instruction_seed stringlengths 5 2.9k | response_seed stringlengths 3 9.55k | input stringclasses 1
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|---|---|---|---|
Let n(d) = -d + 4. Let m be n(5). Suppose -11*s = -15 + 4. Put m, -2, s in ascending order.\n | -2, m, s\n | ibivibiv/math_instruct | |
Let k = -75084 + 74868.2104. Let m = -216 - k. Round m to two decimal places.\n | -0.21\n | ibivibiv/math_instruct | |
Suppose 405*g = 410*g - 20. Let r(l) = -30*l**3 - 4*l**2 + 3*l - 6. Let s be r(g). What is s rounded to the nearest 100?\n | -2000\n | ibivibiv/math_instruct | |
What is -10 + 11 + (-10 - -1)?\n | -8\n | ibivibiv/math_instruct | |
Suppose -9*r + 6*r + 84 = 0. What is the greatest common divisor of 70 and r?\n | 14\n | ibivibiv/math_instruct | |
What is -83 take away -0.0204?\n | -82.9796\n | ibivibiv/math_instruct | |
Let j(g) = -9*g + 654. What is j(72)?\n | 6\n | ibivibiv/math_instruct | |
What is the second smallest value in 433, 1, -0.5, 5, -1?\n | -0.5\n | ibivibiv/math_instruct | |
Let z = 6 + -1. Let j(b) = 6 - 7*b**2 - 5*b - z + 4 + 0*b**2. Let t(x) = -10*x**2 - 7*x + 7. Suppose -1 = -5*q - 26. What is q*t(r) + 7*j(r)?\n | r**2\n | ibivibiv/math_instruct | |
What is the thousands digit of 12824604?\n | 4\n | ibivibiv/math_instruct | |
What is the second derivative of 13544222*w**5 + 42401920*w wrt w?\n | 270884440*w**3\n | ibivibiv/math_instruct | |
Does 72 divide 3181?\n | False\n | ibivibiv/math_instruct | |
Calculate the remainder when 179 is divided by 62.\n | 55\n | ibivibiv/math_instruct | |
Total of -5 and -9005876.\n | -9005881\n | ibivibiv/math_instruct | |
Convert 627711 (base 15) to base 11.\n | 2709215\n | ibivibiv/math_instruct | |
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"# What other monoidal structures exist on the category of sets?
I know of the following monoidal structures over $\mathbf{Set}$ (taken from here):
• The Cartesian product $\otimes=\times$ (categorical product)
• The disjoin... | Monoidal structures on a category provide a way to combine objects and morphisms within that category while preserving its algebraic structure. When it comes to the category of sets, denoted as Set, several monoidal structures have been identified. This discussion will delve into these structures, their properties, an... | ibivibiv/math_instruct | |
Let z(g) = -98393*g + 5116439. Give z(52).\n | 3\n | ibivibiv/math_instruct | |
What is the cube root of 2798954 to the nearest integer?\n | 141\n | ibivibiv/math_instruct | |
Calculate the highest common divisor of 105248 and 13.\n | 13\n | ibivibiv/math_instruct | |
Let d = 5979/5 - 1192. Calculate the common denominator of d and 97/14.\n | 70\n | ibivibiv/math_instruct | |
How many months are there in 0.1837633 years?\n | 2.2051596\n | ibivibiv/math_instruct | |
Work out 1.7076 + 146968300.49.\n | 146968302.1976\n | ibivibiv/math_instruct | |
Expand (676*b**2 - 282*b**2 + 416*b**2)*(-4 + 6 - 4) - 6*b**2 + 2*b**2 + b**2.\n | -1623*b**2\n | ibivibiv/math_instruct | |
In base 12, what is -92 - 89?\n | -15b\n | ibivibiv/math_instruct | |
In base 9, what is -7307 - 8336?\n | -16644\n | ibivibiv/math_instruct | |
