instruction_seed stringlengths 5 2.9k | response_seed stringlengths 3 9.55k | input stringclasses 1
value | _source stringclasses 1
value |
|---|---|---|---|
Find the common denominator of -41/2936 and 17/8.\n | 2936\n | ibivibiv/math_instruct | |
Does 63 divide 4410?\n | True\n | ibivibiv/math_instruct | |
Simplify (k/(k*k*k/(k**(-38)*k)))/(k*k**4) assuming k is positive.\n | k**(-44)\n | ibivibiv/math_instruct | |
Two letters picked without replacement from {m: 1, w: 1, z: 1, p: 1, y: 1}. Give prob of sequence mp.\n | 1/20\n | ibivibiv/math_instruct | |
Let i(c) = -6*c + 25*c - 5*c - 13*c + 99. Let x(d) = 2*d**2. Determine i(x(a)).\n | 2*a**2 + 99\n | ibivibiv/math_instruct | |
What is 430194 to the power of 1/7, to the nearest integer?\n | 6\n | ibivibiv/math_instruct | |
Let j(h) = h + 11. Let p = 60 - 43. List the prime factors of j(p).\n | 2, 7\n | ibivibiv/math_instruct | |
Calculate the least common multiple of 7 and 29234536.\n | 204641752\n | ibivibiv/math_instruct | |
Let x = -279931/14 - -19995. Sort x, 4, 20 in descending order.\n | 20, 4, x\n | ibivibiv/math_instruct | |
Suppose 3*p + 12 - 32 = -5*n, 3*n - 6 = -3*p. Suppose -n + 28 = 7*x. Let c = 3 + 2. Solve -j - c*h = j + 6, -4*j - 12 = -x*h for j.\n | -3\n | ibivibiv/math_instruct | |
Two letters picked without replacement from tettgetteggtg. What is prob of picking 1 t and 1 e?\n | 3/13\n | ibivibiv/math_instruct | |
Let g(b) = -80*b - 28*b + 1 + 7 + 13*b. Let z = -923 + 921. What is the hundreds digit of g(z)?\n | 1\n | ibivibiv/math_instruct | |
What are the prime factors of 3106?\n | 2, 1553\n | ibivibiv/math_instruct | |
Find the first derivative of -37211*m*x**2 + 4*m*x + 11609537*m + 53*x**2 wrt x.\n | -74422*m*x + 4*m + 106*x\n | ibivibiv/math_instruct | |
b"What is the qth term of -299, -615, -935, -1259, -1587, -1919?\n" | -2*q**2 - 310*q + 13\n | ibivibiv/math_instruct | |
Let n = -3552 - -3566. Suppose q + 2*x - 377 = 0, -q + 1134 = 2*q + 3*x. Find the second derivative of n*h - 379 + 17*h**2 + q wrt h.\n | 34\n | ibivibiv/math_instruct | |
Suppose 3*d - 310 = -5*z, 0 = 2*d + 3*z - 0*z - 207. What is the smallest common multiple of d and 300?\n | 2100\n | ibivibiv/math_instruct | |
Let d(t) = 6*t**2 - 118*t + 193. Determine d(18).\n | 13\n | ibivibiv/math_instruct | |
What is the value of 264/64*8/20*(-15)/(-55)*2?\n | 9/10\n | ibivibiv/math_instruct | |
List the prime factors of 20282515.\n | 5, 11, 368773\n | ibivibiv/math_instruct | |
Solve x + 4*b + 11 = 0, 4*x + 826*b - 825*b = 16 for x.\n | 5\n | ibivibiv/math_instruct | |
What is 595095 to the power of 1/3, to the nearest integer?\n | 84\n | ibivibiv/math_instruct | |
Are -35747 and -35747 equal?\n | True\n | ibivibiv/math_instruct | |
Let h(k) = -k**3 - 4*k**2 - 7*k - 4. Let p be h(-4). Suppose -2 + 131 = 5*o - 4*n, n = -o + p. List the prime factors of o.\n | 5\n | ibivibiv/math_instruct | |
What is the highest common divisor of 54 and 126?\n | 18\n | ibivibiv/math_instruct | |
