instruction_seed stringlengths 5 2.9k | response_seed stringlengths 3 9.55k | input stringclasses 1
value | _source stringclasses 1
value |
|---|---|---|---|
Calculate the remainder when 32332 is divided by 20.\n | 12\n | ibivibiv/math_instruct | |
Which is the nearest to -25? (a) -28 (b) 42 (c) 2/3 (d) -2\n | a\n | ibivibiv/math_instruct | |
What is 313 minutes before 3:41 AM?\n | 10:28 PM\n | ibivibiv/math_instruct | |
Put -7, 5, 2, -58 in descending order.\n | 5, 2, -7, -58\n | ibivibiv/math_instruct | |
What is the value of (15/70)/(13/(-52))?\n | -6/7\n | ibivibiv/math_instruct | |
What is the second derivative of r**3*v + 11*r**3 - 1815*r**2*v - 8*r**2 - 394*r*v - r + 2*v - 3520 wrt r?\n | 6*r*v + 66*r - 3630*v - 16\n | ibivibiv/math_instruct | |
What is 21.381 rounded to 1 decimal place?\n | 21.4\n | ibivibiv/math_instruct | |
Let k(z) be the third derivative of 0 - 5/3*z**3 - 2*z**2 + 11/24*z**4 + 0*z. Let u be k(2). Is 14 greater than u?\n | True\n | ibivibiv/math_instruct | |
Collect the terms in -4*b + 5*b - 12*b - 2*b.\n | -13*b\n | ibivibiv/math_instruct | |
Let g = -0.5 - 0. Let q = -0.4 + 3. Let p = q - 0.6. What is the biggest value in g, 3/2, p?\n | p\n | ibivibiv/math_instruct | |
Three letters picked without replacement from {c: 1, s: 1, v: 2}. Give prob of picking 1 c, 1 s, and 1 v.\n | 1/2\n | ibivibiv/math_instruct | |
What is 1500 (base 7) in base 11?\n | 495\n | ibivibiv/math_instruct | |
What comes next: 8237383, 8237384, 8237385?\n | 8237386\n | ibivibiv/math_instruct | |
Let r = 68 + -64. Solve -5*y + 2*y + 4*a = -r, 2*y + 4*a = 16 for y.\n | 4\n | ibivibiv/math_instruct | |
What are the prime factors of 3879?\n | 3, 431\n | ibivibiv/math_instruct | |
Let x(w) be the third derivative of 8*w**7/35 - 157*w**6/210 - 46*w**5/105 + 26*w**4/21 - 16*w**3/21 - 353*w**2. What is t in x(t) = 0?\n | -2/3, 1/4, 2/7, 2\n | ibivibiv/math_instruct | |
List the prime factors of 20320.\n | 2, 5, 127\n | ibivibiv/math_instruct | |
Suppose 3*k = 6*k - 6. Suppose -19 = -k*f - 9. What is the units digit of f?\n | 5\n | ibivibiv/math_instruct | |
What is the third root of 54656318 to the nearest integer?\n | 380\n | ibivibiv/math_instruct | |
Suppose a group of 10 farmers share a common grazing land of 100 acres. Each farmer maximizes their profit by maximizing the number of cattle they graze on the land. The maximum number of cattle that each farmer can graze is 20, and each additional cow grazed by a farmer reduces their profit by $10. The cost of maintai... | Lets denote the number of cattle grazed by each farmer as xi, where i = 1, 2, ..., 10. The total number of cattle grazed on the land is the sum of the cattle grazed by each farmer, which can be represented as X = x1 + x2 + ... + x10.
