instruction_seed stringlengths 5 2.9k | response_seed stringlengths 3 9.55k | input stringclasses 1
value | _source stringclasses 1
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|---|---|---|---|
Let q = 40 + -42. Let b be 0 - 0 - q/2. What is the fourth smallest value in 2/7, b, -0.3, -0.1?\n | b\n | ibivibiv/math_instruct | |
Calculate (1/3 - 128/(-48)) + -6.\n | -3\n | ibivibiv/math_instruct | |
Two letters picked without replacement from qqtptqqtqtq. Give prob of sequence qt.\n | 12/55\n | ibivibiv/math_instruct | |
Suppose 0 = 3*v + 32*v - 4480. What is the remainder when v is divided by 2/(-2) + 88/2?\n | 42\n | ibivibiv/math_instruct | |
Rearrange -z**3 - 2 + 2 + (-1 + 1 - 3*z)*((-z - 2*z + 2*z)*(3 - 2*z - 3) + (0*z + 0*z - 4*z**2)*(0 - 4 + 3)) to the form a*z**3 + t*z + j*z**2 + l and give a.\n | -19\n | ibivibiv/math_instruct | |
Let f(x) be the first derivative of -264 + 0*x**2 - 17*x**4 - 2*x - 62/3*x**3 + 3/5*x**5. Find the third derivative of f(p) wrt p.\n | 72*p - 408\n | ibivibiv/math_instruct | |
Suppose -4*d - 672 = 620. Let y = -220 - d. What is the least common multiple of 10 and y/15 - 2/(-15)?\n | 70\n | ibivibiv/math_instruct | |
Let z = -1035 - -2473. Suppose 2*y - y + 5774 = 4*d, z = d - 3*y. What is the units digit of d?\n | 4\n | ibivibiv/math_instruct | |
Simplify ((x/x**(4/9))/x**(-1/9))/(x/x**(3/5)*x/(x*x**5/x)) assuming x is positive.\n | x**(64/15)\n | ibivibiv/math_instruct | |
What is the square root of 275107322 to the nearest integer?\n | 16586\n | ibivibiv/math_instruct | |
What is next in 72696, 145448, 218200, 290952, 363704, 436456?\n | 509208\n | ibivibiv/math_instruct | |
What is -28853 + 0.048?\n | -28852.952\n | ibivibiv/math_instruct | |
What is the first derivative of 258*c**3*u**2 + 5*c**3 - u**2 + 39 wrt u?\n | 516*c**3*u - 2*u\n | ibivibiv/math_instruct | |
Let k = 8.649 + -8.8. Let j = 0.14761 + k. What is j rounded to four dps?\n | -0.0034\n | ibivibiv/math_instruct | |
Suppose 4*x = 28 - 8. Let v = -3 + x. Suppose v*n + 160 = 6*n. Is 10 a factor of n?\n | True\n | ibivibiv/math_instruct | |
Suppose 53*p - 52*p - 630 = -2*h, 2*p - 1256 = -2*h. Calculate the lowest common multiple of 10 and p.\n | 3130\n | ibivibiv/math_instruct | |
Let x be 274/2055 + (-176)/(-30). Solve -4*q + x = 5*g - 15, 5*q - g - 19 = 0 for q.\n | 4\n | ibivibiv/math_instruct | |
What is -4 (base 6) in base 4?\n | -10\n | ibivibiv/math_instruct | |
Let l(y) = -y**3 + 17*y**2 + 18*y + 27. Let f be l(18). Find the second derivative of -23*d**3 + 3*d**4 - f*d**3 + 42*d**3 + d**4 + 77*d wrt d.\n | 48*d**2 - 48*d\n | ibivibiv/math_instruct | |
((-21)/(-6)*99/(-616))/(3/2)\n | -3/8\n | ibivibiv/math_instruct | |
Suppose 0*d - d = 0. Let z = d + 1. Calculate the highest common factor of 2 and z.\n | 1\n | ibivibiv/math_instruct | |
Rearrange 4*t - 21*t - 7 + 19 - 1 + 2 to m + h*t and give h.\n | -17\n | ibivibiv/math_instruct | |
Write an educational piece suited for college students related to the following text snippet:
