instruction_seed stringlengths 5 2.9k | response_seed stringlengths 3 9.55k | input stringclasses 1
value | _source stringclasses 1
value |
|---|---|---|---|
b"What is the tth term of 0, -14, -38, -78, -140, -230, -354, -518?\n" | -t**3 + t**2 - 10*t + 10\n | ibivibiv/math_instruct | |
Katie had 84 new games and some old games. Her friends had 8 new games and 69 old games. Together, they have 92 new games. How many old games does Katie have? | Katie and her friends together have 92 new games. Katie has 84 new games, and her friends have 8 new games.
To find out how many old games Katie has, we need to know how many old games her friends have, which is given as 69 old games. Since the question only asks for the number of old games Katie has, and there is no... | ibivibiv/math_instruct | |
What is the value of (6/3)/((-14)/14)?\n | -2\n | ibivibiv/math_instruct | |
Let i be 4/(-8)*(-7 - -1). Suppose 2*a + i*a = 20. Suppose -2*t = -2*o + t + 19, 3*t = 4*o - 23. Solve -o = -a*q + 3*n + 2, 3*q - 3 = n for q.\n | 1\n | ibivibiv/math_instruct | |
Solve 188*s - 5*q + 45 = 192*s, -400 = -4*s - 76*q for s.\n | 5\n | ibivibiv/math_instruct | |
How many millimeters are there in eighty-seven quarters of a meter?\n | 21750\n | ibivibiv/math_instruct | |
How many months are there in 1/10 of a decade?\n | 12\n | ibivibiv/math_instruct | |
Let q be (-4)/5 + 205000038/10. Suppose 0 = -5*t + 3*k - 0*k - q, 4*t + 16400005 = 5*k. What is t rounded to the nearest one million?\n | -4000000\n | ibivibiv/math_instruct | |
Calculate 215039 divided by 11.\n | 19549\n | ibivibiv/math_instruct | |
Collect the terms in 236*o**2 + 25748 - 151*o**2 - 25748.\n | 85*o**2\n | ibivibiv/math_instruct | |
Find a such that 2*a**2 - 1300*a + 1298 = 0.\n | 1, 649\n | ibivibiv/math_instruct | |
Is 2758 a multiple of 14?\n | True\n | ibivibiv/math_instruct | |
Let n(y) = -y. Let l(w) = 5*w. Let p(a) = a - 2*a - 5*a. Let r(d) = -2*d**2 + d - 5. Let c be r(0). Let g(t) = c*l(t) - 4*p(t). What is n(g(m))?\n | m\n | ibivibiv/math_instruct | |
Rearrange 9 + 19*i + 4*i - 59 + 17 to the form t + g*i and give g.\n | 23\n | ibivibiv/math_instruct | |
Sort -1/15, 2/9, -8/7, 26 in increasing order.\n | -8/7, -1/15, 2/9, 26\n | ibivibiv/math_instruct | |
Is 29 a factor of 2291?\n | True\n | ibivibiv/math_instruct | |
Suppose 4*i = -i + 265. Let s = 216 + i. Let w = s + -152. What are the prime factors of w?\n | 3, 13\n | ibivibiv/math_instruct | |
Convert -1115331 (base 7) to base 13.\n | -4b1c5\n | ibivibiv/math_instruct | |
What is fourty-three quarters of a century in months?\n | 12900\n | ibivibiv/math_instruct | |
What is eighteen fifths of a tonne in kilograms?\n | 3600\n | ibivibiv/math_instruct | |
Solve -8*s + 44 - 20 = 0 for s.\n | 3\n | ibivibiv/math_instruct | |
What is the next term in 4076, 4081, 4086?\n | 4091\n | ibivibiv/math_instruct | |
Simplify (h**(7/4))**(-30)/(h**13*h**(-1/3)) assuming h is positive.\n | h**(-391/6)\n | ibivibiv/math_instruct | |
25 + -14 + -4 + (-9 - -22)\n | 20\n | ibivibiv/math_instruct | |