The profit of each farmer i can be represented as:
Profit_i = 20xi - 10(xi)^2 - 10
... | ibivibiv/math_instruct | |
What is 19.93 rounded to the nearest ten?\n | 20\n | ibivibiv/math_instruct | |
Let x(q) = -25*q**2 + 2*q - 11. Let u(f) = 12*f**2 - f + 5. Let b(d) = 13*u(d) + 6*x(d). Let m be b(-1). Let i = m + -1. Is 3 a factor of i?\n | False\n | ibivibiv/math_instruct | |
Divide -785 by -6.\n | 785/6\n | ibivibiv/math_instruct | |
Let l(u) = 12*u**2 + 23*u + 27. What is l(-1)?\n | 16\n | ibivibiv/math_instruct | |
Is 161 a factor of 1624926?\n | False\n | ibivibiv/math_instruct | |
Let q = -74 - -74. Suppose 13*i - 16*i = q. Let y be (-65 + i)/(-5) + 1. Calculate the greatest common factor of 28 and y.\n | 14\n | ibivibiv/math_instruct | |
Let k(i) = -912*i - 1630. Does 10 divide k(-6)?\n | False\n | ibivibiv/math_instruct | |
Simplify ((-5 + 5*(sqrt(32) + 0 - sqrt(2)))*-3 - ((sqrt(108)/sqrt(3))/sqrt(2))/(3*(sqrt(45)/sqrt(5) - sqrt(9)) - sqrt(9) - sqrt(9)))**2.\n | -1335*sqrt(2) + 8371/2\n | ibivibiv/math_instruct | |
Calculate -73107907 + -0.256.\n | -73107907.256\n | ibivibiv/math_instruct | |
Do -4018 and -4018 have different values?\n | False\n | ibivibiv/math_instruct | |
Does 9 divide 830538?\n | True\n | ibivibiv/math_instruct | |
Solve -4*o = 7*r - 77, 22*o - 592 = 39*r - 38*r - 129 for r.\n | -1\n | ibivibiv/math_instruct | |
Let b(o) = o**3 - 136*o**2 + 398*o + 244. Give b(133).\n | 111\n | ibivibiv/math_instruct | |
How many micrograms are there in fifty-five halves of a milligram?\n | 27500\n | ibivibiv/math_instruct | |
Sort -4, -5, 0.2, 5, -1 in ascending order.\n | -5, -4, -1, 0.2, 5\n | ibivibiv/math_instruct | |
Round 0.02209684846 to four dps.\n | 0.0221\n | ibivibiv/math_instruct | |
Calculate the greatest common factor of 2080958 and 484.\n | 242\n | ibivibiv/math_instruct | |
What is the closest to -115 in 8, 4, -1, 5?\n | -1\n | ibivibiv/math_instruct | |
-1 (base 6) to base 16\n | -1\n | ibivibiv/math_instruct | |
What is (-2)/1*2/(-12)?\n | 1/3\n | ibivibiv/math_instruct | |
Let y = 50 - 47. Suppose -y*j = -0 - 15. Solve 0 = j*x - 6 - 9 for x.\n | 3\n | ibivibiv/math_instruct | |
Let g(s) be the first derivative of s**6/90 - 26*s**3/3 - 35. Let j(z) be the third derivative of g(z). Let q(b) = 68*b**2 + 62*b**2 - 125*b**2. Give q(j(h)).\n | 80*h**4\n | ibivibiv/math_instruct | |
Solve 17049*w = 16986*w - 5272 + 1240 for w.\n | -64\n | ibivibiv/math_instruct | |
Four letters picked without replacement from {o: 4, j: 7, b: 4, p: 3}. What is prob of picking 2 j and 2 p?\n | 7/340\n | ibivibiv/math_instruct | |
Collect the terms in -7578762*p + 2 - 86 + 3789378*p + 3789386*p.\n | 2*p - 84\n | ibivibiv/math_instruct | |
Let r = -3502 - -7184. Calculate the highest common factor of 14 and r.\n | 14\n | ibivibiv/math_instruct | |
Let i(p) = -2*p**3 - 14*p**2 + 10*p - 45. Let m be i(-8). Solve -m*f + 6*n - n = 13, 2*f - 18 = -2*n for f.\n | 4\n | ibivibiv/math_instruct | |
What is the lowest common multiple of 28 and 102724?\n | 719068\n | ibivibiv/math_instruct | |
Let x = -0.1 + 0.2. Which is the closest to -2? (a) x (b) -0.3 (c) -1/5\n | b\n | ibivibiv/math_instruct | |