Solve -100*k + 97*k = 3*l + 15, -k + 3 = -l for l.\n | -4\n | ibivibiv/math_instruct | |
Suppose 0 = w - 3, -w + 10 = 3*a - 11. Suppose -a*o - 2*o = 0. Let c = 29 + -59/2. Is c at least as big as o?\n | False\n | ibivibiv/math_instruct | |
Rearrange 293395*x - 139448*x - 137014*x to the form l*x + g and give l.\n | 16933\n | ibivibiv/math_instruct | |
What is the second derivative of 2*a**5 + 39*a**3 + 77*a**2 + 1050*a - 3?\n | 40*a**3 + 234*a + 154\n | ibivibiv/math_instruct | |
What is the greatest common divisor of 11 and 11?\n | 11\n | ibivibiv/math_instruct | |
Let k(b) = -35986*b + 611605. Calculate k(17).\n | -157\n | ibivibiv/math_instruct | |
Express -3*l - l + 5*l - 1 + 8*l + 7*l - 5*l + (-2 + 6 - 2)*(-17*l + 30*l - 12*l)*(-6 + 2 + 0) in the form g + m*l and give m.\n | 3\n | ibivibiv/math_instruct | |
How many litres are there in 0.463253 millilitres?\n | 0.000463253\n | ibivibiv/math_instruct | |
What is the hundreds digit of 14805?\n | 8\n | ibivibiv/math_instruct | |
Let l(j) = -j + 9. Let b be l(9). Let t be 0 + -1 - (-2 + b). Let z be t*(1 - (-4)/2). Solve -z*d + 0*d = 0 for d.\n | 0\n | ibivibiv/math_instruct | |
Let h = 318 + 2255. What is the units digit of h?\n | 3\n | ibivibiv/math_instruct | |
Three letters picked without replacement from txxzttttttxtxxttf. What is prob of picking 3 t?\n | 3/17\n | ibivibiv/math_instruct | |
Let h(j) = -4*j**3 - 4*j**2 - 2*j + 3. Let l(v) = -v**3. Let f(m) = -h(m) + 2*l(m). Let a(p) = p - 1. Determine 2*a(i) - f(i).\n | -2*i**3 - 4*i**2 + 1\n | ibivibiv/math_instruct | |
What is the value of (1/6)/(304/23712)?\n | 13\n | ibivibiv/math_instruct | |
Simplify (k/k**(2/7)*k)/k*(k/((k/(k/(k**(25/4)/k))*k)/k)*k)/k*(k**2)**(-4/39) assuming k is positive.\n | k**(-4085/1092)\n | ibivibiv/math_instruct | |
Write an educational piece suited for college students related to the following text snippet:
"# Periodic Orbit property
A topological space $X$ satisfies "Periodic orbit property", briefly POP, if for every continuous map
$f:X \to X$, there exist a natural number $n$ and a point $x_{0}\in X$ such that $f^{n}(x_{0})=... | Let us begin by discussing the concept of a topological space satisfying the Periodic Orbit Property (POP). A topological space $X$ has this property if for every continuous map $f: X o X$, there exists a natural number $n$ and a point $x\_0 o X$ such that $f^n(x\_0)=x\_0$. This means that under any continuous functi... | ibivibiv/math_instruct | |
Put -2/661, -67, 3, -5, 16/77 in descending order.\n | 3, 16/77, -2/661, -5, -67\n | ibivibiv/math_instruct | |
Let c = 2/13 - -7/39. Let l = -4205.5 - -4206. What is the second smallest value in c, -156, l?\n | c\n | ibivibiv/math_instruct | |
Let t(w) be the third derivative of -w**5/15 + 5*w**4/12 + 187*w**3/6 - 93*w**2. What is the first derivative of t(r) wrt r?\n | -8*r + 10\n | ibivibiv/math_instruct | |
What is 158792299 to the power of 1/4, to the nearest integer?\n | 112\n | ibivibiv/math_instruct | |
