instruction_seed stringlengths 5 2.9k | response_seed stringlengths 3 9.55k | input stringclasses 1
value | _source stringclasses 1
value |
|---|---|---|---|
Which is the nearest to -23717? (a) -5 (b) 5 (c) 1.8 (d) -0.3\n | a\n | ibivibiv/math_instruct | |
Rearrange -3 + 6*b**2 + 31*b**3 - 62*b**3 + 30*b**3 - 2 to the form d*b**3 + v*b**2 + g*b + w and give d.\n | -1\n | ibivibiv/math_instruct | |
What is -4304 plus 3?\n | -4301\n | ibivibiv/math_instruct | |
What is the ten thousands digit of 40357?\n | 4\n | ibivibiv/math_instruct | |
What is the smallest common multiple of ((0 - -1) + (-72)/99)/((-12)/(-132)) and 156?\n | 156\n | ibivibiv/math_instruct | |
Simplify sqrt(637) - (sqrt(637) + -1 + 2)**2 - (2 + sqrt(637) + 0 + sqrt(637))**2.\n | -3190 - 63*sqrt(13)\n | ibivibiv/math_instruct | |
What is prob of picking 1 q and 1 j when two letters picked without replacement from jjjjjiqjjqqqiq?\n | 5/13\n | ibivibiv/math_instruct | |
Which is smaller: 7895035 or 7894889?\n | 7894889\n | ibivibiv/math_instruct | |
What is the product of -3 and -37?\n | 111\n | ibivibiv/math_instruct | |
Let p = 6 - 2. Let z(d) = 3*d**2 + 3*d + 2*d + 0*d - 3 - d**3. Determine z(p).\n | 1\n | ibivibiv/math_instruct | |
Let p = 10 - 8. Suppose -3*f = -86 + 11. Let y = f + -21. Solve -3*z - p = y for z.\n | -2\n | ibivibiv/math_instruct | |
What is 181 minutes before 4:25 AM?\n | 1:24 AM\n | ibivibiv/math_instruct | |
((-504)/27)/14*2/8*(-9225)/(-41)\n | -75\n | ibivibiv/math_instruct | |
Let n = -22 + 157. Let o = -134.758 + n. Round o to 2 decimal places.\n | 0.24\n | ibivibiv/math_instruct | |
Factor 6*h**3/17 - 900778*h**2/17 + 33808225090*h/17 + 11269508450/17.\n | 2*(h - 75065)**2*(3*h + 1)/17\n | ibivibiv/math_instruct | |
Solve -4*i - 3*m - 499 + 398 = 0, 4*m - 2*m - 851 = 29*i for i.\n | -29\n | ibivibiv/math_instruct | |
Let x(d) = 433 - 213 - 220 + d. Let v(b) = -314*b. Give v(x(w)).\n | -314*w\n | ibivibiv/math_instruct | |
Let p = -485 - -495. Solve -u = -p + 9 for u.\n | 1\n | ibivibiv/math_instruct | |
Differentiate 6089908*t - 9833380 wrt t.\n | 6089908\n | ibivibiv/math_instruct | |
Three letters picked without replacement from {u: 3, d: 6, i: 2, e: 2}. Give prob of sequence udu.\n | 3/143\n | ibivibiv/math_instruct | |
Work out -3938.986 - -0.02.\n | -3938.966\n | ibivibiv/math_instruct | |
Suppose 0 - 33 = -3*w. Solve -2*t - w = -1 for t.\n | -5\n | ibivibiv/math_instruct | |
What is the lowest common multiple of 1346064 and 87?\n | 1346064\n | ibivibiv/math_instruct | |
What comes next: 580, 2181, 4848, 8569, 13332, 19125?\n | 25936\n | ibivibiv/math_instruct | |
Convert -4d9 (base 14) to base 6.\n | -4303\n | ibivibiv/math_instruct | |
Write an educational piece suited for college students related to the following text snippet:
"# Question e8dd9
Dec 8, 2016
See below.
