instruction_seed stringlengths 5 2.9k | response_seed stringlengths 3 9.55k | input stringclasses 1
value | _source stringclasses 1
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|---|---|---|---|
Let v(d) = 562*d**2 - 50*d - 12. Let q(k) = 337*k**2 - 29*k - 7. Determine -12*q(j) + 7*v(j).\n | -110*j**2 - 2*j\n | ibivibiv/math_instruct | |
Two letters picked without replacement from {f: 4, p: 6, z: 4, j: 4}. Give prob of sequence jz.\n | 8/153\n | ibivibiv/math_instruct | |
Let q(l) = -11*l**2. Let o(z) = 9*z**2. Give q(o(t)).\n | -891*t**4\n | ibivibiv/math_instruct | |
Let i be (2/8)/(-12*(-9)/3024). Suppose -i = 7*r - 0*r. Let d(b) = -b + 5. Let k(q) = 1. Let f(h) = 2*d(h) - 9*k(h). Calculate f(r).\n | 3\n | ibivibiv/math_instruct | |
Expand ((0 - 2*q + 0)*(-7 - 3 + 0) - q - 5*q + 5*q)*(6 + 5 - 5).\n | 114*q\n | ibivibiv/math_instruct | |
Two letters picked without replacement from zxxcyz. Give prob of picking 2 z.\n | 1/15\n | ibivibiv/math_instruct | |
Factor 3*b**2 + 924681*b + 44377776.\n | 3*(b + 48)*(b + 308179)\n | ibivibiv/math_instruct | |
Let t(k) = 3*k - 10*k + 8*k. Let f(s) = -13*s - 2. Calculate t(f(n)).\n | -13*n - 2\n | ibivibiv/math_instruct | |
Suppose -10*x - 21 = -211. Suppose g - 29 = 5*t, 2*g = 2*t + x - 1. What is h in -8/9*h**g - 2/9*h**5 - 8/9*h**2 - 4/3*h**3 - 2/9*h + 0 = 0?\n | -1, 0\n | ibivibiv/math_instruct | |
What is the value of (-819)/(-234)*(-12)/7?\n | -6\n | ibivibiv/math_instruct | |
Let w(k) be the second derivative of -k**4/6 - k**3 - 5*k**2/2 + 3544*k. Let t(b) = -b**2 - 7*b - 6. What is -3*t(m) + 4*w(m)?\n | -5*m**2 - 3*m - 2\n | ibivibiv/math_instruct | |
How many nanometers are there in 1790.323 millimeters?\n | 1790323000\n | ibivibiv/math_instruct | |
Do -1 and -37/70 have different values?\n | True\n | ibivibiv/math_instruct | |
Suppose 2*g - g - 26 = 0. Let t be g - 25 - (-1 + 15). Let a = t + 17. Solve -a*k - 7 = m - 6*m, 5*k + 20 = -5*m for m.\n | -1\n | ibivibiv/math_instruct | |
Let t(j) be the first derivative of -j**4/4 - j**3/3 + j**2/2 + 3*j - 10. Give t(0).\n | 3\n | ibivibiv/math_instruct | |
Which is bigger: -3/425 or -1?\n | -3/425\n | ibivibiv/math_instruct | |
Which is the nearest to 28? (a) 5/3 (b) -1/317 (c) -9 (d) 2.1 (e) -1/2\n | d\n | ibivibiv/math_instruct | |
Evaluate -2 + -20 - (-12 - (23 + -44) - 11).\n | -20\n | ibivibiv/math_instruct | |
What is 251 minutes before 8:40 AM?\n | 4:29 AM\n | ibivibiv/math_instruct | |
Let k = 245.16 - 169.16. What is the third biggest value in -9, k, -2?\n | -9\n | ibivibiv/math_instruct | |
Sort 206.6, -2, 10/8609.\n | -2, 10/8609, 206.6\n | ibivibiv/math_instruct | |
b"What is the th term of -2, 58, 178, 388, 718?\n" | 5*b**3 + 25*b - 32\n | ibivibiv/math_instruct | |