Suppose 0 = 5*j + 4*p - 506, 3*j + 15*p - 286 = 17*p. What is the smallest common multiple of j and 84?\n | 588\n | ibivibiv/math_instruct | |
Find the third derivative of 498630682*q**6 - 338155284*q**2.\n | 59835681840*q**3\n | ibivibiv/math_instruct | |
What is prob of picking 4 v when four letters picked without replacement from vvvvvv?\n | 1\n | ibivibiv/math_instruct | |
Let o = 31714 - 31714. Solve 0 = 3*h + 4*q - 6, 4*h + 4*q + o = 4 for h.\n | -2\n | ibivibiv/math_instruct | |
Simplify (z**(-2/7)*z*z/z**(-6)*(z**(-1)*z)/z**(-2/19))**(2/171) assuming z is positive.\n | z**(2080/22743)\n | ibivibiv/math_instruct | |
Let l(n) = 371*n. Let r(c) = 9082 - 14*c - 4542 - 23*c - 4540. Calculate 2*l(m) + 21*r(m).\n | -35*m\n | ibivibiv/math_instruct | |
What are the prime factors of 392483481?\n | 3, 13, 1667, 6037\n | ibivibiv/math_instruct | |
Round 0.000384961564 to four dps.\n | 0.0004\n | ibivibiv/math_instruct | |
Let h(t) be the third derivative of t**6/720 + t**5/40 + 5*t**4/24 + t**3/3 + 55*t**2. Let q(o) be the second derivative of h(o). Calculate q(5).\n | 8\n | ibivibiv/math_instruct | |
Let o = -37 + 35. Let h = 7 + o. Solve -h*w - 20 = -w for w.\n | -5\n | ibivibiv/math_instruct | |
What is 145432 to the power of 1/3, to the nearest integer?\n | 53\n | ibivibiv/math_instruct | |
Is 45447 a multiple of 2?\n | False\n | ibivibiv/math_instruct | |
What are the prime factors of 2665174022?\n | 2, 7, 190369573\n | ibivibiv/math_instruct | |
Rearrange 13*x - 3*x - x to l + b*x and give b.\n | 9\n | ibivibiv/math_instruct | |
Solve -4*r - z = -4, -107 + 119 = 3*z for r.\n | 0\n | ibivibiv/math_instruct | |
Let h = 21084/13 - 1410561/871. Is 3 at most h?\n | False\n | ibivibiv/math_instruct | |
Calculate 33222400 divided by -320.\n | -103820\n | ibivibiv/math_instruct | |
Let g = 38329911/2198 - -258012/157. Let y = g + -19090. What is the common denominator of y and 103/10?\n | 70\n | ibivibiv/math_instruct | |
Let d be (0 - 3) + (-18)/(-6). Suppose 1217 - 305 = 3*r + 4*n, -r + n + 297 = d. Is r a multiple of 25?\n | True\n | ibivibiv/math_instruct | |
Simplify -2 + 3 + (sqrt(99) + sqrt(99) + sqrt(99)*-1)**2 - ((-4 + sqrt(99) - sqrt(11)) + (-2*sqrt(11) + -2 - sqrt(11)) + sqrt(11))**2.\n | 64\n | ibivibiv/math_instruct | |
Let s be 3064/56 - (1 - 27/21). Is s < 56?\n | True\n | ibivibiv/math_instruct | |
Let g(v) = -4*v**3 + 35*v**2 - 97*v - 12. What is g(5)?\n | -122\n | ibivibiv/math_instruct | |
What are the prime factors of 2108?\n | 2, 17, 31\n | ibivibiv/math_instruct | |
Let y(d) = d**2 - 5*d - 2. Let m be y(5). Let r be m/6 - 2/6. Let u = -17.8 + 20.8. Sort u, r, 0 in descending order.\n | u, 0, r\n | ibivibiv/math_instruct | |
Suppose 0 = -6*i - 15*i + i + 1680. Solve -h = -15*h - i for h.\n | -6\n | ibivibiv/math_instruct | |
Let t(z) = 6*z - 1. Let g(h) = h**2 - 2*h - 11. Let i be g(4). Calculate t(i).\n | -19\n | ibivibiv/math_instruct | |