Let d = 0 + 5. Suppose d*t - 540 = 5*r, 0*t - 2*t + 4*r + 216 = 0. What is t rounded to the nearest 10?\n | 110\n | ibivibiv/math_instruct | |
Calculate the remainder when 98223603 is divided by 7702.\n | 7699\n | ibivibiv/math_instruct | |
Let o(j) = -j**3 - 9*j**2 + 2. Let s be o(-9). Suppose -s*g + 176 = -52. Calculate the remainder when g is divided by 15.\n | 9\n | ibivibiv/math_instruct | |
Let d = 26 - 25.6. Let o = 5 - 2. Let z(k) = -k. Let q be z(2). Which is the closest to -0.1? (a) d (b) q (c) o\n | a\n | ibivibiv/math_instruct | |
Let t = -5 - -3. Let z be 2/(t + 4)*105. Suppose 0*a = 5*a - z. Is a composite?\n | True\n | ibivibiv/math_instruct | |
Divide -6 by 2.\n | -3\n | ibivibiv/math_instruct | |
What is 7540 rounded to the nearest one hundred thousand?\n | 0\n | ibivibiv/math_instruct | |
Solve -2*u = -g - 0*u, -28*u - 1 = -27*u for g.\n | -2\n | ibivibiv/math_instruct | |
Collect the terms in 4*l + 2410977*l**2 - 4*l + 4745638*l**2.\n | 7156615*l**2\n | ibivibiv/math_instruct | |
Convert 120110010 (base 3) to base 2.\n | 10101111111110\n | ibivibiv/math_instruct | |
Is 6863684099 prime?\n | False\n | ibivibiv/math_instruct | |
What is 3.481 rounded to one decimal place?\n | 3.5\n | ibivibiv/math_instruct | |
Collect the terms in -764*a**2 - 19*a**3 + 764*a**2.\n | -19*a**3\n | ibivibiv/math_instruct | |
b"What is the xth term of -2, 8, 42, 112, 230, 408, 658?\n" | 2*x**3 - 4*x\n | ibivibiv/math_instruct | |
Divide 1116873468 by 678.\n | 1647306\n | ibivibiv/math_instruct | |
Suppose -3*g = 4*q - 39, q + 2*g + 2 = 3*q. Let m be 20/(-8) + q/4. Which is the closest to m? (a) -0.2 (b) -6 (c) -0.3\n | c\n | ibivibiv/math_instruct | |
Rearrange (-n + 4*n + 0*n)*(-1 - 6 + 5)*(-n + 6*n + 0*n) to the form m*n**2 + u + i*n and give m.\n | -30\n | ibivibiv/math_instruct | |
Expand (-s**3 + 5*s**3 - 3*s**3 + (0*s**2 + s**2 + 0*s**2)*(-3*s + s + 4*s))*(2*s - 4*s - s).\n | -9*s**4\n | ibivibiv/math_instruct | |
Let o = 7 + -6. Let w(q) = q**3 - 3*q**2 + 2*q + 2. Let a be w(2). Suppose -3*n = a*p + 2*p - 16, -3*p = -5*n - 12. What is the third biggest value in -3, n, o?\n | -3\n | ibivibiv/math_instruct | |
Simplify ((4*(sqrt(77) + (sqrt(77) - (sqrt(77) + -3*sqrt(77))) + sqrt(77)))/(sqrt(2744)/sqrt(8)))**2.\n | 4400/49\n | ibivibiv/math_instruct | |
Suppose 2*s**4/3 - 22*s**3/3 - 32*s**2/3 + 88*s/3 + 32 = 0. Calculate s.\n | -2, -1, 2, 12\n | ibivibiv/math_instruct | |
Two letters picked without replacement from fddwfedfedjddfd. What is prob of sequence jw?\n | 1/210\n | ibivibiv/math_instruct | |
Let o = -8 + 6. Let m = -0.02562 - -2.02562. What is the closest to o in -0.05, m, -4/7?\n | -4/7\n | ibivibiv/math_instruct | |
Let y be 3/(-18)*-16 - 3. Are y and 1 equal?\n | False\n | ibivibiv/math_instruct | |
List the prime factors of 7538.\n | 2, 3769\n | ibivibiv/math_instruct | |
Which is greater: -231629 or -229567?\n | -229567\n | ibivibiv/math_instruct | |
What is 486.494 millennia in centuries?\n | 4864.94\n | ibivibiv/math_instruct | |
Put -3, 3, 1 in ascending order.\n | -3, 1, 3\n | ibivibiv/math_instruct | |
What is 585525 divided by 2775?\n | 211\n | ibivibiv/math_instruct | |