Let h = 6/5485 - -21898/38395. Which is bigger: 380 or h?\n | 380\n | ibivibiv/math_instruct | |
What is the third biggest value in 4.6, 2/13, -2/15, -1.2, -1?\n | -2/15\n | ibivibiv/math_instruct | |
Let c = 14738/5 + -2999. Which is greater: -51 or c?\n | -51\n | ibivibiv/math_instruct | |
What is 12938 to the power of 1/3, to the nearest integer?\n | 23\n | ibivibiv/math_instruct | |
Let u(q) be the first derivative of 17*q**2 - 221*q + 14. List the prime factors of u(18).\n | 17, 23\n | ibivibiv/math_instruct | |
What is 567574 to the power of 1/10, to the nearest integer?\n | 4\n | ibivibiv/math_instruct | |
Let b(n) = -9*n**3 - 2*n**2 + 3*n + 5. Let x be b(-3). Let a = x + -220. Solve -l - 4*w - 2 = -a, 3*w = 3 for l.\n | -5\n | ibivibiv/math_instruct | |
Let w be -6*(-2)/(-4)*-2. Suppose m = -x + 95, 4*x - 188 = -w*m + 4*m. Suppose -37*d - m = -40*d. Is 16 a factor of d?\n | True\n | ibivibiv/math_instruct | |
Let q(g) = -7*g + 47. Let s be q(9). What is the remainder when 87/(-58)*(s - 0/(-1)) is divided by 9?\n | 6\n | ibivibiv/math_instruct | |
Let s = -3 - -2. Let t be (0 - 0)/(s + 0). Let f(k) = -k + t*k - k. Let d(a) = 2*a**2. Give f(d(o)).\n | -4*o**2\n | ibivibiv/math_instruct | |
Is 17123506159 prime?\n | False\n | ibivibiv/math_instruct | |
Put -2, -2/9, -1/4, -2857/6, 5/3 in ascending order.\n | -2857/6, -2, -1/4, -2/9, 5/3\n | ibivibiv/math_instruct | |
Let n(i) = 974*i**3 - i**2 + 1. Let d be n(1). What is the common denominator of (-14)/(-77) + d/88 and 73/44?\n | 44\n | ibivibiv/math_instruct | |
Let d be 2/(-6)*26418/(-49). Let g = -180 + d. Let h be (-8)/15*(-12)/16. What is the third biggest value in h, g, 5/4?\n | g\n | ibivibiv/math_instruct | |
Solve -27*c = 3*s - 6*s + 675, 2*s = 3*c + 3*s - 6 + 81 for c.\n | -25\n | ibivibiv/math_instruct | |
What is the product of -3 and 59.8?\n | -179.4\n | ibivibiv/math_instruct | |
Let k = -1783 - -1783. Solve -3*g - 2*h - 1 = -7, k = -4*g + 5*h + 31 for g.\n | 4\n | ibivibiv/math_instruct | |
Let s be 58/14 + (-2)/(-56)*-4. Let z(i) = -5*i + 17. Give z(s).\n | -3\n | ibivibiv/math_instruct | |
Suppose -2*j + n + 425 = 0, 23*n - 21*n = -j + 200. What is the greatest common divisor of j and 30?\n | 30\n | ibivibiv/math_instruct | |
In base 3, what is -10012010011202 + -110?\n | -10012010012012\n | ibivibiv/math_instruct | |
Calculate the common denominator of -111/48680 and 25/776.\n | 4721960\n | ibivibiv/math_instruct | |
Let g = -47.1 - -40. Let f = -1.76 - g. Let b = f - 0.14. Round b to zero dps.\n | 5\n | ibivibiv/math_instruct | |
Rearrange (22 - 7*p + p - 15)*(-p**3 - 6*p**3 + 3*p**3) to k*p**4 + i*p + j*p**3 + t*p**2 + c and give k.\n | 24\n | ibivibiv/math_instruct | |
Let k = 12.6 - 15.36. Let f = k - -3.524. Let s = f + -0.7. Round s to two decimal places.\n | 0.06\n | ibivibiv/math_instruct | |
Let n(p) = -7*p - 2. Suppose 30 = 20*b - 15*b. Let h(d) = 8*d + 1. Let u(f) = b*n(f) + 5*h(f). Give u(-5).\n | 3\n | ibivibiv/math_instruct | |
Let c = 2.3 - 0.3. Let n = 170699/39 - 56904/13. What is the nearest to c in n, 3, 2/13?\n | 3\n | ibivibiv/math_instruct | |
