instruction_seed stringlengths 5 2.9k | response_seed stringlengths 3 9.55k | input stringclasses 1
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Let b(r) = r**2 - 12*r. Let g be b(11). Let n(f) = -f**2 - 16*f - 25. Let j be n(g). Factor 72*u**3 + 6*u**5 + j*u + 28*u - 24*u**4 - 96*u**2 - 3*u**5 - 10*u.\n | 3*u*(u - 2)**4\n | ibivibiv/math_instruct | |
Three letters picked without replacement from {i: 6, v: 13}. Give prob of picking 3 v.\n | 286/969\n | ibivibiv/math_instruct | |
Expand -1 + 1 - m**5 + (-7*m + 5*m**2 + 7*m)*(-m + m - 2*m**3) + 762*m**5 + 202*m**5 + 1107*m**5.\n | 2060*m**5\n | ibivibiv/math_instruct | |
Divide -45948 by 7.\n | -6564\n | ibivibiv/math_instruct | |
What is 64061 to the power of 1/2, to the nearest integer?\n | 253\n | ibivibiv/math_instruct | |
Suppose -12*u - 26 = -4*m - 7*u, 4 = 2*m + 2*u. Solve 2 - m = s for s.\n | -2\n | ibivibiv/math_instruct | |
Is 711943 composite?\n | True\n | ibivibiv/math_instruct | |
What is the smallest value in -4, -0.241, -1.4, 402?\n | -4\n | ibivibiv/math_instruct | |
Evaluate -1*6/(-57) + 0 - (-361)/(1186607/(-210714)).\n | -64\n | ibivibiv/math_instruct | |
b"What is the yth term of -740027, -740028, -740029, -740030, -740031?\n" | -y - 740026\n | ibivibiv/math_instruct | |
Evaluate (2*1)/(34 - 67 - -23).\n | -1/5\n | ibivibiv/math_instruct | |
What is -4 take away 15710272439971?\n | -15710272439975\n | ibivibiv/math_instruct | |
What is the tens digit of 6831?\n | 3\n | ibivibiv/math_instruct | |
Suppose 4*q - 416 = -96. Suppose z - q = -5*x, x - z = -2*z + 20. Let m(y) = y**2. Let n be m(2). Solve o = n*p + x, -3*o - 5*p - 30 = -7 for o.\n | -1\n | ibivibiv/math_instruct | |
Let j(d) = 2*d + 2. Let t(o) = o**2 - 3*o - 3. Let c be (-2)/12*-2 + 28/(-21). Let g = -2 - c. Let v be (9/(-6))/((-1)/(-3 - g)). Calculate v*j(h) - 2*t(h).\n | -2*h**2\n | ibivibiv/math_instruct | |
(-106)/11 - (-42 - -32)\n | 4/11\n | ibivibiv/math_instruct | |
Which is the nearest to 1? (a) 805 (b) 0 (c) -2/13 (d) 2.7\n | b\n | ibivibiv/math_instruct | |
How many meters are there in 2.58963cm?\n | 0.0258963\n | ibivibiv/math_instruct | |
What is the common denominator of -53/112 and (21/10)/(154/231)?\n | 560\n | ibivibiv/math_instruct | |
Round 14.91933 to the nearest ten.\n | 10\n | ibivibiv/math_instruct | |
What is 300 minutes after 5:25 PM?\n | 10:25 PM\n | ibivibiv/math_instruct | |
Let t = -470.7 - 8.3. Let m = t - -514.9. Let p = m + -35.89999711. Round p to seven decimal places.\n | 0.0000029\n | ibivibiv/math_instruct | |
Let l = 18783 - 18778. Let s(g) = -6*g - 2 - 9 - 4*g**2 + 9. Let d(a) = 5*a**2 + 7*a + 2. Determine l*d(y) + 6*s(y).\n | y**2 - y - 2\n | ibivibiv/math_instruct | |
Is 391926860 a multiple of 65?\n | True\n | ibivibiv/math_instruct | |
Let z = 89975903/1718190 - 2/171819. Let n = 105/2 - z. Let t = 3.07 + -0.07. Sort n, 0.2, t in ascending order.\n | n, 0.2, t\n | ibivibiv/math_instruct | |