b"What is the wth term of -20775, -20864, -20949, -21030, -21107, -21180, -21249?\n" | 2*w**2 - 95*w - 20682\n | ibivibiv/math_instruct | |
Suppose -3*m + 115 = 139. Let c(l) = -l**2 - 9*l + 22. Let v be c(m). Is 2 equal to v?\n | False\n | ibivibiv/math_instruct | |
Sort -239, 5, -14971.\n | -14971, -239, 5\n | ibivibiv/math_instruct | |
Calculate the greatest common divisor of 13425 and 52575.\n | 75\n | ibivibiv/math_instruct | |
Let d(b) = -20*b + 33. Let r(m) = -m + 3. Let l(g) = 2*d(g) - 22*r(g). Let u(t) = -9*t**2. Calculate l(u(x)).\n | 162*x**2\n | ibivibiv/math_instruct | |
Let p(j) = 7*j - 12. Let u(r) be the second derivative of r**2/2 - 3*r. Let g(f) = -p(f) - 4*u(f). Let w(o) = -68 - 82 - 8*o + 230 - 71. Give -7*g(k) + 6*w(k).\n | k - 2\n | ibivibiv/math_instruct | |
Solve -1136*x - 4*i = -1134*x, -438*x + 2616 = 4*i for x.\n | 6\n | ibivibiv/math_instruct | |
-9073982 (base 10) to base 11\n | -5138465\n | ibivibiv/math_instruct | |
b"What is the hth term of 18, 85, 190, 333, 514, 733, 990?\n" | 19*h**2 + 10*h - 11\n | ibivibiv/math_instruct | |
Is 4847 composite?\n | True\n | ibivibiv/math_instruct | |
Suppose 0 = 5*a - 16 - 4. Is (-1266)/a*(-2)/3 composite?\n | False\n | ibivibiv/math_instruct | |
Solve 85*h + h + 32 = 32 for h.\n | 0\n | ibivibiv/math_instruct | |
Let w be 3 - 2/(-6)*0. Suppose d = -5*g + 40, w*g - d = 14 + 10. Calculate the remainder when g is divided by 5.\n | 3\n | ibivibiv/math_instruct | |
Sort 0.4, -1/3, -13/4, 0.02, 5620 in decreasing order.\n | 5620, 0.4, 0.02, -1/3, -13/4\n | ibivibiv/math_instruct | |
Is 193 a factor of 117291359?\n | False\n | ibivibiv/math_instruct | |
What is -12753.696 rounded to the nearest one hundred?\n | -12800\n | ibivibiv/math_instruct | |
What is the derivative of 157*t**2*y**3 + 19*t**2 - 7*t*y - t + 328749*y**3 wrt t?\n | 314*t*y**3 + 38*t - 7*y - 1\n | ibivibiv/math_instruct | |
What is (-2)/(60/(-68) + (-10)/85)?\n | 2\n | ibivibiv/math_instruct | |
Evaluate (1 + (-12)/(-4))*1/(-4).\n | -1\n | ibivibiv/math_instruct | |
Suppose 0 + 10 = 5*n. Suppose 0 = 2*i - n*x + 2, 4*x - 4 = -i - 0*i. Suppose 2*j - 5 = s, -j = -s - 0 - 1. Solve 3*v + s = -i*v for v.\n | -1\n | ibivibiv/math_instruct | |
Is 41629 bigger than 41631?\n | False\n | ibivibiv/math_instruct | |
Let k(b) = 2*b**2 - 174*b + 1573. Determine k(77).\n | 33\n | ibivibiv/math_instruct | |
Suppose -3*j + 43 = -0*j - v, -4*v = 4*j - 52. Let w be j/6 - 7/21. Let b = w - 4. Which is smaller: b or -1?\n | b\n | ibivibiv/math_instruct | |
Calculate the greatest common factor of 451 and 41063.\n | 11\n | ibivibiv/math_instruct | |
Let o(a) = -a. Let v be (-2)/(-4) + 7/2. Let s(b) = -11*b**2. Let p(k) = -11*k**2. Suppose -51*n = -63*n - 60. Let g(f) = n*s(f) + v*p(f). What is g(o(z))?\n | 11*z**2\n | ibivibiv/math_instruct | |
b"What is the kth term of 38, 74, 110, 146?\n" | 36*k + 2\n | ibivibiv/math_instruct | |
What is the sixth root of 190743635 to the nearest integer?\n | 24\n | ibivibiv/math_instruct | |
In base 12, what is 34b2a7 + -5?\n | 34b2a2\n | ibivibiv/math_instruct | |
Which is the closest to 0.05? (a) -1/11 (b) 2/3 (c) -1/5 (d) -3\n | a\n | ibivibiv/math_instruct | |
Evaluate (250/(-20))/((-15)/3 - (-420)/96).\n | 20\n | ibivibiv/math_instruct | |
