instruction_seed stringlengths 5 2.9k | response_seed stringlengths 3 9.55k | input stringclasses 1
value | _source stringclasses 1
value |
|---|---|---|---|
Calculate the remainder when 140 is divided by 13.\n | 10\n | ibivibiv/math_instruct | |
Let t(i) be the first derivative of -10565*i**4/4 - 4084*i**2 - 5126. What is the second derivative of t(p) wrt p?\n | -63390*p\n | ibivibiv/math_instruct | |
Let h(b) = 2*b**2 + 18*b + 13. Give h(-12).\n | 85\n | ibivibiv/math_instruct | |
What is the derivative of -4*d**3*i + 336*d**3 + 14*d**2*i**2 - 10*d**2 - 17*d*i**2 + 2 wrt i?\n | -4*d**3 + 28*d**2*i - 34*d*i\n | ibivibiv/math_instruct | |
Let g(y) = 3*y - 3. Let h be 8*1 + -12*(-10)/(-20). Determine g(h).\n | 3\n | ibivibiv/math_instruct | |
What is the result of the following expression?
61.0954 - -79.1017 | 140.1971 | ibivibiv/math_instruct | |
Find the first derivative of -a*h**4 - 2*a - 1066*h**3 - 2*h + 339039 wrt h.\n | -4*a*h**3 - 3198*h**2 - 2\n | ibivibiv/math_instruct | |
What is 49 minutes after 9:40 AM?\n | 10:29 AM\n | ibivibiv/math_instruct | |
Is 416 a factor of 4872608?\n | True\n | ibivibiv/math_instruct | |
What is the thousands digit of 79505037?\n | 5\n | ibivibiv/math_instruct | |
What is the closest to 0 in -3/17, 1, 0.4?\n | -3/17\n | ibivibiv/math_instruct | |
Calculate prob of picking 1 w and 1 k when two letters picked without replacement from {a: 2, k: 2, m: 1, w: 1}.\n | 2/15\n | ibivibiv/math_instruct | |
Let w(l) = -5*l**3 + 2*l**2 - 2*l - 3. Let d be w(-1). What is the first derivative of -51 - 2*o**2 + 4*o**2 - 10*o**2 + d wrt o?\n | -16*o\n | ibivibiv/math_instruct | |
Suppose 3*i = -19*i + 72*i + 185*i. Let c(j) = j**3 - 2*j + 2. Calculate c(i).\n | 2\n | ibivibiv/math_instruct | |
Is 294911 prime?\n | True\n | ibivibiv/math_instruct | |
Which is greater: 2722216/51 or 53376?\n | 2722216/51\n | ibivibiv/math_instruct | |
In base 4, what is 0 - 201120?\n | -201120\n | ibivibiv/math_instruct | |
What is the tens digit of (-15)/(-2)*300/45?\n | 5\n | ibivibiv/math_instruct | |
What is the eighth root of 2438136299 to the nearest integer?\n | 15\n | ibivibiv/math_instruct | |
Let a(q) = 4*q + q + 0 - 8*q + 2 + 5*q. Suppose 3*s = 5*h + 32 - 5, 2*h - 2*s + 10 = 0. Give a(h).\n | -10\n | ibivibiv/math_instruct | |
Let i = -37 - -19. What is the tens digit of 2/((-57)/i - 3)?\n | 1\n | ibivibiv/math_instruct | |
Let u = 418 - 418. Solve p + 3 = -5*k, -5*p + 3*k - 7 - 8 = u for p.\n | -3\n | ibivibiv/math_instruct | |
Let x be (-56)/(-35) - (1 + (-7)/5). Suppose x*l + b - 951 + 76 = 0, 1302 = 3*l + 5*b. What is the tens digit of l?\n | 3\n | ibivibiv/math_instruct | |
What is the second biggest value in -5, 15, 1/47?\n | 1/47\n | ibivibiv/math_instruct | |
b"What is the qth term of 374, 353, 306, 221, 86?\n" | -2*q**3 - q**2 - 4*q + 381\n | ibivibiv/math_instruct | |
Factor -o**4/4 + 15907*o**3/4 + 47727*o**2/4 + 47729*o/4 + 7955/2.\n | -(o - 15910)*(o + 1)**3/4\n | ibivibiv/math_instruct | |
Let f = -41857 + 4185611/100. Find the common denominator of -21/100 and f.\n | 100\n | ibivibiv/math_instruct | |
What is the least common multiple of 240442 and 14?\n | 1683094\n | ibivibiv/math_instruct | |
