instruction_seed stringlengths 5 2.9k | response_seed stringlengths 3 9.55k | input stringclasses 1
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Let b be ((-6800)/(-15))/((-1 - -2)/(-3)). Let g be (-1)/(b/(-455) + -3). Let a = g + -78. Solve -2*s + 3*i = -14, s + 2*i - a = 5*i for s.\n | 1\n | ibivibiv/math_instruct | |
What is the units digit of 609?\n | 9\n | ibivibiv/math_instruct | |
-1 divided by -24\n | 1/24\n | ibivibiv/math_instruct | |
What is the nearest to -0.04 in 1/3039, 1, 2?\n | 1/3039\n | ibivibiv/math_instruct | |
Suppose -4*h + o = -18, -2*h + 0*o = -3*o - 4. Suppose 3*r - 8 = 2*u + 10, 5*u + h*r + 20 = 0. Does 6 divide (9/u)/((-6)/56)?\n | False\n | ibivibiv/math_instruct | |
Round 15.431801 to the nearest integer.\n | 15\n | ibivibiv/math_instruct | |
Collect the terms in 2581*k**2 - 1290*k**2 - 1291*k**2 - 9 + 23*k**3.\n | 23*k**3 - 9\n | ibivibiv/math_instruct | |
Let w = -407.0936 - -407. Let g = -11.8464 + w. Round g to the nearest integer.\n | -12\n | ibivibiv/math_instruct | |
What is the closest to 2/11 in 14, 0.6, 3?\n | 0.6\n | ibivibiv/math_instruct | |
Calculate -11 + 7 + -36 + (51 - 63).\n | -52\n | ibivibiv/math_instruct | |
Let l(o) = 5*o + 2. Let m = 7 - 3. Let p be l(m). Let f = p + -10. What is the units digit of f?\n | 2\n | ibivibiv/math_instruct | |
Calculate prob of picking 4 z when four letters picked without replacement from zzzjzzogzzggoo.\n | 5/143\n | ibivibiv/math_instruct | |
Let v(g) be the first derivative of -3*g**2 - g - 287. Let l(m) = 1. Determine -2*l(t) - v(t).\n | 6*t - 1\n | ibivibiv/math_instruct | |
Simplify (((3*1*sqrt(660))/(sqrt(12) - 2*sqrt(48)))/(2*6*(sqrt(125) + sqrt(125)*-4)))**2.\n | 11/32400\n | ibivibiv/math_instruct | |
Simplify (1*sqrt(112) + -2 - ((4 + sqrt(112)*3)**2 + sqrt(112)))*-6.\n | 576*sqrt(7) + 6156\n | ibivibiv/math_instruct | |
Let t be (5/5)/((-1)/(3 + -33)). Suppose -t = 5*a - z - 4*z, 5*a = -4*z - 30. Calculate the remainder when 75 is divided by 11 - a/(-6)*(0 + -2).\n | 10\n | ibivibiv/math_instruct | |
What is the closest to -139/3 in 2, 4, 0.5?\n | 0.5\n | ibivibiv/math_instruct | |
Let m(k) be the third derivative of 7*k**4/24 - k**2. Let d(x) be the second derivative of -x**4/4 + 12393*x. Calculate d(m(r)).\n | -147*r**2\n | ibivibiv/math_instruct | |
Let o(x) = x**3 + 2*x**2 - 2*x + 1. Let c be (-262)/(-917) - (-40)/7. Let h(q) = q**3 + q**2 - q. What is c*h(p) - 3*o(p)?\n | 3*p**3 - 3\n | ibivibiv/math_instruct | |
Calculate the remainder when 1632 is divided by 247.\n | 150\n | ibivibiv/math_instruct | |
Suppose -4*x - 31 + 115 = 0. Suppose -x*j + 25 = -16*j. Solve t - j = 5*t - f, 3*f + 1 = -4*t for t.\n | -1\n | ibivibiv/math_instruct | |
Let w be (1038/18)/((-3)/(-63)). Suppose 6*r - 127 = w. Is r a composite number?\n | False\n | ibivibiv/math_instruct | |
Suppose 4*r - 3 = 9. Suppose -3*t - r*v = -21, -2*v - 3 + 1 = 0. What is the units digit of (-1 - 2)*t/(-12)?\n | 2\n | ibivibiv/math_instruct | |
Which is the closest to -23? (a) 1 (b) 0.2 (c) -0.07\n | c\n | ibivibiv/math_instruct | |
Write an educational piece suited for college students related to the following text snippet:
"# Graph with n nodes and 2n arrows revisited
Let G be a weakly-connected directed graph on n nodes such that:
1. n is odd.
