct | |
Calculate -11 + 19 + -15 + 38 + 31 + (-2 - -9).\n | 69\n | ibivibiv/math_instruct | |
What are the prime factors of 19737?\n | 3, 17, 43\n | ibivibiv/math_instruct | |
Let b be ((-15)/2)/(33/(-616)). Is 8 a factor of 395*(b/25 - 5)?\n | False\n | ibivibiv/math_instruct | |
Solve -64/7*z - 2/7*z**4 - 48/7*z**2 - 16/7*z**3 - 32/7 = 0 for z.\n | -2\n | ibivibiv/math_instruct | |
Let k(d) = -25*d + 93. Let f(c) = 22*c - 94. Calculate 9*f(b) + 8*k(b).\n | -2*b - 102\n | ibivibiv/math_instruct | |
Convert 9 (base 14) to base 8.\n | 11\n | ibivibiv/math_instruct | |
Suppose v + 60 = 13*v. Solve -3*o + v*o = -6 for o.\n | -3\n | ibivibiv/math_instruct | |
Solve 187 = 23*l + 3 for l.\n | 8\n | ibivibiv/math_instruct | |
-754479500 divided by -188619875\n | 4\n | ibivibiv/math_instruct | |
In base 11, what is -5 + 35182?\n | 35178\n | ibivibiv/math_instruct | |
Let w(h) = -2*h**2 - 3*h - 3. Let g(n) = -4*n**2 - n + 2. Let o = -74 + 75. Let d be g(o). Let b(t) = -15*t**2 - 20*t - 20. Determine d*b(z) + 20*w(z).\n | 5*z**2\n | ibivibiv/math_instruct | |
What is the value of -6 + (4 - 19) + (2 - -8)?\n | -11\n | ibivibiv/math_instruct | |
Suppose -s + 63 = 4*t, s + 4*t - 8*t - 95 = 0. Let y = s + -70. List the prime factors of y.\n | 3\n | ibivibiv/math_instruct | |
What is next in -11687, -11803, -11919?\n | -12035\n | ibivibiv/math_instruct | |
Three letters picked without replacement from {m: 1, p: 1, z: 1, i: 2, v: 1, d: 2}. What is prob of picking 1 v, 1 i, and 1 d?\n | 1/14\n | ibivibiv/math_instruct | |
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"# Theta theta cos theta
2/26/2011
cos(theta) = b / c. sec(theta) = 1 / cos(theta) = c / b. tan(theta) = sin(theta) / cos(theta) = a / b. cot(theta) = 1/ 6 Jun 2020 If x =a (cos theta +theta sin theta ), y =a (sin theta -t... | Let's delve into the world of trigonometry and explore some fundamental concepts, identities, and derivatives. Our starting point will be the function cos(θ), which is one of the six basic trigonometric functions. This function is defined as the ratio of the length of the adjacent side to the hypotenuse in a right tri... | ibivibiv/math_instruct | |
What is 7.323554 milligrams in grams?\n | 0.007323554\n | ibivibiv/math_instruct | |
Suppose -2*c - 7 = -h, -3*h + 28 = h - 3*c. Suppose -8*g + h*g = -11. Let y(m) = -m**2 - 7*m - 3. What is the lowest common multiple of y(-6) and g?\n | 33\n | ibivibiv/math_instruct | |
Let n(p) = p**3 + 14*p**2 + p - 10. Let q be n(-14). Let o = q - -38. What is the tens digit of o?\n | 1\n | ibivibiv/math_instruct | |
Let h(s) = -s**3 + 4*s**2 + s - 3. Suppose -3*d = 2*f - 12, 5*f - 25 = d - 6*d. Suppose 0 = -d*b + 3*b - 3. What are the prime factors of h(b)?\n | 3\n | ibivibiv/math_instruct | |
What is the hundreds digit of 9467016?\n | 0\n | ibivibiv/math_instruct | |
Put -5, -3, -1, 0, 4, -23, -96 in decreasing order.\n | 4, 0, -1, -3, -5, -23, -96\n | ibivibiv/math_instruct | |
b"What is the vth term of 1168, 1190, 1206, 1210, 1196, 1158?\n" | -v**3 + 3*v**2 + 20*v + 1146\n | ibivibiv/math_instruct | |