Let t = 110 - 113. Let x(p) = 3*p**3 + 3*p - 3. Let r(z) = 3*z**3 + 2*z - 2. Give t*r(j) + 2*x(j).\n | -3*j**3\n | ibivibiv/math_instruct | |
Calculate 6160/22050 + 1*8/(-36).\n | 2/35\n | ibivibiv/math_instruct | |
Suppose -2*k = -2*g + 871160, -4*g + 434*k + 1742347 = 439*k. Is g prime?\n | True\n | ibivibiv/math_instruct | |
Suppose -30 = -6*v + 4*v. Suppose -35 - 20 = -2*h + 5*g, h - 2*g = 25. What is the greatest common divisor of v and h?\n | 15\n | ibivibiv/math_instruct | |
What is ((-4)/5)/((99/(-495))/(0 + 1))?\n | 4\n | ibivibiv/math_instruct | |
What is 636 minutes before 4:57 AM?\n | 6:21 PM\n | ibivibiv/math_instruct | |
Let z(r) = 7*r**2 - 2*r - 6. Calculate z(3).\n | 51\n | ibivibiv/math_instruct | |
Suppose -4*t = 3*a - 230, -3*a - 2*a - 4*t + 386 = 0. Is a a multiple of 26?\n | True\n | ibivibiv/math_instruct | |
Suppose 0 = p + 2 - 3, 3*c + 12 = 3*p. Let q be (-32)/c - 18/27. Suppose -3*o = -q*o + 42. Calculate the remainder when 11 is divided by o.\n | 5\n | ibivibiv/math_instruct | |
Let q = -11 + 23. What is the highest common divisor of 60 and q?\n | 12\n | ibivibiv/math_instruct | |
Suppose 2*z + 5*s = 4*z - 44, 5*z = -3*s + 110. Let m = -16 + z. What is the third derivative of 13*v**6 + 62*v - v**6 + m*v**2 - 62*v wrt v?\n | 1440*v**3\n | ibivibiv/math_instruct | |
b"What is the ath term of -427, -1728, -3959, -7174, -11427, -16772?\n" | -9*a**3 - 411*a**2 - 5*a - 2\n | ibivibiv/math_instruct | |
b"What is the rth term of 7155799, 7155784, 7155771, 7155760?\n" | r**2 - 18*r + 7155816\n | ibivibiv/math_instruct | |
Is 13 a factor of 3/(5 + -2)*117?\n | True\n | ibivibiv/math_instruct | |
Put 1/7, -0.7, -1, 0.2 in descending order.\n | 0.2, 1/7, -0.7, -1\n | ibivibiv/math_instruct | |
b"What is the hth term of 192, 187, 184, 171, 136, 67, -48, -221?\n" | -2*h**3 + 13*h**2 - 30*h + 211\n | ibivibiv/math_instruct | |
Calculate the highest common factor of 215 and 4085.\n | 215\n | ibivibiv/math_instruct | |
Collect the terms in 26*v - 6*v - 11*v + 6827*v**3 - 17*v + 8*v.\n | 6827*v**3\n | ibivibiv/math_instruct | |
Calculate 1247786948462 + -33.5.\n | 1247786948428.5\n | ibivibiv/math_instruct | |
95/9880*156*10/12*28/6\n | 35/6\n | ibivibiv/math_instruct | |
Rearrange -3*w + 2*w - 4*w**3 - 12 - 2 + 17 + w**2 to b + t*w**2 + l*w + o*w**3 and give l.\n | -1\n | ibivibiv/math_instruct | |
Suppose 0 = 53*k - 42*k - 8217. Let j = -268 + k. Is j a prime number?\n | True\n | ibivibiv/math_instruct | |
Let t = -54 - -84. Suppose 5*h - m + 17 + 10 = 0, -4*m = 3*h + t. Let a be (-40)/h + (-30)/45. Solve 7*u - a = 5*u for u.\n | 3\n | ibivibiv/math_instruct | |
Let q(f) = -f - 7. Let y be q(-9). Let c(d) = -d**2 - 4*d + 11. Let s be c(-5). What is the units digit of (s - -30) + (0 + -1)*y?\n | 4\n | ibivibiv/math_instruct | |
Let c(i) = -i**3 - 4*i**2 - 7*i - 6. Let z be c(-4). What is the highest common factor of 242 and z?\n | 22\n | ibivibiv/math_instruct | |
Suppose 2*q - 7 = 3*p + 8, p - 3*q + 5 = 0. Let o(f) be the third derivative of 0 + 0*f + 1/3*f**4 + 1/60*f**5 + 7/6*f**3 - f**2. Determine o(p).\n | -8\n | ibivibiv/math_instruct | |
Suppose m - 3 = -0. Let s(d) = -d**3 + 5*d**2 - 3*d - 3. Let h be s(m). Let l be (-2 + (2 - 0))/1. Solve h = -l*q - 2*q for q.\n | -3\n | ibivibiv/math_instruct | |
