instruction_seed stringlengths 5 2.9k | response_seed stringlengths 3 9.55k | input stringclasses 1
value | _source stringclasses 1
value |
|---|---|---|---|
Collect the terms in -14 + 61 + 144 + 120 - 11*d.\n | -11*d + 311\n | ibivibiv/math_instruct | |
Let p(i) = -i**2 - 2*i - 2. Let k be p(-1). Sort -8, -4, k.\n | -8, -4, k\n | ibivibiv/math_instruct | |
Let x(f) = f**3 - f**2 - f + 4. Let c be x(-4). Let v be (-34)/c - 22/99. Suppose 3*b - 5*b + 2 = 0. Which is smaller: b or v?\n | v\n | ibivibiv/math_instruct | |
Let n be -40 + 5 + 2/1. Let a = 39 + n. Suppose -2*d + a*d - 100 = 0. What is the units digit of d?\n | 5\n | ibivibiv/math_instruct | |
Let q = -14 - -4. Let i = 15 + q. Solve n + 0*n + i = 0 for n.\n | -5\n | ibivibiv/math_instruct | |
Let m(q) = -q. Let t(l) = -2*l**2. Let v(o) = o + 4*o - 5*o + 4*o**2. Let z(b) = -10*t(b) - 4*v(b). Give z(m(d)).\n | 4*d**2\n | ibivibiv/math_instruct | |
Calculate -6345 divided by 15.\n | -423\n | ibivibiv/math_instruct | |
Suppose 4*z = -0*z + 20. Let n = 178/51 - -386/357. Is z smaller than n?\n | False\n | ibivibiv/math_instruct | |
If James buys two puzzles, each consisting of 2000 pieces, and he can complete 100 pieces every 10 minutes, how long will it take for him to finish both puzzles? | If James buys two puzzles, each consisting of 2000 pieces, then he has a total of 2 * 2000 = 4000 pieces to complete.
If he can complete 100 pieces every 10 minutes, then he can complete 4000 pieces / 100 pieces per 10 minutes = 40 sets of 10 minutes.
So it will take him 40 sets of 10 minutes * 10 minutes = 400 minutes... | ibivibiv/math_instruct | |
What is the third derivative of -221*c**3*n**3 - 127*c**3*n*v**2 + 2*c**2*n**3*v - 2*c**2*n**3 + 14*c**2*n**2*v**2 - 2*c**2*n**2 - 9*c**2*n*v + 8*n**2*v wrt c?\n | -1326*n**3 - 762*n*v**2\n | ibivibiv/math_instruct | |
Let a(t) = t + 4. Let s(u) be the first derivative of -u**3/3 - 4*u**2 - 9*u + 12. Let f be s(-5). Give a(f).\n | 10\n | ibivibiv/math_instruct | |
Let k(g) = g**2 - 5*g - 2. Let r be k(6). Let c(z) = -2 + 3*z + 2*z**3 + 18*z**3 + r*z**3. Let t be c(1). Solve 2*q = 7*q - t for q.\n | 5\n | ibivibiv/math_instruct | |
What is the smallest common multiple of 154 and 140?\n | 1540\n | ibivibiv/math_instruct | |
Sort 1, -2120, 3410 in descending order.\n | 3410, 1, -2120\n | ibivibiv/math_instruct | |
Let s(x) = -x**2 + 2. Let k(f) = 183*f**3 - 4*f**2 + f + 12. Let q(j) = k(j) - 4*s(j). What is the second derivative of q(d) wrt d?\n | 1098*d\n | ibivibiv/math_instruct | |
Express -223*a - 1 - 209*a + 421*a + 146*a**3 in the form l + p*a + x*a**3 + z*a**2 and give p.\n | -11\n | ibivibiv/math_instruct | |
What are the prime factors of 6/(9/((-540)/(-8)))?\n | 3, 5\n | ibivibiv/math_instruct | |
Collect the terms in 8*i + 6*i + 39*i**2 - 11*i - 8*i**2.\n | 31*i**2 + 3*i\n | ibivibiv/math_instruct | |