#### Explanation:
Given a model
$y \left(a , t\right) = {a}_{1} t + {a}_{2} + {a}_{3} \sin \left({\omega}_{0} t\right)$
and a set of points
$P = \left(\left({t}_{1} , {y}_{1}\rig... | The problem presented here involves finding the best fit parameters a₁, a₂, and a₃ for the given model y(a,t) = a₁*t + a₂ + a₃*\sin(ω₀*t) using a set of data points P = {(t₁, y₁), ..., (tᵢ, yᵢ), ..., (tₙ, yₙ)}. To accomplish this, you need to minimize the error function E(a) which measures the difference between the a... | ibivibiv/math_instruct | |
Is 374753 prime?\n | True\n | ibivibiv/math_instruct | |
Solve -16*i + 5*i - 3*x = 30, 2*i + 9 = 3*x for i.\n | -3\n | ibivibiv/math_instruct | |
Rearrange -6*p + 2 - 3 + 1 to a + g*p and give g.\n | -6\n | ibivibiv/math_instruct | |
What is the cube root of 284439 to the nearest integer?\n | 66\n | ibivibiv/math_instruct | |
What is 527507 + -0.4?\n | 527506.6\n | ibivibiv/math_instruct | |
Simplify -4*4*(sqrt(343) - sqrt(343)*1) - (-1*(sqrt(343) + 1 + sqrt(343)) + -4).\n | 5 + 14*sqrt(7)\n | ibivibiv/math_instruct | |
What is the second smallest value in -0.3, -47, -1, 1061, 3/8, -2/5?\n | -1\n | ibivibiv/math_instruct | |
Solve 5148 = -65*d - 331*d for d.\n | -13\n | ibivibiv/math_instruct | |
Simplify ((t**9)**(-8/5))**(2/19) assuming t is positive.\n | t**(-144/95)\n | ibivibiv/math_instruct | |
Let k = 533 - 479. Suppose 5*j + a - 382 = 0, 2*j - 220 = -j + 4*a. Suppose -2*x = 2*x - j. What is the remainder when k is divided by x?\n | 16\n | ibivibiv/math_instruct | |
Expand (0*h - h**2 + 0*h)*(-14 + 14 - 20*h)*(h**2 - 2*h**2 - h**2) + 3*h**5 + 36 - 36 + 2*h.\n | -37*h**5 + 2*h\n | ibivibiv/math_instruct | |
Simplify (c**(2/9)/(c/(c**(1/5)*c))*(((c**25/c)/c)/c)/(c*(((c*c/(c/(c/(c/c**(-5)))))/c)/c)/c))**(4/9) assuming c is positive.\n | c**(5116/405)\n | ibivibiv/math_instruct | |
Is 1137527 composite?\n | False\n | ibivibiv/math_instruct | |
What is the thousands digit of 1374?\n | 1\n | ibivibiv/math_instruct | |
Put -4, -2, 7, -3 in ascending order.\n | -4, -3, -2, 7\n | ibivibiv/math_instruct | |
Simplify ((1 + (1*(6*sqrt(110)/sqrt(2))/sqrt(11) - ((((sqrt(80) - (sqrt(80) + -1)) + sqrt(80))*3 - sqrt(80)) + 4))*-3)*3)**2.\n | 2376*sqrt(5) + 5976\n | ibivibiv/math_instruct | |
Suppose 2*o = 5 + 1. Suppose 5*n - 2*c - 32 = -6*c, 2*n + o*c - 17 = 0. Solve -n*g + g = -3 for g.\n | 1\n | ibivibiv/math_instruct | |
Solve 41 = 9*u + 23 for u.\n | 2\n | ibivibiv/math_instruct | |
Which is smaller: -297896 or -6851632/23?\n | -6851632/23\n | ibivibiv/math_instruct | |
Let b = -2359 - -27285. Does 22 divide b?\n | True\n | ibivibiv/math_instruct | |
Let j(u) = -3*u**2 - 37*u + 4. Give j(-12).\n | 16\n | ibivibiv/math_instruct | |
Is 21734 a multiple of 203?\n | False\n | ibivibiv/math_instruct | |