2. Every node has exactly 2 arrows going into it.
3. Every node has exactly 2 arrows going out of ... | We begin by examining the given conditions for the directed graph \(G\) with \(n\) nodes. Let us restate and analyze these properties one by one:
1. The number of nodes, \(n\), is odd. This implies that \(n \geq 3\), since a graph with only one or two nodes cannot satisfy the remaining conditions.
2. Each node has ex... | ibivibiv/math_instruct | |
Let d be ((-2)/(-5))/1*-5. Let w be d/4*(8 - (-280)/(-30)). Suppose -w*x**2 - 8/3*x - 8/3 = 0. Calculate x.\n | -2\n | ibivibiv/math_instruct | |
Let z be 4/6*(3 - 0). Let v = z - -1. Let l(s) = 13*s - 2. Let h be l(2). Solve g = 3 - 0, 0 = v*y - 3*g + h for y.\n | -5\n | ibivibiv/math_instruct | |
Express 8*h + 0*h**2 - 17*h**2 - 9*h + (-h**2 + 19*h**2 - h**2)*(-2 + 3 - 3) as w*h + a*h**2 + n and give w.\n | -1\n | ibivibiv/math_instruct | |
Let s = 4 - 3. Suppose 2*m = -4*o - s + 7, o - 5*m = 29. Let f(q) = 2*q**2 - 5*q. What is the tens digit of f(o)?\n | 1\n | ibivibiv/math_instruct | |
Let p = 133 - 133.0000226. What is p rounded to 6 dps?\n | -0.000023\n | ibivibiv/math_instruct | |
Is 4585 a multiple of 4?\n | False\n | ibivibiv/math_instruct | |
Let r(x) = 12*x**2 + x - 11. Calculate r(2).\n | 39\n | ibivibiv/math_instruct | |
((-645)/35 - -20) + 6/14\n | 2\n | ibivibiv/math_instruct | |
Suppose 3*b = 4*q + q + 34, 8 = b - q. Suppose -b*s = 2*s - 220. What is the highest common divisor of s and 11?\n | 11\n | ibivibiv/math_instruct | |
What is the second derivative of 2*s**4*y + 79*s**4 + 12*s**2 - 13775*s*y wrt s?\n | 24*s**2*y + 948*s**2 + 24\n | ibivibiv/math_instruct | |
What is 325282 to the power of 1/8, to the nearest integer?\n | 5\n | ibivibiv/math_instruct | |
What is the derivative of -24646*c**3*x**3 + c**2*x**3 - 336*x**3 + 39*x**2 + 1 wrt c?\n | -73938*c**2*x**3 + 2*c*x**3\n | ibivibiv/math_instruct | |
Are -30/53 and -2 nonequal?\n | True\n | ibivibiv/math_instruct | |
What is ((-18*297/33)/(6/(-4)))/2?\n | 54\n | ibivibiv/math_instruct | |
Evaluate (-4 - 0 - -11) + (-5 - 4) + 30 + -25.\n | 3\n | ibivibiv/math_instruct | |
Simplify (u**(-11))**(2/5) assuming u is positive.\n | u**(-22/5)\n | ibivibiv/math_instruct | |
Let a(n) = n + 7. Let j be a(-5). Suppose j*f - 1 = g - 0, -5*g + 5*f + 5 = 0. Let x(y) = -y**3 + 3*y**2 - 2*y + 4. Calculate x(g).\n | -2\n | ibivibiv/math_instruct | |
Round 2.0931571 to 2 dps.\n | 2.09\n | ibivibiv/math_instruct | |
Let v(l) be the second derivative of 19*l**3/6 + 297*l. Let b(f) = 2*f. Calculate b(v(c)).\n | 38*c\n | ibivibiv/math_instruct | |
What is -358632 divided by 204?\n | -1758\n | ibivibiv/math_instruct | |
List the prime factors of 129777443.\n | 53, 2448631\n | ibivibiv/math_instruct | |
Solve -78*s = 6*s + 588 for s.\n | -7\n | ibivibiv/math_instruct | |
Suppose u = -r + 5, -3*u = 4*r - u - 26. Let m = -10 + r. Let i be (-9)/m*(-4 + 6). Solve -2*c = c + i for c.\n | -3\n | ibivibiv/math_instruct | |
Let j = -12 - -17. Suppose 0 = -j*y - 0*r + 3*r - 14, -3*y = -4*r + 15. Let v be (-1 - (-1 + 1))/(y/(-2)). Which is smaller: v or -16?\n | -16\n | ibivibiv/math_instruct | |