Let x(l) = -1413*l**2 - 1596*l. Let g(v) = -353*v**2 - 399*v. Let z(c) = 18*g(c) - 4*x(c). Find the second derivative of z(r) wrt r.\n | -1404\n | ibivibiv/math_instruct | |
b"What is the yth term of -3316, -4017, -4702, -5365, -6000?\n" | y**3 + 2*y**2 - 714*y - 2605\n | ibivibiv/math_instruct | |
Let q = 12441.1628 + -12446.1628043. Let k = 11 + -6. Let c = q + k. Round c to six dps.\n | -0.000004\n | ibivibiv/math_instruct | |
Suppose 22*o - 2761 + 165 = 0. Suppose -3*y - o = -3*j - 733, j - 213 = -y. Is 211 smaller than y?\n | False\n | ibivibiv/math_instruct | |
Let n = -0.9 + 1.4. Let l be -2 - ((-27)/(-12))/(-1). Let f = 0.27 + 0.03. Sort n, f, l in descending order.\n | n, f, l\n | ibivibiv/math_instruct | |
Does 22 divide 194?\n | False\n | ibivibiv/math_instruct | |
Let v = -41.034 + 41. Let s = 4366.066 - 4359. Let q = s - v. Round q to zero decimal places.\n | 7\n | ibivibiv/math_instruct | |
Let o = 99 - -50. Suppose 2*v + 2*f + 106 = 6*v, 0 = -5*v - 3*f + o. What is the remainder when 220 is divided by v?\n | 24\n | ibivibiv/math_instruct | |
Let g = 93/28 - 15/4. Which is the closest to -1/2? (a) 0.5 (b) -1 (c) g\n | c\n | ibivibiv/math_instruct | |
Let q = 16 + -16. Which is smaller: 2 or q?\n | q\n | ibivibiv/math_instruct | |
Sort 3, -445, -25, 376 in ascending order.\n | -445, -25, 3, 376\n | ibivibiv/math_instruct | |
Suppose -3*y = -3*n - 13 + 1, y - 2 = -n. Let i be ((-1)/(-1))/(1/595). Suppose 7 + 2 = y*p, -s + i = 4*p. Is s a prime number?\n | False\n | ibivibiv/math_instruct | |
List the prime factors of 2364.\n | 2, 3, 197\n | ibivibiv/math_instruct | |
Let s(n) = n**2 - 2*n + 2. Suppose 7*b - 3 = 18. Give s(b).\n | 5\n | ibivibiv/math_instruct | |
When a train travels at a speed of 100 kmph, it reaches the destination on time. When the same train travels at a speed of 50 kmph, it reaches its destination late. The length of the journey is 15 km. How many minutes late does the train reach its destination when traveling at 50 kmph? | First, let's calculate the time it takes for the train to reach the destination when it travels at 100 kmph.
Speed = Distance / Time
Time = Distance / Speed
Time at 100 kmph = 15 km / 100 kmph = 0.15 hours
Now, lets calculate the time it takes for the train to reach the destination when it travels at 50 kmph.
Time ... | ibivibiv/math_instruct | |
Let m(v) = v. Let r(z) = -z - 5. Let i be 5 - 1/1 - -1. Let b(g) = 0 - g - i - 1. Let h(x) = 5*b(x) - 6*r(x). Determine h(m(u)).\n | u\n | ibivibiv/math_instruct | |
Is 91984829 a composite number?\n | False\n | ibivibiv/math_instruct | |
Write an educational piece suited for college students related to the following text snippet:
"# Is it possible that a left coset of $H$ contains more than one right coset of $H$?
Let $H$ be a subgroup of group $G$.
Is it possible that a left coset of $H$ contains more than one right coset of $H$?