Collect the terms in 647*j - 49*j - 2672*j.\n | -2074*j\n | ibivibiv/math_instruct | |
Does 154 divide (34839/98)/((-1)/(-86))?\n | False\n | ibivibiv/math_instruct | |
What is the closest to 11 in -1, -39/4, -5?\n | -1\n | ibivibiv/math_instruct | |
Let y(p) be the second derivative of 43*p**4/3 - 2*p**3/3 + p**2 - 27*p. Is y(1) a multiple of 30?\n | False\n | ibivibiv/math_instruct | |
What is 10 - -14 - (72 + -24) - 9?\n | -33\n | ibivibiv/math_instruct | |
What is the nearest to -2 in 1/5, 3/13, -0.1?\n | -0.1\n | ibivibiv/math_instruct | |
Let g(b) = -b**2 - 2*b + 67. Let d be g(7). Suppose -a + 175 = d*a. Solve -5*s = -4*y + a, 3*s - 9 = -3*y + s for y.\n | 5\n | ibivibiv/math_instruct | |
Calculate (18/(-60))/((14946/(-371))/47).\n | 7/20\n | ibivibiv/math_instruct | |
Expand (0*r + 0*r - 3*r)*(10 - 11 + 11 + (1 + 2 - 4)*(2 + 1 - 2) + 3 - 3 - 1) + 2 + 2*r - 2.\n | -22*r\n | ibivibiv/math_instruct | |
(-62 - (100 - 284)) + 9\n | 131\n | ibivibiv/math_instruct | |
What is the closest to -40.9 in 1, 1317, -37?\n | -37\n | ibivibiv/math_instruct | |
Evaluate 2/(-4*(-4)/32*2).\n | 2\n | ibivibiv/math_instruct | |
What is 738 - 105356972?\n | -105356234\n | ibivibiv/math_instruct | |
Calculate the common denominator of -47/6 and -2 - (-195)/25*1.\n | 30\n | ibivibiv/math_instruct | |
Let i(w) be the second derivative of 34*w**6/5 + w**5/10 + w**4/12 + 7*w**3/6 - 315*w**2/2 + 5732*w. Find the second derivative of i(z) wrt z.\n | 2448*z**2 + 12*z + 2\n | ibivibiv/math_instruct | |
Collect the terms in -9*c**2 + 25 - 79 + 140915*c - 140915*c + 54.\n | -9*c**2\n | ibivibiv/math_instruct | |
What is 456 minutes before 8:34 PM?\n | 12:58 PM\n | ibivibiv/math_instruct | |
b"What is the th term of 61450, 61456, 61464, 61474?\n" | b**2 + 3*b + 61446\n | ibivibiv/math_instruct | |
Let r(b) be the first derivative of 0*b**2 + 3/2*b**4 + 11 + 0*b - 7/3*b**3. Find the third derivative of r(g) wrt g.\n | 36\n | ibivibiv/math_instruct | |
Four letters picked without replacement from kkpkkkspkspksp. Give prob of sequence kskp.\n | 3/143\n | ibivibiv/math_instruct | |
Expand (0 + 1 + 1)*(3*g - 3*g + g)*(0*g + 0*g - g)*(-25 + 37 - 19).\n | 14*g**2\n | ibivibiv/math_instruct | |
Sort -5, 3, 54, 2, -2 in decreasing order.\n | 54, 3, 2, -2, -5\n | ibivibiv/math_instruct | |
Evaluate (-110)/(33/(-11) - 20/10).\n | 22\n | ibivibiv/math_instruct | |
Convert -e (base 15) to base 12.\n | -12\n | ibivibiv/math_instruct | |
Let f(q) = -q**2 + 2. Let x(g) = -60 + 34 + 29 - 2*g**2. Suppose 0 = -v - 3*v - 12. Let t(c) = v*f(c) + 2*x(c). Factor t(b).\n | -b**2\n | ibivibiv/math_instruct | |
Expand (-b + 5 - 2 - b)*(-2 - 4 + 4) + 0*b + 0*b + 4*b - 3*b + 2*b - b.\n | 6*b - 6\n | ibivibiv/math_instruct | |
Let i = 3.5 + 107.5. Let a = -111.36 + i. Round a to one dp.\n | -0.4\n | ibivibiv/math_instruct | |
What is 5.36 times -0.1?\n | -0.536\n | ibivibiv/math_instruct | |