What is 336662 to the power of 1/7, to the nearest integer?\n | 6\n | ibivibiv/math_instruct | |
What is the nearest to 0 in 1/3, 0.5, -3, -3/2?\n | 1/3\n | ibivibiv/math_instruct | |
Calculate prob of picking 1 l and 1 p when two letters picked without replacement from lzzzpzzll.\n | 1/12\n | ibivibiv/math_instruct | |
What is -0.080166 minus -0.052?\n | -0.028166\n | ibivibiv/math_instruct | |
Let q(j) = j + 70627 - 70627 + 3*j. Let w(y) = y + 1. Let u = 1 + -2. Let x(z) = 15*z + 20. Let p(s) = u*x(s) + 20*w(s). Calculate p(q(k)).\n | 20*k\n | ibivibiv/math_instruct | |
Let j(k) = 185*k**2 + 50*k + 408. What are the prime factors of j(-9)?\n | 3, 17, 293\n | ibivibiv/math_instruct | |
Let n = 16 + -67. Suppose 0 = -6*u + 7*u + 47. Let q = u - n. Calculate the remainder when q is divided by 2.\n | 0\n | ibivibiv/math_instruct | |
Is 3579 a prime number?\n | False\n | ibivibiv/math_instruct | |
What is 2871.002us in milliseconds?\n | 2.871002\n | ibivibiv/math_instruct | |
Solve g + 4*c + 27 = 0, 121*c = 122*c + 8 for g.\n | 5\n | ibivibiv/math_instruct | |
Let v = 18 + 0. Let y be (9814/v - -1) + (-402)/1809. What is the greatest common divisor of 26 and y?\n | 26\n | ibivibiv/math_instruct | |
What are the prime factors of 30130?\n | 2, 5, 23, 131\n | ibivibiv/math_instruct | |
Let k(i) = i - 3. Let c be k(-10). Let r(h) = -10*h**2 - 11*h - 4. Let j(s) = -20*s**2 - 23*s - 9. Let f(y) = c*r(y) + 6*j(y). What is the tens digit of f(3)?\n | 0\n | ibivibiv/math_instruct | |
Find the common denominator of 89/11424 and 71/4857648.\n | 68007072\n | ibivibiv/math_instruct | |
b"What is the nth term of 115, 151, 105, -23, -233, -525?\n" | -41*n**2 + 159*n - 3\n | ibivibiv/math_instruct | |
Find the third derivative of 39*m**4 - 5*m**3*q**2 + 314*m**3 + 4*m**2*q**2 - 1846*m**2*q + 2 wrt m.\n | 936*m - 30*q**2 + 1884\n | ibivibiv/math_instruct | |
Let w = 17.3 + -18. What is the second biggest value in 0, -2/13, w?\n | -2/13\n | ibivibiv/math_instruct | |
Let z(t) = -21*t**2 - 2454*t - 70494. Give z(-66).\n | -6\n | ibivibiv/math_instruct | |
Let d(v) = -v - 15. Let g be d(-12). Let n = g + 5. Suppose f = 10 - n. Calculate the lowest common multiple of f and 9.\n | 72\n | ibivibiv/math_instruct | |
Collect the terms in -4*m + 33658 - 2*m - m.\n | -7*m + 33658\n | ibivibiv/math_instruct | |
Suppose c - 14 + 4 = 0. Solve 15 = i + c for i.\n | 5\n | ibivibiv/math_instruct | |
Put 0, 2/13, 28146573 in increasing order.\n | 0, 2/13, 28146573\n | ibivibiv/math_instruct | |
Let q(y) = 3*y**3 - 5*y - 2. Let d(z) = -6*z**3 + 11*z + 5. Calculate -4*d(i) - 9*q(i).\n | -3*i**3 + i - 2\n | ibivibiv/math_instruct | |
Calculate 13268 + 0.006897314.\n | 13268.006897314\n | ibivibiv/math_instruct | |
Let v be (-1 + (-2)/(-2))/3. Suppose 3*m - m + 1400 = v. What is m rounded to the nearest one hundred?\n | -700\n | ibivibiv/math_instruct | |
Let p(h) = -4*h**3 - 5*h**2 - 3*h. Let k(z) = -9*z**3 - 10*z**2 - 5*z. Give -3*k(o) + 5*p(o).\n | 7*o**3 + 5*o**2\n | ibivibiv/math_instruct | |