Factor 2*o**2/15 + 175420*o + 2631298/15.\n | 2*(o + 1)*(o + 1315649)/15\n | ibivibiv/math_instruct | |
Collect the terms in -890 + 9*c**3 - 892 + 1782.\n | 9*c**3\n | ibivibiv/math_instruct | |
Divide -7 by 54.\n | -7/54\n | ibivibiv/math_instruct | |
Suppose 260 - 50 = -2*w. Let c = w - -363. Suppose -3*g = -5*j - 160, -4*j - c = -4*g - g. Calculate the remainder when g is divided by 17.\n | 16\n | ibivibiv/math_instruct | |
How many minutes are there between 3:06 PM and 9:45 PM?\n | 399\n | ibivibiv/math_instruct | |
Suppose s + 0*s = -c + 110, -5*s = -4*c - 595. Is s prime?\n | False\n | ibivibiv/math_instruct | |
Three letters picked without replacement from {n: 2, c: 1, g: 3, m: 4}. Give prob of picking 2 g and 1 m.\n | 1/10\n | ibivibiv/math_instruct | |
Suppose -4*z + 8 = 0, 2*z = -2*i + 4*i. Find b such that -8/7 + 2*b**3 + 40/7*b - 46/7*b**i = 0.\n | 2/7, 1, 2\n | ibivibiv/math_instruct | |
What is the closest to -0.1 in -0.1, -0.5, 2/27, 4?\n | -0.1\n | ibivibiv/math_instruct | |
Suppose 0*f - 215 = -3*t - 2*f, 287 = 4*t + 3*f. Suppose 5*z + d = -3*d + 135, -5*d + t = 2*z. What is the greatest common divisor of 92 and z?\n | 23\n | ibivibiv/math_instruct | |
What is (2/3)/((-1470)/63 - -25)?\n | 2/5\n | ibivibiv/math_instruct | |
Calculate 37 + -21 + 1 + -9 + 17.\n | 25\n | ibivibiv/math_instruct | |
Which is the fourth smallest value? (a) 580 (b) 1/3 (c) -0.1 (d) 2/5\n | a\n | ibivibiv/math_instruct | |
Let t be (-21030870)/(-21031170) + (0 - 0) + -1. Let y = -207531994/1714040355 - t. Let g = 2/163 - y. What is the biggest value in -2/17, -4, g?\n | g\n | ibivibiv/math_instruct | |
Let 4*u**3 - 103797408*u**2 + 673368973017300*u - 1346737530845000 = 0. Calculate u.\n | 2, 12974675\n | ibivibiv/math_instruct | |
Let g = -17 - -22. What is the fourth smallest value in g, 3, 1/4, 0.1?\n | g\n | ibivibiv/math_instruct | |
Is 1354664651 a prime number?\n | True\n | ibivibiv/math_instruct | |
Write an educational piece suited for college students related to the following text snippet:
"# Proving $e^{\binom{n}{2}}>n!$
Prove that $$e^{\binom{n}{2}}>n!$$
$n \in \mathbb{Z_+}$
Sorry, couldn't attempt it.
• It will have to be $n \in \mathbb{Z}_+$, not $\mathbb{Z}$. – Jeppe Stig Nielsen Aug 11 '13 at 14:10
• I... | To prove that $e^\binom{n}{2}>n!$ for all positive integers $n$, we can employ several mathematical concepts, including the definition of the exponential function, factorials, and binomial coefficients. We will present these concepts rigorously and guide you through their connections to ultimately establish the desire... | ibivibiv/math_instruct | |
What is the difference between 1.0113579 and 0.29?\n | 0.7213579\n | ibivibiv/math_instruct | |
Round -155.31 to the nearest 10.\n | -160\n | ibivibiv/math_instruct | |
Let h(k) = 8*k - 44. Determine h(8).\n | 20\n | ibivibiv/math_instruct | |
In base 10, what is 4 - 991257?\n | -991253\n | ibivibiv/math_instruct | |
30% of all fishermen in Piscataquis County are also hunters while only 20% of all hunters are fishermen. If there are 1500 hunters in Piscataquis County then how many fishermen are there?