Let p be (-55 + 93)*2/((-4)/(-3)). Let b = -38 + p. What is the tens digit of b?\n | 1\n | ibivibiv/math_instruct | |
Let t(p) = -p**2. Let x(a) = 151*a**2 - 11*a + 1. Let r = 126 + -124. Let q(l) = -30*l**2 + 2*l. Let u(k) = r*x(k) + 11*q(k). Give u(t(g)).\n | -28*g**4 + 2\n | ibivibiv/math_instruct | |
Let v(l) = -l**3 - 6*l**2 + 5*l - 9. Suppose -4*b = 4*z + 24, 0*z + 2*b - 30 = 4*z. Let y be v(z). Let g = -42 - -42. Solve y*f + g*f = -2*o, o = f for o.\n | 0\n | ibivibiv/math_instruct | |
-6161751 (base 9) to base 3\n | -20012001211201\n | ibivibiv/math_instruct | |
Let r be (30/(-2 + 4))/(24/(-16)). Let s(z) = z**2 + 11*z + 7. Let q be s(r). Is 1805 + q + 2 + -3 a composite number?\n | False\n | ibivibiv/math_instruct | |
Is 5859569 composite?\n | False\n | ibivibiv/math_instruct | |
What is (72/756)/(1/(-6))?\n | -4/7\n | ibivibiv/math_instruct | |
What is v in 2312*v**4 + 80919*v**3 + 665821*v**2 - 749376*v + 324 = 0?\n | -18, 1/2312, 1\n | ibivibiv/math_instruct | |
Let g be (72/20)/((-4)/(-30)). Suppose 7 = -r + g. Is r a multiple of 10?\n | True\n | ibivibiv/math_instruct | |
Let l(w) be the first derivative of 0*w - 1/18*w**4 - 5/2*w**2 - 1/90*w**5 - 1/9*w**3 + 4. Let y(n) be the second derivative of l(n). Factor y(a).\n | -2*(a + 1)**2/3\n | ibivibiv/math_instruct | |
In base 9, what is 11852 + 4?\n | 11856\n | ibivibiv/math_instruct | |
Product of -2 and -0.886.\n | 1.772\n | ibivibiv/math_instruct | |
What is the value of 70 + -62 - (-1 + 7)?\n | 2\n | ibivibiv/math_instruct | |
What is the greatest common divisor of 13280 and 14525?\n | 415\n | ibivibiv/math_instruct | |
Rearrange -4 + 2*j**2 + 4 + 95*j**2 + 8*j**2 + 42*j**2 + (3 - 3 + 2*j)*(j + 1 - 1) - 6*j**2 - j**2 + 0*j**2 to the form w*j**2 + c*j + p and give w.\n | 142\n | ibivibiv/math_instruct | |
Let z = 397/5 + -79. Is -1 not equal to z?\n | True\n | ibivibiv/math_instruct | |
Suppose 2*a - 5*t = -1, -3*t + 33 = a + 6. Let i be (6/a)/(1/10). Solve d + 12 = i*d for d.\n | 3\n | ibivibiv/math_instruct | |
Calculate 818 divided by 62.\n | 409/31\n | ibivibiv/math_instruct | |
What is the greatest common factor of 5251 and 979?\n | 89\n | ibivibiv/math_instruct | |
Collect the terms in 4*p + 17 + 11 - 20*p - 32.\n | -16*p - 4\n | ibivibiv/math_instruct | |
Put 87, 111752, 1.3 in decreasing order.\n | 111752, 87, 1.3\n | ibivibiv/math_instruct | |
What is the ten millions digit of 1682869251?\n | 8\n | ibivibiv/math_instruct | |
Is 28231370 a multiple of 410?\n | True\n | ibivibiv/math_instruct | |
Solve 0 = 229*t + 229*t - 469*t - 77 for t.\n | -7\n | ibivibiv/math_instruct | |
Product of -106.7 and -44.\n | 4694.8\n | ibivibiv/math_instruct | |
Simplify 0 + -1*sqrt(1088).\n | -8*sqrt(17)\n | ibivibiv/math_instruct | |