Round -0.0000064433941 to six dps.\n | -0.000006\n | ibivibiv/math_instruct | |
What is prob of picking 2 c and 2 f when four letters picked without replacement from jcfcjcfc?\n | 3/35\n | ibivibiv/math_instruct | |
Find the first derivative of 241213640*f**2 + 775086817.\n | 482427280*f\n | ibivibiv/math_instruct | |
Let r be (2/(-24))/((-111)/(-6956)) + -5 + 10. Let l = 87 - 86.7. What is the nearest to -0.2 in l, 1, r?\n | r\n | ibivibiv/math_instruct | |
Let m(v) = v**2 - 9*v - 11. Suppose 417 = 2*x + 123. What is the remainder when x is divided by m(-3)?\n | 22\n | ibivibiv/math_instruct | |
What is the hundreds digit of 1360048?\n | 0\n | ibivibiv/math_instruct | |
Simplify (i/(i/(i/(i*i*i**(6/5)*i)))*i**10)**(-4/35) assuming i is positive.\n | i**(-136/175)\n | ibivibiv/math_instruct | |
Let r(w) = -6*w - 8. Let o be r(-9). Suppose 0 = 5*k + 3*m - o, -2*k + 22 = 2*m + m. Suppose -4 = 2*y - k. Solve -3*n + y*n = 0 for n.\n | 0\n | ibivibiv/math_instruct | |
Simplify u**(6/5)/u*(u*u**(-1))/u*(u*u*u**(-2/3)*u)**(-31) assuming u is positive.\n | u**(-1097/15)\n | ibivibiv/math_instruct | |
Calculate prob of picking 1 k and 1 o when two letters picked without replacement from gllloggkglg.\n | 1/55\n | ibivibiv/math_instruct | |
Calculate the smallest common multiple of 65 and 312.\n | 1560\n | ibivibiv/math_instruct | |
Suppose -m + 6 - 3 = 0. Suppose -u - 1 = 0, -5*h - 1 = m*u + 17. Let v(q) = -1011111*q**2 + q + 2. Let j be v(h). Round j to the nearest 1000000.\n | -9000000\n | ibivibiv/math_instruct | |
What is the third root of 74024 to the nearest integer?\n | 42\n | ibivibiv/math_instruct | |
Let l = -41828/3 - -13941. Which is the third biggest value? (a) -2/5 (b) 95 (c) 5/4 (d) -3 (e) l\n | a\n | ibivibiv/math_instruct | |
Suppose 46*m - 43*m + 33 = 0. Let y = m + 15. Suppose 0*a + 4 = -3*a - 4*n, -4 = y*n. Solve a = u + 3*x - 4*x, 2*u - x - 2 = 0 for u.\n | 2\n | ibivibiv/math_instruct | |
Calculate the remainder when 73255 is divided by 2519.\n | 204\n | ibivibiv/math_instruct | |
In base 3, what is -10210121 - -11222211120?\n | 11212000222\n | ibivibiv/math_instruct | |
Three letters picked without replacement from cnccccncccccccccnn. Give prob of picking 1 n and 2 c.\n | 91/204\n | ibivibiv/math_instruct | |
Calculate the least common multiple of 17472 and 42.\n | 17472\n | ibivibiv/math_instruct | |
Let f be (-14)/(-4) + (-4)/8*-3. Suppose -3*c - f*a = -279, 2*c = -2*a + 63 + 127. What are the prime factors of c?\n | 2, 7\n | ibivibiv/math_instruct | |
Which is the closest to -0.26? (a) -2 (b) 0 (c) -4/3 (d) -37/12\n | b\n | ibivibiv/math_instruct | |
Calculate the lowest common multiple of 51 and 3.\n | 51\n | ibivibiv/math_instruct | |
Let n(c) = -4*c**3 - 124*c**2 - 236*c - 106. Let q(t) = 20*t**3 + 620*t**2 + 1180*t + 525. Let g(s) = -11*n(s) - 2*q(s). Factor g(a).\n | 4*(a + 1)**2*(a + 29)\n | ibivibiv/math_instruct | |
Sort 0, 892, -6, -2, 3 in decreasing order.\n | 892, 3, 0, -2, -6\n | ibivibiv/math_instruct | |
What is -85ab (base 14) in base 7?\n | -124204\n | ibivibiv/math_instruct |
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