It is clear to me ... | Let us begin by defining some terms and laying out important concepts. A group \(G\) consists of a set of elements together with a binary operation that combines any two of its elements to form a third element in such a way that four conditions called group axioms are satisfied. One fundamental aspect of group theory ... | ibivibiv/math_instruct | |
Let h(q) = -4*q**2 - 7*q + 1. Determine h(-5).\n | -64\n | ibivibiv/math_instruct | |
What comes next: 1, 18, 53, 112, 201?\n | 326\n | ibivibiv/math_instruct | |
9c40 (base 15) to base 5\n | 2030020\n | ibivibiv/math_instruct | |
Let d(w) = -11*w + 1. Suppose -3*l - 12 = 5*x - 0, 0 = -3*l + 5*x + 18. Calculate d(l).\n | -10\n | ibivibiv/math_instruct | |
Let v(x) = -x**2 + 12*x - 15. Give v(10).\n | 5\n | ibivibiv/math_instruct | |
Let x(l) = -l**3 - 2*l**2 + l - 2. Let b(z) = -7*z**2 - 3 + 4*z - 2*z**3 - 3 - 1. Let p(s) = -2*b(s) + 7*x(s). Find the second derivative of p(f) wrt f.\n | -18*f\n | ibivibiv/math_instruct | |
What is the third biggest value in -157, -4, 81?\n | -157\n | ibivibiv/math_instruct | |
Which is the second smallest value? (a) 8/5 (b) -0.2 (c) -2/3 (d) 7564\n | b\n | ibivibiv/math_instruct | |
Simplify b**(-1/4)*b/b**6*b*b**(2/7)/(b/b**(-3)) assuming b is positive.\n | b**(-223/28)\n | ibivibiv/math_instruct | |
Simplify (sqrt(1053) + sqrt(1053) + (sqrt(1053) - ((sqrt(1053) - (sqrt(1053) + -1 + sqrt(1053) + sqrt(1053))) + -2)) + 1*sqrt(1053)*-1)*-6.\n | -216*sqrt(13) - 6\n | ibivibiv/math_instruct | |
Calculate the remainder when 9587 is divided by 35.\n | 32\n | ibivibiv/math_instruct | |
Let b be (2 + -1)*1*-1. Let m = -5699/660 + 12/55. Find the common denominator of m and (b*85)/(28/2).\n | 84\n | ibivibiv/math_instruct | |
What is the square root of 19950983 to the nearest integer?\n | 4467\n | ibivibiv/math_instruct | |
Collect the terms in 3*b + 75*b**2 - 76*b**2 - 3*b.\n | -b**2\n | ibivibiv/math_instruct | |
Suppose 3*h - 4*j - 25 + 21 = 0, 0 = -3*h - 3*j - 24. Let i = -2 + 4. Let q(g) = 3*g**2 - 4*g - 2*g - 5*g**i. What is q(h)?\n | -8\n | ibivibiv/math_instruct | |
In seven years, Talia will be 20 years old. Talia's mom is currently three times as old as Talia is today. In three years, Talia's father will be the same age as Talia's mom is today. Currently, how many years old is Talias father? | In seven years, Talia will be 20 years old, so currently she is 20 - 7 = 13 years old.
Talia's mom is currently three times as old as Talia is today, so her mom is 13 * 3 = 39 years old.
In three years, Talia's father will be the same age as Talia's mom is today, so in three years, Talia's father will be 39 years old.
... | ibivibiv/math_instruct | |
Let p(u) be the first derivative of u**3/3 - 6. Let w(j) = 33*j**2. Give w(p(a)).\n | 33*a**4\n | ibivibiv/math_instruct | |
What is the common denominator of -91/50 and -99/328720?\n | 1643600\n | ibivibiv/math_instruct | |
Simplify (o**(-2)*o*o/o**(-2))**12 assuming o is positive.\n | o**24\n | ibivibiv/math_instruct | |
Which is greater: 982 or 981?\n | 982\n | ibivibiv/math_instruct | |
What is 322 minutes before 2:57 PM?\n | 9:35 AM\n | ibivibiv/math_instruct | |
Sort 0.5, 0.7, 2.1 in ascending order.\n | 0.5, 0.7, 2.1\n | ibivibiv/math_instruct | |
Let w(d) = 2*d**2 - 12*d - 15. Let t be w(6). Let k be (748/6)/((t/18)/(-5)). Suppose 2*r - 1 = 3, 0 = -5*i + r + k. Does 30 divide i?\n | True\n | ibivibiv/math_instruct | |
Suppose 0 = 5*i - 0*i - 25. Let k(a) = a**2 + a + 25. Let c be k(0). Suppose t - c = -5. Calculate the highest common factor of t and i.\n | 5\n | ibivibiv/math_instruct | |
Suppose -2*z + 4*z - 96 = 0. Suppose -r + z = r. Suppose -27*s + r*s + 711 = 0. Is s composite?\n | True\n | ibivibiv/math_instruct | |
Which is the smallest value? (a) -29 (b) 0.4 (c) 4 (d) -1/4\n | a\n | ibivibiv/math_instruct | |