Let m be -1*(-12)/(16/4). Suppose -3*t = -5*n + 11 - 2, 3*n - 15 = -m*t. Solve -q = n + 2 for q.\n | -5\n | ibivibiv/math_instruct | |
Let g(o) = -o**3 - o**2 - 3*o - 3. Let y be g(5). Let k = 187 + y. Is k a multiple of 3?\n | False\n | ibivibiv/math_instruct | |
Let h be (-86)/129 - (-2)/3. Solve w - 3*g - 3 = h, 0 = 3*g - 4*g - 1 for w.\n | 0\n | ibivibiv/math_instruct | |
Calculate (6/28)/(15/20)*56/12.\n | 4/3\n | ibivibiv/math_instruct | |
Let i(x) be the first derivative of x**4/4 + 2*x**3 + 2*x**2 - 2*x + 2. Let v be i(-5). Suppose 0 = -2*d, -4*g + v*d + 84 = -2*g. Is g a multiple of 16?\n | False\n | ibivibiv/math_instruct | |
What is the lowest common multiple of 116 and 4?\n | 116\n | ibivibiv/math_instruct | |
Let p = 589 + -586. Suppose -2*l = -7*l + 3*s - 114, 0 = 3*l + 3*s + 78. Let o = l + 66. Calculate the least common multiple of p and o.\n | 42\n | ibivibiv/math_instruct | |
Let z(l) = -5*l. Let y = 2525 - 1767. Let x(d) = -d**2 - y*d + 758*d. Determine z(x(n)).\n | 5*n**2\n | ibivibiv/math_instruct | |
Expand 4 - 4 - f**4 + (f**3 - 2*f**3 + 2*f**3)*(f - 4*f + f) - 6*f - 5*f - 1301*f**4 + 1273*f**4.\n | -31*f**4 - 11*f\n | ibivibiv/math_instruct | |
What is the tens digit of 1045?\n | 4\n | ibivibiv/math_instruct | |
Convert 11 (base 15) to base 6.\n | 24\n | ibivibiv/math_instruct | |
Write an educational piece suited for college students related to the following text snippet:
"# FA19:Lecture 4 Proof techniques
We finished our proof that and used this as a way to demonstrate several proof techniques.
Note: We did not finish the proof in lecture; I have finished it below, but its also a good exerci... | In the realm of mathematical logic and formal systems, a proof is an argument that establishes the truth of a given statement within a certain mathematical framework. Proofs serve as the foundation upon which mathematics stands, providing rigorous justification for various propositions, theorems, and corollaries. The ... | ibivibiv/math_instruct | |
b"What is the th term of 1874, 7830, 17868, 31988, 50190, 72474, 98840?\n" | 2041*b**2 - 167*b\n | ibivibiv/math_instruct | |
b"What is the ith term of 4908, 5174, 5618, 6240, 7040, 8018?\n" | 89*i**2 - i + 4820\n | ibivibiv/math_instruct | |
Let a(k) = k - 21. Let o be a(17). Let x be (2/o)/(3/156). Let b = 54 + x. List the prime factors of b.\n | 2, 7\n | ibivibiv/math_instruct | |
Expand (-s + 2*s + s)*(-1 - 5 + 2) + 1 + 0 - 2*s - 3.\n | -10*s - 2\n | ibivibiv/math_instruct | |
Rearrange (102 + 108 - 16)*(-6*d + 9*d - 5*d + (4 - 1 + 2)*(3*d - 3*d - d)) to the form c + b*d and give c.\n | 0\n | ibivibiv/math_instruct | |
Write an educational piece suited for college students related to the following text snippet:
"Very accessible explanation to why variances of independent random variables add up when the random variables are added or subtracted.