Calculate -2 - ((-63 - -27) + -28).\n | 62\n | ibivibiv/math_instruct | |
Suppose -33 = 57*n - 60*n. Let o(l) = 3*l - 31. Let m be o(n). Solve 0 = -w + 1 - m for w.\n | -1\n | ibivibiv/math_instruct | |
What is the value of -4 - ((-2 - -5) + -2)?\n | -5\n | ibivibiv/math_instruct | |
Convert 1a26 (base 12) to base 13.\n | 15c0\n | ibivibiv/math_instruct | |
Let x(k) = 7*k. Let v(i) = -25*i - 2. Determine v(x(y)).\n | -175*y - 2\n | ibivibiv/math_instruct | |
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"Base class for polyhedra over $$\ZZ$$¶
class sage.geometry.polyhedron.base_ZZ.Polyhedron_ZZ(parent, Vrep, Hrep, **kwds)
Base class for Polyhedra over $$\ZZ$$
Minkowski_decompositions(*args, **kwds)
Deprecated: Use minkows... | The `Polyhedron_ZZ` class is part of Sages geometry module and serves as the base class for all polyhedra over the integers ($\ZZ$). A polyhedron can be represented either by its vertices ($V_{rep}$) or its halfspaces and hyperplanes forming the facets ($H_{rep}$). This class uses these representations to create insta... | ibivibiv/math_instruct | |
List the prime factors of 24673.\n | 11, 2243\n | ibivibiv/math_instruct | |
Let o be ((-24)/(-9) - 3)/(3/(-54)). Let g(t) = -t**2 + 3*t - 4. Give g(o).\n | -22\n | ibivibiv/math_instruct | |
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"01.3-TrigDefns
# Basic Trigonometry Definitions
{“tri” =3, “gon” = angle, “metry” = measurement, so “trigonometry” = measurement of triangles}
Trigonometry is a fundamental part of many branches of science, engineering and... | Trigonometry, derived from the Greek words "tri," meaning three, "gon," meaning angles, and "metry," meaning measurement, is fundamentally the study and measurement of triangles. This branch of mathematics is essential in various fields including science, engineering, and technology due to its wide range of applicatio... | ibivibiv/math_instruct | |
What is the highest common factor of 4 and 1058?\n | 2\n | ibivibiv/math_instruct | |
What is the third derivative of b**3*d + 32738*b**3 - 48*b**2*d - 9*b**2 - 154*b*d wrt b?\n | 6*d + 196428\n | ibivibiv/math_instruct | |
Which is smaller: -69 or -3434522?\n | -3434522\n | ibivibiv/math_instruct | |
Suppose 3*n - 1047 = -27. Suppose -12*t + 13*t = 0, 0 = -5*r - 4*t + n. Let b = -50 - -119. Is b equal to r?\n | False\n | ibivibiv/math_instruct | |
Collect the terms in -546*g**2 + 1675*g**2 - 548*g**2 - 553*g**2.\n | 28*g**2\n | ibivibiv/math_instruct | |
Expand (24 - 24 - 4*n)*(-3 + 4 - 2).\n | 4*n\n | ibivibiv/math_instruct | |
What is the fifth biggest value in -9, -1/5, 0, -0.7, 0.5?\n | -9\n | ibivibiv/math_instruct | |
(40/16)/(10/12)\n | 3\n | ibivibiv/math_instruct | |
Rearrange i**2 + 1 + i - i**2 - 2*i**3 + 3*i**3 to s + m*i**2 + k*i**3 + j*i and give k.\n | 1\n | ibivibiv/math_instruct | |
What is -ba6bd9 (base 15) in base 6?\n | -514213440\n | ibivibiv/math_instruct | |
What is the result of the following expression?