Let o = -392.1787 - -392.07970082. Let r = 0.099 + o. What is r rounded to seven decimal places?\n | 0.0000008\n | ibivibiv/math_instruct | |
Let d(g) = 9*g + 7. Let u be d(6). Let v = u - 19. Let s(q) = -q + 28. Let y be s(0). What is the greatest common divisor of v and y?\n | 14\n | ibivibiv/math_instruct | |
Let m(g) = 10*g**2. Let z be (1 - (-18 + 5))*80/28. Let a(p) be the first derivative of 0*p + 0*p**2 - 1/3*p**3 + z. Give a(m(f)).\n | -100*f**4\n | ibivibiv/math_instruct | |
What are the prime factors of 100310?\n | 2, 5, 7, 1433\n | ibivibiv/math_instruct | |
Let k = 18 + -11. Suppose 3*c - k*c = -16. Calculate the remainder when 14 is divided by c.\n | 2\n | ibivibiv/math_instruct | |
Let l = 3/4199 + -911195/16796. Let h = l - -54. Which is the nearest to h? (a) -3 (b) 5 (c) 4\n | a\n | ibivibiv/math_instruct | |
What is the third derivative of 14*d**4*l**3 - 2*d**4 + 62*d**2*l**3 + 2*d*l**3 wrt d?\n | 336*d*l**3 - 48*d\n | ibivibiv/math_instruct | |
Four letters picked without replacement from {q: 14, t: 5}. What is prob of sequence qttt?\n | 35/3876\n | ibivibiv/math_instruct | |
What are the prime factors of 1199509959?\n | 3, 399836653\n | ibivibiv/math_instruct | |
Is 10468643 prime?\n | False\n | ibivibiv/math_instruct | |
Does 104 divide 13331?\n | False\n | ibivibiv/math_instruct | |
Let r(x) be the first derivative of 5*x**8/336 - x**6/24 + 15*x**2/2 - 20. Let f(o) be the second derivative of r(o). Factor f(a).\n | 5*a**3*(a - 1)*(a + 1)\n | ibivibiv/math_instruct | |
Which is smaller: 3 or -192?\n | -192\n | ibivibiv/math_instruct | |
Let k(g) = -163*g**2 + 10929*g - 38. Determine k(67).\n | 498\n | ibivibiv/math_instruct | |
What is the result of the following expression?
(81.0259 * -39.5754) / (15.6055 + 43.8177) | -53.9626 | ibivibiv/math_instruct | |
Evaluate 29 + (8 + 4 - 36 - -13).\n | 18\n | ibivibiv/math_instruct | |
In base 8, what is 10 + 4002?\n | 4012\n | ibivibiv/math_instruct | |
Let k(c) = -3 - 4*c + 5 - 1. Suppose s + 3 = 2*t - 2, 5*s + 13 = 4*t. Let w be k(s). Solve -5*j + 7 - 2 = -5*m, 1 = -w*m + j for m.\n | 0\n | ibivibiv/math_instruct | |
Calculate -2095 divided by -5.\n | 419\n | ibivibiv/math_instruct | |
Let j = -4666 + 10721. What is the hundreds digit of j?\n | 0\n | ibivibiv/math_instruct | |
Is 404 at least as big as 404?\n | True\n | ibivibiv/math_instruct | |
What are the prime factors of 54306972?\n | 2, 3, 37, 40771\n | ibivibiv/math_instruct | |
Let i(c) = c + 15. Let j = 118 - 113. What is the remainder when j is divided by i(-11)?\n | 1\n | ibivibiv/math_instruct | |
Is 120 at most -756?\n | False\n | ibivibiv/math_instruct | |
Let x(y) = 6*y + 6. Let n(h) = -h - 1. Let f(l) = -5*n(l) - x(l). Let w be (-1)/3 + (-50)/30. Let k(c) = -11 + 6 + 5 - 1. Calculate w*k(r) + f(r).\n | -r + 1\n | ibivibiv/math_instruct | |
Let j(x) be the first derivative of -17*x**2 - 28*x + 9. Find the first derivative of j(t) wrt t.\n | -34\n | ibivibiv/math_instruct | |
Let h(i) = i**2 + 8*i + 12. Let w be h(-6). Solve w*x - u - 17 = 4*x, -7 = -x + 2*u for x.\n | -3\n | ibivibiv/math_instruct | |
Collect the terms in -2 + 24029*g**2 + 24044*g**2 - 48034*g**2.\n | 39*g**2 - 2\n | ibivibiv/math_instruct | |
Sort -2064, 5619, -3.\n | -2064, -3, 5619\n | ibivibiv/math_instruct | |
What is the second derivative of -336 + 3627*x**3 - 134 + 474 + 1556*x wrt x?\n | 21762*x\n | ibivibiv/math_instruct | |
List the prime factors of 46749999.\n | 3, 83, 187751\n | ibivibiv/math_instruct | |
Calculate the remainder when 3582346 is divided by 2.\n | 0\n | ibivibiv/math_instruct | |
Product of 38.12 and -5.\n | -190.6\n | ibivibiv/math_instruct | |
b"What is the ith term of 1369809, 1369805, 1369797, 1369785, 1369769?\n" | -2*i**2 + 2*i + 1369809\n | ibivibiv/math_instruct |
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