## The Pythagorean Theorem of Statistics
Quick. What’s the most important theorem in sta... | The Pythagorean Theorem is a fundamental concept in geometry, stating that in a right triangle, the square of the length of the hypothenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This idea has been generalized and extended to many areas of mathemat... | ibivibiv/math_instruct | |
Let x = -4 + -2. Let z be 2/x - (-16)/(-6). Which is smaller: -4 or z?\n | -4\n | ibivibiv/math_instruct | |
Let v = 34 + -33. Suppose -v - 1 = -b. What are the prime factors of b?\n | 2\n | ibivibiv/math_instruct | |
Is 1696249 a multiple of 13?\n | False\n | ibivibiv/math_instruct | |
Let y = 0.103 - -4.897. Let x be ((-2)/(-4))/((-2)/12). Let k = x - -14/5. Which is the biggest value? (a) k (b) y (c) 2\n | b\n | ibivibiv/math_instruct | |
What is 0.003251971 rounded to four dps?\n | 0.0033\n | ibivibiv/math_instruct | |
Expand (121*u**2 + 715*u**2 + 526*u**2)*(-5*u + 2*u + 0*u).\n | -4086*u**3\n | ibivibiv/math_instruct | |
Sort -6, -1, 1, -3 in decreasing order.\n | 1, -1, -3, -6\n | ibivibiv/math_instruct | |
Let p(s) = -319*s**3 + s**2 - 2*s + 2. Let u be p(1). Let q = -277 - u. Is q even?\n | False\n | ibivibiv/math_instruct | |
b"What is the yth term of -477, -1113, -1713, -2259, -2733?\n" | 3*y**3 - 657*y + 177\n | ibivibiv/math_instruct | |
What is the next term in -125, -379, -633, -887?\n | -1141\n | ibivibiv/math_instruct | |
Collect the terms in 2*w + 0*w - 5257*w**2 + 39731*w**2 + 1760*w**2.\n | 36234*w**2 + 2*w\n | ibivibiv/math_instruct | |
Solve -i - 2*w - 3*w - 2 = 0, -4*i + 5*w - 8 = 0 for i.\n | -2\n | ibivibiv/math_instruct | |
Collect the terms in 0 - 1 - 16*t - 10*t - 6 + 8*t.\n | -18*t - 7\n | ibivibiv/math_instruct | |
Suppose 5*y - 14 = 4*f - 3*f, -4*f + 1 = -y. Solve -4*h + 3*a = -14, -3*h - y*a + 31 = 2*h for h.\n | 5\n | ibivibiv/math_instruct | |
What is the result of the following expression?
(-70.7705 - -70.8219) + (65.653 + 28.0314) | 93.7358 | ibivibiv/math_instruct | |
Let j = 22 + -10. Let x be j/(0 + -2) - -2. Let k(l) = l**2 + 6*l - 5. What is k(x)?\n | -13\n | ibivibiv/math_instruct | |
What is (((-32)/120)/((-14)/(-40)))/(24/(-14))?\n | 4/9\n | ibivibiv/math_instruct | |
Let y(g) = 50*g**2 - 121*g + 869. Let z be y(-21). Is 25459 != z?\n | True\n | ibivibiv/math_instruct | |
What is the value of ((-80)/50)/((-4)/(-10))?\n | -4\n | ibivibiv/math_instruct | |
What is the common denominator of -31/45200 and 107/32400?\n | 3661200\n | ibivibiv/math_instruct | |
Rearrange (4*m**2 - 3*m**2 - 3*m**2)*(-2 + 2 - m - 5) to u + b*m**3 + y*m**2 + t*m and give b.\n | 2\n | ibivibiv/math_instruct | |
Factor 5*p**4 - 165*p**3 - 42930*p**2 + 262440*p.\n | 5*p*(p - 108)*(p - 6)*(p + 81)\n | ibivibiv/math_instruct | |
What is the remainder when 429 is divided by ((4 - 2)/2)/((-11)/(-396))?\n | 33\n | ibivibiv/math_instruct | |
In base 7, what is -44 - 3263242?\n | -3263316\n | ibivibiv/math_instruct | |
Calculate the common denominator of -47/27 and 6096/1188 - 1/(27/6).\n | 297\n | ibivibiv/math_instruct | |
Simplify (g**(-1)*g**(-6)/g*g*((g**(-10)*g)/g)/g**(3/2))**(13/7) assuming g is positive.\n | g**(-481/14)\n | ibivibiv/math_instruct | |
What is the least common multiple of 77 and 63497?\n | 698467\n | ibivibiv/math_instruct | |
What is 573 minutes after 5:24 PM?\n | 2:57 AM\n | ibivibiv/math_instruct | |
What is -530 (base 8) in base 11?\n | -293\n | ibivibiv/math_instruct | |
Let i be 20/(-1026)*-21*2. Let w = -24/19 + i. Put -1/9, w, -0.06 in decreasing order.\n | -0.06, -1/9, w\n | ibivibiv/math_instruct | |