"## Section3.2Nilpotent Linear Transformations
We will discover that nilpotent linear transformations are the essential obstacle in a non-diagonalizable linear transformation. So we will study them carefully, both as an objec... | Nilpotent linear transformations are fundamental to understanding non-diagonalizable linear transformations. These transformations have unique properties that make them worthy of careful study. We will begin our investigation by defining what it means for a linear transformation to be nilpotent, then explore their sig... | ibivibiv/math_instruct | |
Solve 4*d = 4*i + 16, 0*d + 6 + 10 = -d - 4*i for d.\n | 0\n | ibivibiv/math_instruct | |
2103012 (base 5) to base 7\n | 203222\n | ibivibiv/math_instruct | |
Let i(z) = -z**3 - 11*z**2 + 26*z + 2. Let l be i(-13). Find g such that 25*g + 22*g - 2*g - g**2 + 35*g + 3*g**l = 0.\n | -40, 0\n | ibivibiv/math_instruct | |
Is 137031 a multiple of 25?\n | False\n | ibivibiv/math_instruct | |
List the prime factors of 163742497.\n | 23, 29, 127, 1933\n | ibivibiv/math_instruct | |
What is the least common multiple of 135 and 50?\n | 1350\n | ibivibiv/math_instruct | |
Evaluate 3 - (10 + -15 - (1 + -3)).\n | 6\n | ibivibiv/math_instruct | |
Let n(g) = g + 11. Let t be n(-6). Suppose -8*u = -t*u. Let s(m) = -13*m**2 + 13*m - 11. Let a(k) = -7*k**2 + 7*k - 6. Let y(b) = -11*a(b) + 6*s(b). Give y(u).\n | 0\n | ibivibiv/math_instruct | |
Suppose -a - 3 = -2*a. Let h(l) = -4*l. Let p(v) = v + 1. Let r(o) = a*p(o) + h(o). Differentiate r(y) with respect to y.\n | -1\n | ibivibiv/math_instruct | |
Suppose 2 = -3*n - 2*s + 21, -5*s + 25 = 0. Let d = 4 + -3. What is the lowest common multiple of n and d?\n | 3\n | ibivibiv/math_instruct | |
Let m = 166 + -145. Is 7/m*-15 + 42 a composite number?\n | False\n | ibivibiv/math_instruct | |
How many millilitres are there in eighteen fifths of a litre?\n | 3600\n | ibivibiv/math_instruct | |
Simplify (-1*(sqrt(75) + 0) + 0 + -2*sqrt(75) + 5)**2 + 5 + 5*((-1 + sqrt(75))*2)**2.\n | -350*sqrt(3) + 2225\n | ibivibiv/math_instruct | |
Let l = 3 - 0. Let p be 82/8 + 0 - (-32)/(-128). Solve o = l*g + p, -o + 6*o - g = 22 for o.\n | 4\n | ibivibiv/math_instruct | |
Which is the fourth smallest value? (a) -92 (b) -1.7 (c) 20 (d) -7/4 (e) -0.1\n | e\n | ibivibiv/math_instruct | |
Calculate the remainder when 23127 is divided by 413.\n | 412\n | ibivibiv/math_instruct | |
Let z = -15/16 + 13/48. Is 1 at least z?\n | True\n | ibivibiv/math_instruct | |
Suppose 2*s - 3*g = 6*s - 35, -g + 41 = 5*s. Solve 2*n + 2*n = -s for n.\n | -2\n | ibivibiv/math_instruct | |
Suppose 5*x + 5*k = 4 + 1, -4*k = 3*x - 1. Suppose 3*p - 2*c = -2, 0 = 4*p - 5*c + 2 + x. Suppose 6*z - 25 = z + m, p = -z + 4*m - 14. Is z composite?\n | True\n | ibivibiv/math_instruct | |
Let z = 34 - 47. Let l = z + 13.4. Suppose 22*d - 24 = 10*d. Which is the closest to -1? (a) 5 (b) l (c) d\n | b\n | ibivibiv/math_instruct | |
What is the value of 2 - -14 - 12 - (-21 + 13 + 93)?\n | -81\n | ibivibiv/math_instruct | |