Let a(q) = -3*q**2. Let y(p) = -6*p - 11. Determine y(a(r)).\n | 18*r**2 - 11\n | ibivibiv/math_instruct | |
Let j(o) = 2*o**2 + 2*o + 3. Suppose -3*q - 7 = 4*m, 0 = -4*m - 2*q - 2. Suppose m - 9 = -2*s + 3*h, 3*h + 5 = 4*s. Let u be -1 + -2 + s + 2. Calculate j(u).\n | 7\n | ibivibiv/math_instruct | |
Let k = -15 - -6. Let w be 22/6 - (-6)/k. Solve 4*c - 5*c - 1 = -3*x, 10 = w*c + 4*x for c.\n | 2\n | ibivibiv/math_instruct | |
Is -33665 at most -33663?\n | True\n | ibivibiv/math_instruct | |
Let n(c) be the third derivative of c**4/4 - 45*c**3/2 - 3018*c**2. Calculate n(18).\n | -27\n | ibivibiv/math_instruct | |
Rearrange -3*g + 0*g**4 + 1 + 8*g - 5*g**2 - g**4 - 3*g to the form l*g**4 + d*g**2 + n + a*g + t*g**3 and give n.\n | 1\n | ibivibiv/math_instruct | |
What is 39 minutes before 9:48 PM?\n | 9:09 PM\n | ibivibiv/math_instruct | |
b"What is the yth term of 122, 1019, 1928, 2855, 3806, 4787, 5804?\n" | y**3 + 890*y - 769\n | ibivibiv/math_instruct | |
Let k = 5 - 4. Is k*(49 - -2 - 2) prime?\n | False\n | ibivibiv/math_instruct | |
Suppose a = -2*i + 2, 2*i = -4*a + 11 + 3. Let x = 1224 - 1230. Sort a, x, -3 in decreasing order.\n | a, -3, x\n | ibivibiv/math_instruct | |
Suppose 0 = -2*z + z + 8. Let u = -67290 + 67292. Calculate the smallest common multiple of u and z.\n | 8\n | ibivibiv/math_instruct | |
Let m(j) = 3*j - 28. What is the lowest common multiple of 80 and m(12)?\n | 80\n | ibivibiv/math_instruct | |
Suppose m + 15*g - 17*g = -6, -5*g + 29 = m. Let t(w) = 2*w - 4. Let s be t(4). Suppose s*h = 12 + 4. Solve 8 = j + 2*a + 3*a, -m*a + 16 = -h*j for j.\n | -2\n | ibivibiv/math_instruct | |
Find q, given that q**5/5 - 1521*q**4/5 + 796847*q**3/5 - 166049359*q**2/5 + 11850573648*q/5 + 12017421376/5 = 0.\n | -1, 193, 568\n | ibivibiv/math_instruct | |
Factor -3*u**3 - 21552*u**2.\n | -3*u**2*(u + 7184)\n | ibivibiv/math_instruct | |
Expand (29183 - 29183 - 29*h - 57*h)*(6*h - 6 + 6) + 2*h - 2*h - 2*h**2.\n | -518*h**2\n | ibivibiv/math_instruct | |
Convert 0 (base 13) to base 2.\n | 0\n | ibivibiv/math_instruct | |
Calculate the common denominator of -115/29754 and -21/20.\n | 297540\n | ibivibiv/math_instruct | |
Let q = -9485 + 13377. What is the remainder when q is divided by 118?\n | 116\n | ibivibiv/math_instruct | |
Calculate the highest common divisor of 2925 and 150228.\n | 117\n | ibivibiv/math_instruct | |
Is 10912123 composite?\n | True\n | ibivibiv/math_instruct | |
Let p be (-2)/(-4) + (-75)/6. Let d = p - -26. Does 14 divide d?\n | True\n | ibivibiv/math_instruct | |
b"What is the rth term of -457, -148, 657, 1958?\n" | 248*r**2 - 435*r - 270\n | ibivibiv/math_instruct | |
Factor 0 + 1/2*f**5 - 5*f**2 + 6*f**3 - 3*f**4 + 3/2*f.\n | f*(f - 3)*(f - 1)**3/2\n | ibivibiv/math_instruct | |
What is 0.33381 rounded to one decimal place?\n | 0.3\n | ibivibiv/math_instruct | |
Let j(d) = -8*d**3 - d**2 - 3*d + 5. Let m(h) = -9*h**3 - h**2 - 3*h + 6. Calculate 6*j(f) - 5*m(f).\n | -3*f**3 - f**2 - 3*f\n | ibivibiv/math_instruct | |
Which is the fourth biggest value? (a) -17/417 (b) 1 (c) -0.5 (d) -1/5\n | c\n | ibivibiv/math_instruct | |
Suppose 200 = 14*w + 4. What is the lowest common multiple of w and 176?\n | 1232\n | ibivibiv/math_instruct | |