Let p(h) = 189*h**2. Let x(g) = 40*g - 1. Determine p(x(i)).\n | 302400*i**2 - 15120*i + 189\n | ibivibiv/math_instruct | |
Let w(i) = 2*i**2 + 3*i + 1. Let h be w(-3). Calculate the greatest common divisor of h and 1.\n | 1\n | ibivibiv/math_instruct | |
Round -0.0014636 to three decimal places.\n | -0.001\n | ibivibiv/math_instruct | |
Let r(g) = 7*g**2 + g - 1. Calculate r(1).\n | 7\n | ibivibiv/math_instruct | |
What is the highest common divisor of 30530 and 82345?\n | 215\n | ibivibiv/math_instruct | |
Let 3*y**2 + 264*y + 4080 = 0. Calculate y.\n | -68, -20\n | ibivibiv/math_instruct | |
Find z, given that -2*z**5/7 - 130*z**4/7 + 142*z**3/7 + 666*z**2/7 + 396*z/7 = 0.\n | -66, -1, 0, 3\n | ibivibiv/math_instruct | |
Evaluate ((-2)/5)/((9/2)/9).\n | -4/5\n | ibivibiv/math_instruct | |
Calculate the common denominator of -121/18 and 1/23160812.\n | 208447308\n | ibivibiv/math_instruct | |
Let r = -47 + 50. Suppose -r*c - 38 = -419. List the prime factors of c.\n | 127\n | ibivibiv/math_instruct | |
What is 612 minutes before 1:38 AM?\n | 3:26 PM\n | ibivibiv/math_instruct | |
Calculate the common denominator of (17215/(-41850) - (-2)/5)*(-11)/22 and -67/540.\n | 16740\n | ibivibiv/math_instruct | |
Collect the terms in 1 - 12*r**3 + 7*r**3 - r**3.\n | -6*r**3 + 1\n | ibivibiv/math_instruct | |
Which is the nearest to -4/7? (a) -45 (b) -0.3 (c) 0.5\n | b\n | ibivibiv/math_instruct | |
Let r(j) = -j**3 - 13*j**2 - 55*j - 1299. Let v be r(-15). Suppose -52 = 26*u - 22*u. Which is smaller: u or v?\n | v\n | ibivibiv/math_instruct | |
Four letters picked without replacement from {v: 3, i: 8}. Give prob of sequence ivvi.\n | 7/165\n | ibivibiv/math_instruct | |
What is the hundred thousands digit of 2594613?\n | 5\n | ibivibiv/math_instruct | |
Let d = 93 + -88. What is the third derivative of 220072*l**3 - 220073*l**3 - 95*l**d + 0*l**2 - 15*l - l**2 wrt l?\n | -5700*l**2 - 6\n | ibivibiv/math_instruct | |
What is the closest to -2/19 in 129, 4, 55/4, 5?\n | 4\n | ibivibiv/math_instruct | |
What is the third smallest value in 0, -1, 1.8, 0.1?\n | 0.1\n | ibivibiv/math_instruct | |
1122110122221 (base 3) to base 14\n | 18ada4\n | ibivibiv/math_instruct | |
Let v be (3/(-2))/(15/(-40)). Suppose 0 = -v*z - 12 - 4, 0 = -5*g - 5*z + 50. Let d(j) = -j**2 + 16*j - 9. What is the remainder when d(8) is divided by g?\n | 13\n | ibivibiv/math_instruct | |
Two letters picked without replacement from {l: 4, r: 16}. Give prob of sequence rr.\n | 12/19\n | ibivibiv/math_instruct | |
b"What is the ith term of 118395, 118400, 118405?\n" | 5*i + 118390\n | ibivibiv/math_instruct | |
Which is smaller: 101/986 or -1?\n | -1\n | ibivibiv/math_instruct | |
Is 3165847 prime?\n | True\n | ibivibiv/math_instruct | |
Write an educational piece suited for college students related to the following text snippet:
"# Finding general solution of elementary differential equation
Can this equation be solved using extended linearity principle?