-4 divided by 5475\n | -4/5475\n | ibivibiv/math_instruct | |
What is the second derivative of 9*f**2*z**3 - 2*f**2*z**2 + 450*f**2 - 3*f*z**3 - 12*f*z - 2*z**3 - 2*z wrt f?\n | 18*z**3 - 4*z**2 + 900\n | ibivibiv/math_instruct | |
Which is smaller: -56389 or -56402?\n | -56402\n | ibivibiv/math_instruct | |
Suppose 2*m - 785 = -r, 5*r + 3*m + 1605 = 7*r. Suppose 0 = -13*k + 16*k - r. What is the greatest common divisor of 106 and k?\n | 53\n | ibivibiv/math_instruct | |
Find the second derivative of 9991733*m**2 - 10*m + 290616.\n | 19983466\n | ibivibiv/math_instruct | |
How many minutes are there between 3:00 PM and 3:42 PM?\n | 42\n | ibivibiv/math_instruct | |
What is the least common multiple of 2365 and 2365?\n | 2365\n | ibivibiv/math_instruct | |
Simplify ((c**(-6))**(4/11))**(-35) assuming c is positive.\n | c**(840/11)\n | ibivibiv/math_instruct | |
Let v(p) be the second derivative of 0 - 49*p - 1/3*p**3 + 1/2*p**2. Calculate v(-5).\n | 11\n | ibivibiv/math_instruct | |
Solve -2696*g + 927 = -2029 + 260 for g.\n | 1\n | ibivibiv/math_instruct | |
Expand -13*w**2 + 13*w**2 - 5*w**3 + (0 + 2 - 3)*(2 - 2 + w**3) + 3*w**3 + 2*w**3 - 3*w**3 - 2*w**3 + 4*w**3 - w**3.\n | -3*w**3\n | ibivibiv/math_instruct | |
Let y(k) = k + 9. Let a be y(2). Suppose 4*p + 0*i - a = -i, 0 = 3*p + 2*i - 7. Determine w, given that -3*w**2 + 12*w - 9*w**3 + 6*w**p + 7 + 5 = 0.\n | -2, -1, 2\n | ibivibiv/math_instruct | |
What is the second smallest value in -33, 2/3, -1/9?\n | -1/9\n | ibivibiv/math_instruct | |
Solve -469*m + 6365 + 7297 = -4629 for m.\n | 39\n | ibivibiv/math_instruct | |
Evaluate ((-3)/(27/6))/(22/66).\n | -2\n | ibivibiv/math_instruct | |
Let u(s) = s - 1. Let t = 14 - 25. Let y = t + 13. Let k be u(y). Solve -2*q - 7 = -k for q.\n | -3\n | ibivibiv/math_instruct | |
Let q be 9/(-63) - 15/(-7). Suppose -q*w + 8 = 28. Calculate the common denominator of -22 and (-36)/9 + 84/w.\n | 5\n | ibivibiv/math_instruct | |
What is prob of sequence fwfb when four letters picked without replacement from {f: 2, r: 7, w: 7, b: 1}?\n | 1/4080\n | ibivibiv/math_instruct | |
What is the tens digit of 3/7 - (5 - 7604/28)?\n | 6\n | ibivibiv/math_instruct | |
Is 65 a factor of 80141?\n | False\n | ibivibiv/math_instruct | |
What is 238 minutes after 9:25 PM?\n | 1:23 AM\n | ibivibiv/math_instruct | |
Suppose -b = 7*b + 240. What is the units digit of 15/b*(683 - -1)/(-2)?\n | 1\n | ibivibiv/math_instruct | |
Solve -22 = 5*t + q, 0*t = 4*t + 4*q + 24 for t.\n | -4\n | ibivibiv/math_instruct | |
Solve -125*y + 445*y - 1920 = 160*y for y.\n | 12\n | ibivibiv/math_instruct | |
Is 813479 a composite number?\n | True\n | ibivibiv/math_instruct | |
Let s be 1600/48*(657/(-108) + 6). Which is the closest to s? (a) -0.4 (b) 2 (c) -1/4\n | a\n | ibivibiv/math_instruct | |
What is the least common multiple of 2116 and 30?\n | 31740\n | ibivibiv/math_instruct | |