Let p be (-150)/9 - (-7)/(-21). Does 27 divide (996/9)/(p/(1530/(-12)))?\n | False\n | ibivibiv/math_instruct | |
Collect the terms in 42*s**2 - 13*s**2 - 28*s**2.\n | s**2\n | ibivibiv/math_instruct | |
What is the cube root of 3943 to the nearest integer?\n | 16\n | ibivibiv/math_instruct | |
-1103740 (base 8) to base 3\n | -120002022100\n | ibivibiv/math_instruct | |
Find the common denominator of 117/2680 and 34/219445.\n | 117622520\n | ibivibiv/math_instruct | |
Determine r, given that -2*r**2 - 543608*r - 5979446 = 0.\n | -271793, -11\n | ibivibiv/math_instruct | |
Is 40 a factor of 43200?\n | True\n | ibivibiv/math_instruct | |
Let g(x) = -x + 3. Let o be g(-3). Suppose 4*y - o - 2 = 0. Solve 4*m = 5*q - 2*q - 14, 0 = -3*m + y*q - 11 for m.\n | -5\n | ibivibiv/math_instruct | |
What is 44436 to the power of 1/2, to the nearest integer?\n | 211\n | ibivibiv/math_instruct | |
Let m = 2 + -1. Let a be (12/(-15))/(m/(-5)). Suppose a*x - 19 + 7 = 0. What is the greatest common factor of 24 and x?\n | 3\n | ibivibiv/math_instruct | |
Let a = 9 + -6. Find the second derivative of -2*y + 3*y**2 - 6*y**2 + a - 3 wrt y.\n | -6\n | ibivibiv/math_instruct | |
Let q(y) be the first derivative of -6*y**2 + 10*y - 4. What is the first derivative of q(w) wrt w?\n | -12\n | ibivibiv/math_instruct | |
What is the highest common factor of 321 and 107?\n | 107\n | ibivibiv/math_instruct | |
Sort -8, 2, 12, -5, 1, 4, -317 in ascending order.\n | -317, -8, -5, 1, 2, 4, 12\n | ibivibiv/math_instruct | |
Find s, given that -27*s**3/2 + 63*s**2/2 + 12*s = 0.\n | -1/3, 0, 8/3\n | ibivibiv/math_instruct | |
What is the highest common divisor of 14672 and 112?\n | 112\n | ibivibiv/math_instruct | |
Sort 0.04, -4, 1/4 in increasing order.\n | -4, 0.04, 1/4\n | ibivibiv/math_instruct | |
What is the square root of 42904806 to the nearest integer?\n | 6550\n | ibivibiv/math_instruct | |
-565*-0.3\n | 169.5\n | ibivibiv/math_instruct | |
Expand 10*k**2 - 10*k**2 + 2*k**5 + (0*k**3 + k**3 + 0*k**3)*(-k**2 - k**2 + 14*k**2).\n | 14*k**5\n | ibivibiv/math_instruct | |
What is -3360517 divided by -6?\n | 3360517/6\n | ibivibiv/math_instruct | |
b"What is the tth term of 8634, 6683, 3440, -1089, -6898, -13981?\n" | t**3 - 652*t**2 - 2*t + 9287\n | ibivibiv/math_instruct | |
What is -0.619 minus 0.40945709085?\n | -1.02845709085\n | ibivibiv/math_instruct | |
Suppose -32*r + 30*r + 5*x - 10 = 0, 2*x - 4 = 5*r. Solve r = -17*j + 21*j + 8 for j.\n | -2\n | ibivibiv/math_instruct | |
Let d(s) = s**3 - 5*s**2 + 6*s - 6. Let g = -5 + 9. Let v be d(g). Differentiate h**2 - 2*h**v - 6 - h**2 - 5*h**2 wrt h.\n | -14*h\n | ibivibiv/math_instruct | |
1 + (3 - (-6 - -3)) + 3\n | 10\n | ibivibiv/math_instruct | |
Let k = -0.94 - -5.94. What is the nearest to 5 in 2, k, -5?\n | k\n | ibivibiv/math_instruct | |
Suppose 91 = 5*f - 3*g, 2*f - 28 = -5*g + 2*g. Let n(m) = m - 1. Let i be n(1). What is the remainder when (5 - i)/5*31 is divided by f?\n | 14\n | ibivibiv/math_instruct | |
Let n = -44 - -54. Sort -0.3, n, 2.\n | -0.3, 2, n\n | ibivibiv/math_instruct | |
What is (-84)/770*-5 + (-18)/(-33)*-23?\n | -12\n | ibivibiv/math_instruct | |
Calculate the remainder when 2087499 is divided by 1129.\n | 1107\n | ibivibiv/math_instruct | |
What is next in 1977, 1960, 1943, 1926, 1909, 1892?\n | 1875\n | ibivibiv/math_instruct | |
Determine p, given that 3*p**2 + 106617*p - 2133540 = 0.\n | -35559, 20\n | ibivibiv/math_instruct | |
Let o(t) = 2*t**2. Let n(v) = -58*v - 3. Let g(m) = 117*m + 5. Let q(j) = -3*g(j) - 5*n(j). Give o(q(i)).\n | 7442*i**2\n | ibivibiv/math_instruct |
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