-38.1966 * -9.753 | 372.5314 | ibivibiv/math_instruct | |
Collect the terms in -3*y**2 + y - y - y**2.\n | -4*y**2\n | ibivibiv/math_instruct | |
Suppose n - 5*c = 65, 0 = -2*n - n + c + 153. Let l be ((-9)/90)/((-47)/3760). Solve l*g = -2*g - n for g.\n | -5\n | ibivibiv/math_instruct | |
What is next in -1373, -2706, -4039?\n | -5372\n | ibivibiv/math_instruct | |
How many minutes are there between 12:34 AM and 11:49 AM?\n | 675\n | ibivibiv/math_instruct | |
Which is the smallest value? (a) -14.606 (b) 3 (c) 1/9 (d) -3/10 (e) -3 (f) 4 (g) 0\n | a\n | ibivibiv/math_instruct | |
Suppose 0 = -888*l + 898*l - 30. Determine n, given that 9/7*n**2 + 0 - 2/7*n - n**l = 0.\n | 0, 2/7, 1\n | ibivibiv/math_instruct | |
How many minutes are there between 4:49 AM and 11:33 AM?\n | 404\n | ibivibiv/math_instruct | |
Collect the terms in 18751*t + 73 - 18750*t - 73.\n | t\n | ibivibiv/math_instruct | |
Simplify -6*6*(-1*sqrt(84)/sqrt(2) - (sqrt(42) + sqrt(168) - sqrt(42))*-5)/(-3*(sqrt(384) + sqrt(384)*2 + sqrt(384))).\n | 27*sqrt(7)/8\n | ibivibiv/math_instruct | |
What are the prime factors of 5269345?\n | 5, 683, 1543\n | ibivibiv/math_instruct | |
Let o = 35638181224.200000627 + -35638181268. Let s = -43.8 - o. Round s to seven dps.\n | -0.0000006\n | ibivibiv/math_instruct | |
Differentiate 7*k**4*p**3 - k*p**3 + 187543*k + 29*p**3 - 853*p**2 + 41 with respect to k.\n | 28*k**3*p**3 - p**3 + 187543\n | ibivibiv/math_instruct | |
Let r be (2/7)/((-4)/(-28)). Which is bigger: r or 0.2?\n | r\n | ibivibiv/math_instruct | |
What is 20 minutes before 10:11 AM?\n | 9:51 AM\n | ibivibiv/math_instruct | |
Let g be 9/(-54) - (-1)/(-54)*-3. Which is the second biggest value? (a) 1 (b) g (c) -1 (d) 2/101\n | d\n | ibivibiv/math_instruct | |
Let h be 11 + -7 - 1054/1. Let j = h - -1571. Is j composite?\n | False\n | ibivibiv/math_instruct | |
Convert 1380947 (base 10) to base 12.\n | 5671ab\n | ibivibiv/math_instruct | |
What is the value of (-3 - (1 + -1)) + (130 - 135) - -36?\n | 28\n | ibivibiv/math_instruct | |
Sort 4, -9774, 16 in decreasing order.\n | 16, 4, -9774\n | ibivibiv/math_instruct | |
Suppose -3*v = 3*p - 1854, -6*v + 5*v = -2. What is the hundreds digit of p?\n | 6\n | ibivibiv/math_instruct | |
Three letters picked without replacement from {h: 2, y: 1, i: 1, r: 2}. What is prob of picking 1 r, 1 i, and 1 h?\n | 1/5\n | ibivibiv/math_instruct | |
In base 8, what is -2 - -5?\n | 3\n | ibivibiv/math_instruct | |
What is the third root of 9847779 to the nearest integer?\n | 214\n | ibivibiv/math_instruct | |
Sort 47, -1, -6 in ascending order.\n | -6, -1, 47\n | ibivibiv/math_instruct | |
How many minutes are there between 1:51 AM and 8:35 AM?\n | 404\n | ibivibiv/math_instruct | |
What is the next term in 132065, 261789, 391513, 521237?\n | 650961\n | ibivibiv/math_instruct |
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