Suppose 3*d = -v + 644, -17*v + 20*v - 1932 = 3*d. What is the lowest common multiple of v and 9?\n | 5796\n | ibivibiv/math_instruct | |
Let w = 0.5 - -47.5. Let m = 17 - w. Let d = 30 + m. What is the closest to 3 in -0.3, d, -4/3?\n | -0.3\n | ibivibiv/math_instruct | |
Let w(o) = -2210*o**2 + 6641*o - 7. Calculate w(3).\n | 26\n | ibivibiv/math_instruct | |
Let r(t) = -t**2 + t - 4. Let x(h) = -2*h + 0 + 3*h - 5. Let d(c) = 5*r(c) - 4*x(c). Let n be -1 + 1 - (-3 + 2). What is d(n)?\n | -4\n | ibivibiv/math_instruct | |
Let z(o) be the first derivative of -2/3*o**3 + 0*o**2 + 49*o + 7/4*o**4 - 48. Differentiate z(t) with respect to t.\n | 21*t**2 - 4*t\n | ibivibiv/math_instruct | |
Convert 44013102 (base 5) to base 14.\n | 9b071\n | ibivibiv/math_instruct | |
Find the second derivative of -21290817*l**2 + 199*l - 71167 wrt l.\n | -42581634\n | ibivibiv/math_instruct | |
Let y(j) = 904*j**2 - 176*j - 1. Is y(-3) a composite number?\n | False\n | ibivibiv/math_instruct | |
Suppose -11 = -7*j + 17. Suppose -u + 4*x = 3*x - 10, j*u - 2*x = 30. Solve 0 = 2*y - d - u, -5*y = d + 2*d - 7 for y.\n | 2\n | ibivibiv/math_instruct | |
What is the highest common factor of 22875 and 4209?\n | 183\n | ibivibiv/math_instruct | |
Evaluate (7 - 1) + (-4 - -6) + -2.\n | 6\n | ibivibiv/math_instruct | |
Let w = -7 - -4. Let d = -143/261 + 3/29. Put d, -2/7, w in descending order.\n | -2/7, d, w\n | ibivibiv/math_instruct | |
Let m = -3 - -3. Let t(v) = -v**2 - 3*v**2 - 5*v + m*v**2 + v**3 + 2. What is the units digit of t(5)?\n | 2\n | ibivibiv/math_instruct | |
1122 (base 3) to base 13\n | 35\n | ibivibiv/math_instruct | |
Expand (-p + p + p)*(p**4 - p**4 - 2*p**4) + (208*p**2 - 121*p**2 - 110*p**2 + (-4*p + 3*p + 2*p)*(0 - 2*p + 0))*(-2*p**3 + 20*p - 20*p).\n | 48*p**5\n | ibivibiv/math_instruct | |
Suppose -4*x = -g - 14, -2*x + 1 = -3*g - 1. Let i = 5 - 3. Suppose -i*c + 9 = c. Calculate the remainder when c is divided by g.\n | 1\n | ibivibiv/math_instruct | |
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"# Let X 1 ,...,X n be i.i.d. continuous r.v.s with PDF f and a strictly increasing CDF F. Suppose... 1 answer below »
Let X1,...,Xn be i.i.d. continuous r.v.s with PDF f and a strictly increasing CDF F. Suppose that we know ... | Order statistics refer to the arrangement of a set of random variables from smallest to largest. When discussing the jth order statistic of a set of independent and identically distributed (i.i.d.) continuous random variables (r.v.s), denoted by X(j), it's helpful to consider the uniform distribution case first. Speci... | ibivibiv/math_instruct | |
Express b + 0 + 1 + 9*b - 27*b in the form c + a*b and give a.\n | -17\n | ibivibiv/math_instruct | |
List the prime factors of 1608888.\n | 2, 3, 43, 1559\n | ibivibiv/math_instruct | |
(-7 - -1) + -4 + 10\n | 0\n | ibivibiv/math_instruct | |
Let w(h) be the third derivative of h**8/20160 - h**5/10 + 2*h**2. Let p(z) be the third derivative of w(z). Let b(u) = 8*u. What is p(b(n))?\n | 64*n**2\n | ibivibiv/math_instruct |
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