What is -0.000001151753766 rounded to seven decimal places?\n | -0.0000012\n | ibivibiv/math_instruct | |
Let x(o) = 648*o + 23644. Determine x(-36).\n | 316\n | ibivibiv/math_instruct | |
b"What is the wth term of -5870, -11820, -17850, -23960?\n" | -40*w**2 - 5830*w\n | ibivibiv/math_instruct | |
What is -0.05 + -6932413345.92?\n | -6932413345.97\n | ibivibiv/math_instruct | |
In base 15, what is 2 - 3bb?\n | -3b9\n | ibivibiv/math_instruct | |
What is seventeen halves of a century in years?\n | 850\n | ibivibiv/math_instruct | |
What is the third derivative of 17504510*g**4 + 31*g**2 + 99*g + 242 wrt g?\n | 420108240*g\n | ibivibiv/math_instruct | |
Let p = 33 + -31. Suppose 18 = a - p*b, a + a = 2*b + 28. What is the tens digit of a?\n | 1\n | ibivibiv/math_instruct | |
Is 13 a factor of 129058997?\n | False\n | ibivibiv/math_instruct | |
Let n = 609.62 + -609. Let l = n + -0.22. Sort 5, 46/7, l.\n | l, 5, 46/7\n | ibivibiv/math_instruct | |
0.1 times -99\n | -9.9\n | ibivibiv/math_instruct | |
Sort 0, 5, 4, -70732 in decreasing order.\n | 5, 4, 0, -70732\n | ibivibiv/math_instruct | |
What is 5 + 0 - 4 - 4?\n | -3\n | ibivibiv/math_instruct | |
What is the next term in 245, 1753, 5825, 13745, 26797?\n | 46265\n | ibivibiv/math_instruct | |
Suppose 4*o = o - 4*l + 5319, -l = 3. Is o a composite number?\n | False\n | ibivibiv/math_instruct | |
Suppose 737*t - 20767 + 5542 = 722*t. Calculate the least common multiple of t and 725.\n | 5075\n | ibivibiv/math_instruct | |
What is the hundreds digit of -31329*(1270/(-2667) - (0 + -2)/14)?\n | 4\n | ibivibiv/math_instruct | |
Simplify (m**(-17))**(36/5)/((m*m**(2/15))/(m*(m*(m/m**(-2/121))/m*m)/m)) assuming m is positive.\n | m**(-220553/1815)\n | ibivibiv/math_instruct | |
Let x(b) = -20*b**2 - 24*b - 24. Let d(u) = -4*u**2 - 5*u - 5. Determine 24*d(t) - 5*x(t).\n | 4*t**2\n | ibivibiv/math_instruct | |
Suppose -4*p - 8*p = -6*p - 48. What is the least common multiple of p and 718?\n | 2872\n | ibivibiv/math_instruct | |
Let u = -27 - -26.8. Which is the closest to 5? (a) 3/7 (b) u (c) -0.5\n | a\n | ibivibiv/math_instruct | |
Let t(u) be the second derivative of -u**5/20 + 5*u**3/2 + 7*u. What is the second derivative of t(p) wrt p?\n | -6*p\n | ibivibiv/math_instruct | |
Collect the terms in 234 - 35*s + 69*s - 234.\n | 34*s\n | ibivibiv/math_instruct | |
What are the prime factors of 123108?\n | 2, 3, 10259\n | ibivibiv/math_instruct | |
Which is the closest to -19/4? (a) -10 (b) 4 (c) -3/2\n | c\n | ibivibiv/math_instruct | |
Let j be 5*(0 - 12/(-15)). Suppose j*p + 5 = 5*c, -p = p + 4*c - 30. Suppose -s - 4*s = 5*g + 1305, 4*s + 1304 = -p*g. Round g to the nearest 100.\n | -300\n | ibivibiv/math_instruct |
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