Let q = 2 + -1. Let i be (q/(-3))/(8/3). Let f be (-52)/(-39)*(-2 + (-711)/(-342)). Which is the nearest to f? (a) i (b) -2/5 (c) -5\n | a\n | ibivibiv/math_instruct | |
Let t = 102011/33 + -3091. Calculate the common denominator of t and 61/60.\n | 660\n | ibivibiv/math_instruct | |
What is 3581 to the power of 1/10, to the nearest integer?\n | 2\n | ibivibiv/math_instruct | |
Is 303220333 a multiple of 15?\n | False\n | ibivibiv/math_instruct | |
What is 13 (base 5) in base 12?\n | 8\n | ibivibiv/math_instruct | |
What is the greatest common factor of 1515714 and 957?\n | 87\n | ibivibiv/math_instruct | |
Let h(x) = -19*x**2. Let g(l) = 250*l**2 - 4*l + 16. Let p(y) = 1998*y**2 - 33*y + 132. Let m(w) = -33*g(w) + 4*p(w). Give h(m(s)).\n | -1264716*s**4\n | ibivibiv/math_instruct | |
In base 8, what is 257 - 0?\n | 257\n | ibivibiv/math_instruct | |
Suppose 5*v - k + 38 = 0, v + 2*k + 18 = -3*k. Let i = v - -21. Suppose 5*q - 39 = 4*q. What is the greatest common divisor of q and i?\n | 13\n | ibivibiv/math_instruct | |
What is -10 (base 10) in base 2?\n | -1010\n | ibivibiv/math_instruct | |
Is 63507 composite?\n | True\n | ibivibiv/math_instruct | |
Let h(s) be the first derivative of -7*s**3/3 - 2*s - 4. What is the derivative of h(b) wrt b?\n | -14*b\n | ibivibiv/math_instruct | |
Rearrange 38*l - 660*l + 0 + 0 - 1404*l to the form k + f*l and give f.\n | -2026\n | ibivibiv/math_instruct | |
Let v(a) = a**2 - 6*a + 4. Suppose -f = -0*f - 6. Let l be v(f). Let g = 8 - l. Put 6, g, 2 in ascending order.\n | 2, g, 6\n | ibivibiv/math_instruct | |
Factor 2*r**2 - 42284*r - 84576.\n | 2*(r - 21144)*(r + 2)\n | ibivibiv/math_instruct | |
Let q(o) = o**2 + 5*o - 3. Let s(d) = -d**2 - 5*d. Let k be s(-6). Let n be q(k). Find the second derivative of 18*w**3 + 37*w + 29*w - 26*w + 6*w**n wrt w.\n | 144*w\n | ibivibiv/math_instruct | |
Simplify (-1 + sqrt(19) + 0 - (1*sqrt(76) + sqrt(19)))**2 + sqrt(57)/(sqrt(147) - sqrt(147)*3).\n | 55*sqrt(19)/14 + 77\n | ibivibiv/math_instruct | |
What is the units digit of 542/6 + (-2)/(-3)?\n | 1\n | ibivibiv/math_instruct | |
Evaluate 575/1012*22*-12*5/10.\n | -75\n | ibivibiv/math_instruct | |
What is 86332729 to the power of 1/2, to the nearest integer?\n | 9292\n | ibivibiv/math_instruct | |
What is 418 minutes after 8:53 PM?\n | 3:51 AM\n | ibivibiv/math_instruct | |
What is 2012001111121 (base 3) in base 5?\n | 244144033\n | ibivibiv/math_instruct | |
Does 21 divide 557069?\n | False\n | ibivibiv/math_instruct | |
What is -2071020 rounded to the nearest 10000?\n | -2070000\n | ibivibiv/math_instruct | |
Which is the smallest value? (a) -7 (b) -1 (c) -2/19 (d) -2 (e) -5\n | a\n | ibivibiv/math_instruct | |
Multiply -0.4952 and 3564.\n | -1764.8928\n | ibivibiv/math_instruct | |
Which is the closest to 0.1? (a) 0.2 (b) 26 (c) -2/13\n | a\n | ibivibiv/math_instruct | |
Solve -5*x + 2*g - 15 + 5 = 0, -5*x + 3*g - 5 = 0 for x.\n | -4\n | ibivibiv/math_instruct | |
Convert 82 (base 14) to base 12.\n | 96\n | ibivibiv/math_instruct |
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