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"# Thread: Calculating Fundamental Groups
1. ## Calculating Fundamental Groups
Calculate the fundamental groups of the following spaces:
i) $X_{1} = \{ (x, y, z) \in \mathbb{R}^3 | x>0 \}$
ii) $X_{2} = \{ (x, y, z) \in \ma... | To understand the problem at hand, let's begin by defining what a fundamental group is. The fundamental group of a topological space X, denoted by π1(X), is a mathematical object that encapsulates information about loops in X and how these loops can be deformed into one another. Specifically, the elements of π1(X) are... | ibivibiv/math_instruct | |
What is next in -3219, -3653, -4861, -7239, -11183?\n | -17089\n | ibivibiv/math_instruct | |
Factor -25*s**4 - 2585*s**3 - 7605*s**2 - 7555*s - 2510.\n | -5*(s + 1)**3*(5*s + 502)\n | ibivibiv/math_instruct | |
Calculate 4*-12.33733.\n | -49.34932\n | ibivibiv/math_instruct | |
Let w = -18 - -12. Is 2*((-9)/w + 0) a multiple of 3?\n | True\n | ibivibiv/math_instruct | |
What is (-2*(-21)/(-42))/((-1)/(-3))?\n | -3\n | ibivibiv/math_instruct | |
Calculate the remainder when 1251 is divided by ((-16)/18)/(-1) - (-189376)/4842.\n | 11\n | ibivibiv/math_instruct | |
Rearrange (185*h + 268*h - 133*h)*(46 - 45*h - h - 44) to the form w*h + c + u*h**2 and give u.\n | -14720\n | ibivibiv/math_instruct | |
Let b(p) = 18*p - 29*p - 3 + 0 + 15*p - 39*p**2. Let y be b(2). Let a = -78 - y. Is 23 a factor of a?\n | False\n | ibivibiv/math_instruct | |
Calculate 70/(-28)*(-24)/(-80)*44.\n | -33\n | ibivibiv/math_instruct | |
Let u = -9.6 - -10. Suppose -3*n - 5 + 1 = -5*i, 2*i = 3*n - 2. Which is the third smallest value? (a) 0 (b) n (c) u\n | b\n | ibivibiv/math_instruct | |
Simplify ((x*x**(-3))/x**(1/9))**(2/7) assuming x is positive.\n | x**(-38/63)\n | ibivibiv/math_instruct | |
List the prime factors of 335717.\n | 97, 3461\n | ibivibiv/math_instruct | |
Find the second derivative of -1804*q**3*t - 6*q**3 + 5581*q*t - 2*t wrt q.\n | -10824*q*t - 36*q\n | ibivibiv/math_instruct | |
Suppose -3 = -w + 1. Calculate the smallest common multiple of (w/3)/((-26)/(-117)) and 9.\n | 18\n | ibivibiv/math_instruct | |
Express -4619*a - 15791*a - 170*a + 4294*a - 6851*a in the form o + i*a and give i.\n | -23137\n | ibivibiv/math_instruct | |
Simplify (s*s*s**(-3/5))/(s/(s*s/s**28*s*s*s)) assuming s is positive.\n | s**(-113/5)\n | ibivibiv/math_instruct | |
Let v(t) = 8*t**2 + 209*t + 2226. What is v(-14)?\n | 868\n | ibivibiv/math_instruct | |
Let m(h) = h**3 + h**2 + h + 1. Suppose 2*d + 3 = 1. Let f be m(d). Suppose f = 2*y - y - 3. Solve -v - 4*v = -25, -22 = -y*n - 2*v for n.\n | 4\n | ibivibiv/math_instruct | |
Let p = 1 + -3. Let z(l) = 31*l**2 - 15*l - 6. Let a(h) = -13*h**2 + 7*h + 3. Let j(c) = 7*a(c) + 3*z(c). Calculate j(p).\n | 3\n | ibivibiv/math_instruct | |
What is the common denominator of (9/(-24))/(6/62) and 79/6?\n | 24\n | ibivibiv/math_instruct | |
Let q(a) = -47*a - 1. Let y(g) = 50*g - 63*g**2 + 65*g**2 - 96*g + 46*g. Calculate q(y(f)).\n | -94*f**2 - 1\n | ibivibiv/math_instruct | |
Is 6 a factor of 39402?\n | True\n | ibivibiv/math_instruct | |