Sort 0.0668, 4, -2/7, 1/5.\n | -2/7, 0.0668, 1/5, 4\n | ibivibiv/math_instruct | |
Calculate the remainder when 149 is divided by -5 + 33 + ((-18)/2 - -3).\n | 17\n | ibivibiv/math_instruct | |
Let l(q) = -12106*q + 12163. What is l(1)?\n | 57\n | ibivibiv/math_instruct | |
What is the next term in -2487, -3763, -5889, -8865, -12691, -17367?\n | -22893\n | ibivibiv/math_instruct | |
Let s be (-1)/(-9) + (-78)/(-27). Is 3*((3 - s) + (-2179)/(-3)) prime?\n | True\n | ibivibiv/math_instruct | |
Let a(g) = 246*g + 64. Let k(m) = 2*m + 16. Let r(u) = a(u) - 4*k(u). Let h(y) = -15*y**2. Give h(r(q)).\n | -849660*q**2\n | ibivibiv/math_instruct | |
What is 25/2 of a millimeter in micrometers?\n | 12500\n | ibivibiv/math_instruct | |
Three letters picked without replacement from pfmlpflptfllllpppt. What is prob of picking 1 l, 1 f, and 1 p?\n | 9/68\n | ibivibiv/math_instruct | |
Factor v**2/5 + 22634*v/5 - 113295.\n | (v - 25)*(v + 22659)/5\n | ibivibiv/math_instruct | |
Suppose 3*p = 6*p - 3. Suppose 3*d = 2*d + p. Let f(t) = 1. Let z(k) = k + 7. Let m(q) = 2*q + 14. Let j(x) = 2*m(x) - 5*z(x). Determine d*j(g) + 6*f(g).\n | -g - 1\n | ibivibiv/math_instruct | |
Which is the third biggest value? (a) 22/3 (b) -36 (c) 0 (d) 23\n | c\n | ibivibiv/math_instruct | |
Put 3, -381046, 1, -2, 2, 5 in decreasing order.\n | 5, 3, 2, 1, -2, -381046\n | ibivibiv/math_instruct | |
Round 9615719 to the nearest 10000.\n | 9620000\n | ibivibiv/math_instruct | |
Suppose -5*h - 8 - 7 = 0. Let p = -0.26 - -0.06. Which is the biggest value? (a) p (b) 5 (c) h\n | b\n | ibivibiv/math_instruct | |
Expand (4 + 3*o**2 - 4)*(5 + 0 - 4)*(39 + 19*o - 39).\n | 57*o**3\n | ibivibiv/math_instruct | |
How many minutes are there between 8:04 PM and 12:04 AM?\n | 240\n | ibivibiv/math_instruct | |
Three letters picked without replacement from {b: 1, m: 8, q: 3, x: 3, i: 5}. What is prob of picking 1 b, 1 x, and 1 m?\n | 2/95\n | ibivibiv/math_instruct | |
Write an educational piece suited for college students related to the following text snippet:
"# 1R: Chapter 1 Review Exercises
True or False? Justify your answer with a proof or a counterexample.
1) A function is always one-to-one.
2) $$f∘g=g∘f$$, assuming $$f$$ and $$g$$ are functions.
False
3) A relation that ... | Let's delve into the exciting world of mathematics by exploring the review exercises from Chapter 1. We will cover various essential topics, including functions, domains and ranges, polynomials, and trigonometry.
A function need not always be one-to-one; this property depends upon how the function is defined. For exa... | ibivibiv/math_instruct | |
Rearrange -4 + 2 - i**2 - 4*i**3 + 0*i**4 + i**4 to o*i + q + l*i**4 + b*i**2 + y*i**3 and give l.\n | 1\n | ibivibiv/math_instruct | |
Let z = 10367.407 - 10456.3. Let k = 0.107 - z. Put -0.4, k, 2 in increasing order.\n | -0.4, 2, k\n | ibivibiv/math_instruct | |
Express -w**4 + w**3 - w**3 + (4 - 1 - 2)*(-3*w**4 + 0*w**4 + 0*w**4) + 45*w**4 + 905*w**2 - 905*w**2 in the form h + d*w**2 + z*w + k*w**3 + l*w**4 and give l.\n | 41\n | ibivibiv/math_instruct |
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