Calculate the lowest common multiple of 766 and 12.\n | 4596\n | ibivibiv/math_instruct | |
What is the value of -3 - ((-12 - -6) + 5)?\n | -2\n | ibivibiv/math_instruct | |
Which is bigger: 48/19 or 4?\n | 4\n | ibivibiv/math_instruct | |
What is the difference between -14010897968 and 31?\n | 14010897999\n | ibivibiv/math_instruct | |
Solve -678*n = 173 - 3244 + 17309 for n.\n | -21\n | ibivibiv/math_instruct | |
In base 16, what is 1 - e3ee?\n | -e3ed\n | ibivibiv/math_instruct | |
What is the thousands digit of 4420?\n | 4\n | ibivibiv/math_instruct | |
What are the prime factors of 74342855?\n | 5, 1951, 7621\n | ibivibiv/math_instruct | |
What is 96 minutes before 9:31 PM?\n | 7:55 PM\n | ibivibiv/math_instruct | |
Let b = -37 + 61. Suppose -4 = 5*o - 3*s + 15, b = -4*o - 2*s. Sort o, 3, 0 in increasing order.\n | o, 0, 3\n | ibivibiv/math_instruct | |
Suppose -u + 6 = 3*r, 2 - 7 = -3*u + 4*r. Let z be (4/(-10))/(1/(-5)). Sort 0, u, z in increasing order.\n | 0, z, u\n | ibivibiv/math_instruct | |
Three letters picked without replacement from {e: 3, a: 5}. What is prob of sequence eea?\n | 5/56\n | ibivibiv/math_instruct | |
What is 0.00345257 rounded to 3 dps?\n | 0.003\n | ibivibiv/math_instruct | |
Simplify sqrt(25)/(-3*sqrt(5)) + sqrt(45)/(sqrt(36) + sqrt(9)) + sqrt(5).\n | sqrt(5)\n | ibivibiv/math_instruct | |
Calculate the remainder when 1794951 is divided by 652.\n | 647\n | ibivibiv/math_instruct | |
Collect the terms in -16*v**2 + 101*v - 101*v.\n | -16*v**2\n | ibivibiv/math_instruct | |
Suppose 16*l = 13*l - 1479. Let z = -98 - l. Is z a composite number?\n | True\n | ibivibiv/math_instruct | |
Which is the third smallest value? (a) 4 (b) -1.32 (c) 10 (d) -13\n | a\n | ibivibiv/math_instruct | |
Sort -373, -20, -2724.\n | -2724, -373, -20\n | ibivibiv/math_instruct | |
b"What is the sth term of 1045, 2156, 3269, 4384?\n" | s**2 + 1108*s - 64\n | ibivibiv/math_instruct | |
Two letters picked without replacement from pphfffhfphdhmeddehh. What is prob of picking 2 p?\n | 1/57\n | ibivibiv/math_instruct | |
What is the common denominator of 65/465032 and -55/994?\n | 231120904\n | ibivibiv/math_instruct | |
Let s = 5.38 - 2.98. Let w = -1.4 + s. Which is the third biggest value? (a) 4 (b) -3 (c) w (d) 0\n | d\n | ibivibiv/math_instruct | |
What is 458 minutes before 4:14 AM?\n | 8:36 PM\n | ibivibiv/math_instruct | |
Divide -15176 by 1.\n | -15176\n | ibivibiv/math_instruct | |
Collect the terms in -15*n**2 - 15*n**2 - 6*n**2.\n | -36*n**2\n | ibivibiv/math_instruct | |
What is next in 811, 930, 1071, 1246, 1467, 1746?\n | 2095\n | ibivibiv/math_instruct | |
Let h(u) = u**2 - 7*u - 1. Let q(a) be the second derivative of 0*a**3 + 3 - 2*a**3 + 0*a**3 + a**3 - 3*a. Give 2*h(z) - 3*q(z).\n | 2*z**2 + 4*z - 2\n | ibivibiv/math_instruct | |
Let v = 0.01 + -3.31. Let z = -10.6 - -13.5. Let j = z + v. Put j, 1/9, -7 in ascending order.\n | -7, j, 1/9\n | ibivibiv/math_instruct |
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