Answer Choices: (A) 800 (B) 1000 (C) 1200 (D) 1500 (E) 1800 Please respond by writing a program in Python. | hunters = 1500
# 20% of all hunters are fishermen
fishermen_from_hunters = 0.20 * hunters
# 30% of all fishermen are also hunters, so fishermen_from_hunters is 30% of total fishermen
total_fishermen = fishermen_from_hunters / 0.30
print(total_fishermen) | ibivibiv/math_instruct | |
What is 1024318 to the power of 1/3, to the nearest integer?\n | 101\n | ibivibiv/math_instruct | |
Is 22951337 a multiple of 6?\n | False\n | ibivibiv/math_instruct | |
Is 465278977 prime?\n | True\n | ibivibiv/math_instruct | |
Let a(u) be the third derivative of u**5/15 - 2*u**3/3 + 11*u**2. Factor a(l).\n | 4*(l - 1)*(l + 1)\n | ibivibiv/math_instruct | |
Let g be 2730/(-1092)*(-2)/(-5)*-116. What is the highest common divisor of 13108 and g?\n | 116\n | ibivibiv/math_instruct | |
What is 663 minutes before 7:44 PM?\n | 8:41 AM\n | ibivibiv/math_instruct | |
Solve 22*n + 1338176*x + 52 = 1338171*x, -3*x - 84 = 0 for n.\n | 4\n | ibivibiv/math_instruct | |
Solve -314*v + 3977 = -19*v + 437 for v.\n | 12\n | ibivibiv/math_instruct | |
How many minutes are there between 9:30 AM and 1:56 PM?\n | 266\n | ibivibiv/math_instruct | |
Two letters picked without replacement from srrj. Give prob of sequence jr.\n | 1/6\n | ibivibiv/math_instruct | |
Let r(q) = -q**2 + 20*q + 38. What is r(-9)?\n | -223\n | ibivibiv/math_instruct | |
How many micrometers are there in 527.8577km?\n | 527857700000\n | ibivibiv/math_instruct | |
Let h(u) = u**3 + u**2 + u. Let d = 155 - 154. Let k(o) = -3*o**3 - 4*o**2 - 2*o. Determine d*k(a) + 2*h(a).\n | -a**3 - 2*a**2\n | ibivibiv/math_instruct | |
Solve 3*q + 16 = 5*s, -q = -3*s + 8 - 0 for s.\n | 2\n | ibivibiv/math_instruct | |
In Javiers household, which consists of Javier, his wife, and 3 children, as well as 2 dogs and 1 cat, how many legs are there in total? | Javier and his wife have 2 legs each, so they have a total of 2 x 2 = 4 legs.
Each child has 2 legs, so the 3 children have a total of 3 x 2 = 6 legs.
Each dog has 4 legs, so the 2 dogs have a total of 2 x 4 = 8 legs.
The cat has 4 legs.
Therefore, in total, there are 4 + 6 + 8 + 4 = 22 legs in Javiers household.
#### ... | ibivibiv/math_instruct | |
What is the fifth smallest value in -7, -1/8, 0.3, -1.6, 2?\n | 2\n | ibivibiv/math_instruct | |
Solve -97*y + 693 = 176 - 356 for y.\n | 9\n | ibivibiv/math_instruct | |
What is 0 times 0.22?\n | 0\n | ibivibiv/math_instruct | |
Let r(s) = s**3 + 8*s**2 + 21*s + 27. Let k be r(-10). Let l = k + 828. What are the prime factors of l?\n | 5, 89\n | ibivibiv/math_instruct | |
What are the prime factors of 67305021?\n | 3, 7, 61, 52541\n | ibivibiv/math_instruct | |
What is the ten thousands digit of 11287625?\n | 8\n | ibivibiv/math_instruct | |
Evaluate -13 + 10 + -4 + (2 - 0 - -1).\n | -4\n | ibivibiv/math_instruct |
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