Determine p so that -2*p**4 - 3*p**4 - 14*p**3 - 95*p**2 - 465*p - 26*p**3 + 405*p = 0.\n | -4, -3, -1, 0\n | ibivibiv/math_instruct | |
In base 8, what is 455702 - -4?\n | 455706\n | ibivibiv/math_instruct | |
Let w be ((-174)/6 - -4)*3. What is the hundreds digit of (-53865)/w - (1/1)/5?\n | 7\n | ibivibiv/math_instruct | |
What is the value of 0 - -8 - (-15 + (4 - -1) + 14)?\n | 4\n | ibivibiv/math_instruct | |
b"What is the mth term of 13, -2, -41, -116, -239, -422?\n" | -2*m**3 - m + 16\n | ibivibiv/math_instruct | |
b"What is the uth term of -38278, -77582, -116886, -156190, -195494?\n" | -39304*u + 1026\n | ibivibiv/math_instruct | |
Let -4*n**3 + 2483400*n**2 - 74499300*n + 558738000 = 0. Calculate n.\n | 15, 620820\n | ibivibiv/math_instruct | |
Find the third derivative of -118*m*s**5 + 154*m*s**2 wrt s.\n | -7080*m*s**2\n | ibivibiv/math_instruct | |
Which is smaller: 27 or 28?\n | 27\n | ibivibiv/math_instruct | |
In base 10, what is -70887617 + 7?\n | -70887610\n | ibivibiv/math_instruct | |
How many hours are there in 7/6 of a day?\n | 28\n | ibivibiv/math_instruct | |
In base 8, what is 13 - -67124?\n | 67137\n | ibivibiv/math_instruct | |
Write an educational piece suited for college students related to the following text snippet:
"# Frequency-Domain Eigensolver
In these notes, we describe the mathematical background for the frequency-domain eigensolver algorithms in Meep (used by the solve_eigfreq function), which build on the frequency-domain solver ... | The frequency-domain eigensolver algorithms are crucial components of the Meep computational package, utilized by the `solve_eigfreq` function to analyze electromagnetic systems. These algorithms stem from the frequency-domain solver methodology outlined in the Meep paper. To comprehend their underpinnings, it is esse... | ibivibiv/math_instruct | |
What is prob of sequence npn when three letters picked without replacement from ppnpnnnnpnpp?\n | 3/22\n | ibivibiv/math_instruct | |
What are the prime factors of 233137363?\n | 557, 418559\n | ibivibiv/math_instruct | |
What is the square root of 19872 to the nearest integer?\n | 141\n | ibivibiv/math_instruct | |
Calculate prob of picking 2 z when two letters picked without replacement from {z: 3, h: 3, j: 1, f: 3, t: 1}.\n | 3/55\n | ibivibiv/math_instruct | |
What is next in 148, 157, 166, 175, 184?\n | 193\n | ibivibiv/math_instruct | |
Let l = -507799/180 + 2821. Find the common denominator of l and -59/180.\n | 180\n | ibivibiv/math_instruct | |
Let b = 3 - -2. Suppose 9 = 2*d + 3*p, -4*d - 2*p + b*p - 9 = 0. Is 6 a factor of 9 + (4 - d) + -2?\n | False\n | ibivibiv/math_instruct | |
Calculate the remainder when 8 is divided by 2.\n | 0\n | ibivibiv/math_instruct | |
Suppose 0 = -4*h + 2*t + 1578, 2*h + h - 1185 = t. Does 12 divide h?\n | True\n | ibivibiv/math_instruct | |
Calculate ((-252)/210*(-10)/(-56))/(1/(-1)).\n | 3/14\n | ibivibiv/math_instruct | |
What is next in -916, -880, -846, -814, -784, -756, -730?\n | -706\n | ibivibiv/math_instruct |
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