$$\frac{dy}{dt} - 2y = 7e^{2t}$$
I found the general solution to the homogeneous portion: $y = ... | Differential equations are mathematical expressions that describe how a quantity changes relative to other quantities. They have wide applications in various fields such as physics, engineering, economics, biology, and many others. This discussion focuses on solving a specific type of first-order linear differential e... | ibivibiv/math_instruct | |
Suppose 0 = -13*x + 8*x + 5. Let c be 3 + x*(-4)/2. What is the nearest to c in 0.5, 0.2, -5?\n | 0.5\n | ibivibiv/math_instruct | |
What is the common denominator of -121/20 and -97/198?\n | 1980\n | ibivibiv/math_instruct | |
What is 1021250 to the power of 1/6, to the nearest integer?\n | 10\n | ibivibiv/math_instruct | |
Let s(y) be the third derivative of -3*y**4/8 + 11*y**3/6 + y**2. Let x = 2351 - 2344. Let a(d) = 2514 - 5012 - 13*d + 2514. What is x*s(h) - 5*a(h)?\n | 2*h - 3\n | ibivibiv/math_instruct | |
In base 15, what is -2 + -1bc90e17?\n | -1bc90e19\n | ibivibiv/math_instruct | |
Rearrange 2*q**4 + 9*q**4 - 2 - 2*q**4 - q**3 to the form c*q + s*q**2 + a*q**4 + o + m*q**3 and give a.\n | 9\n | ibivibiv/math_instruct | |
Suppose 15 = 4*p + p - k, -2*p - 3*k + 23 = 0. Let m be p + -1 + (-2 - -4). Solve -m*c + w = -0*c - 16, -12 = -3*w for c.\n | 4\n | ibivibiv/math_instruct | |
Suppose 5*k + 4*o = 2, 255 - 263 = 4*o. Solve k*l - 3*u + 7 = 0, 0*u + 6 = -3*l + 3*u for l.\n | 1\n | ibivibiv/math_instruct | |
Let t(d) = 3*d**2 + 226*d + 5989. Let q be t(-135). What is q rounded to the nearest ten thousand?\n | 30000\n | ibivibiv/math_instruct | |
Which is bigger: 66/4293143 or -1?\n | 66/4293143\n | ibivibiv/math_instruct | |
What is 539 minutes before 8:56 PM?\n | 11:57 AM\n | ibivibiv/math_instruct | |
What is the first derivative of -2*l*y**4 - 711562*l*y**2 + 2*l*y - 5215999*l wrt y?\n | -8*l*y**3 - 1423124*l*y + 2*l\n | ibivibiv/math_instruct | |
Let f = 11 - 7. Suppose -f*u = -u. Suppose u = 3*q + 2*q - 75. Solve -3*l - 15 = -5*t - 0*l, -5*t + q = 5*l for t.\n | 3\n | ibivibiv/math_instruct | |
What is the result of the following expression?
-82.6625 * -0.322 | 26.6173 | ibivibiv/math_instruct | |
Let c(h) = 10*h. Let j be c(-1). Calculate the common denominator of 42/11 and 24/(-28)*j/(-6).\n | 77\n | ibivibiv/math_instruct | |
Solve -7 + 13 = -3*q + t, -2*q - 15 = 3*t for q.\n | -3\n | ibivibiv/math_instruct | |
Is 1722 a multiple of 19?\n | False\n | ibivibiv/math_instruct | |
Let l(t) = t**2 + 6*t - 3. Let q be l(-7). Suppose 0 = -r - q*r. Let p(s) = 23 + r*s**2 - 6*s - 17 + s**2. Give p(4).\n | -2\n | ibivibiv/math_instruct | |
Collect the terms in 0*u**3 - u**3 - 4*u**3.\n | -5*u**3\n | ibivibiv/math_instruct | |
What is the least common multiple of 23400 and 95238?\n | 9523800\n | ibivibiv/math_instruct |
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