instruction_seed stringlengths 5 2.9k | response_seed stringlengths 3 9.55k | input stringclasses 1
value | _source stringclasses 1
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|---|---|---|---|
Simplify -2*(sqrt(99)/(sqrt(63)/sqrt(7)) + sqrt(55)/sqrt(5) + 2).\n | -4*sqrt(11) - 4\n | ibivibiv/math_instruct | |
Suppose -4*m = t + 4*t + 74, 3*t = m + 10. Let k be (12/96)/((-6)/m). Find z, given that z**4 + 2/3*z**3 - 2/3*z**2 - 1/3 - z + k*z**5 = 0.\n | -1, 1\n | ibivibiv/math_instruct | |
Let y = 2081 - 1566. Calculate the remainder when y is divided by 12.\n | 11\n | ibivibiv/math_instruct | |
Find f such that -4*f**3 - 28192*f**2 - 140836*f + 169032 = 0.\n | -7043, -6, 1\n | ibivibiv/math_instruct | |
What is the value of (-54)/(-30) - (-126)/(-70)?\n | 0\n | ibivibiv/math_instruct | |
Let w(s) be the second derivative of s**5/80 + 3*s**4/16 - s**3/2 - 5*s**2/2 + 162*s. Factor w(n).\n | (n - 2)*(n + 1)*(n + 10)/4\n | ibivibiv/math_instruct | |
Let d = -0.059 - 7.941. Let g = d + 7.7. Sort 3, g, -37, 2 in descending order.\n | 3, 2, g, -37\n | ibivibiv/math_instruct | |
b"What is the ath term of -925, -3675, -8343, -15019, -23793, -34755, -47995?\n" | -15*a**3 - 869*a**2 - 38*a - 3\n | ibivibiv/math_instruct | |
Calculate prob of sequence imf when three letters picked without replacement from ffmifefmiimff.\n | 9/286\n | ibivibiv/math_instruct | |
What is the first derivative of 171*b**2 + 36*b - 1251?\n | 342*b + 36\n | ibivibiv/math_instruct | |
What is the greatest common divisor of 220 and 13145?\n | 55\n | ibivibiv/math_instruct | |
-3.9+-57635.3802\n | -57639.2802\n | ibivibiv/math_instruct | |
Is 567 a factor of 78529?\n | False\n | ibivibiv/math_instruct | |
Calculate the remainder when 3682 is divided by 194.\n | 190\n | ibivibiv/math_instruct | |
What is the value of (-8497)/290 + 32 - 21/63*(2 - -7)?\n | -3/10\n | ibivibiv/math_instruct | |
(2/(-66))/((45/(-150))/((-270)/(-50)))\n | 6/11\n | ibivibiv/math_instruct | |
What is the value of 1/(-9) - 0 - 704/(-99)?\n | 7\n | ibivibiv/math_instruct | |
Divide 56353 by 2.\n | 56353/2\n | ibivibiv/math_instruct | |
Let q = 30.7 + -15.7. Let k = 0.0216 + -17.1016. Let a = k + q. What is a rounded to 1 dp?\n | -2.1\n | ibivibiv/math_instruct | |
Suppose 3*l + l = 12. Suppose 148 + 49 = 2*n - l*q, 5*q = -4*n + 339. Round n to the nearest 10.\n | 90\n | ibivibiv/math_instruct | |
Is 6245 prime?\n | False\n | ibivibiv/math_instruct | |
Suppose -j + 11 = -3*a, 2*a + 2 = j - 3*j. Suppose -j*s - 2*s + 204 = 0. Calculate the greatest common factor of 17 and s.\n | 17\n | ibivibiv/math_instruct | |
Expand w**2 + w**3 - w**2 + w**3 - 4*w**3 + 4*w**3 + (-3*w**2 + 5*w**2 - 4*w**2)*(-3*w + w + 0*w) - 9 + 20*w**3 + 9.\n | 26*w**3\n | ibivibiv/math_instruct | |
Calculate the remainder when 60 is divided by 11.\n | 5\n | ibivibiv/math_instruct | |
What is the next term in -17573, -140517, -474217, -1124051, -2195397, -3793633, -6024137?\n | -8992287\n | ibivibiv/math_instruct | |
b"What is the jth term of 234337, 468832, 703327, 937822, 1172317, 1406812?\n" | 234495*j - 158\n | ibivibiv/math_instruct | |
Factor -2*b**2 - 222*b - 1260.\n | -2*(b + 6)*(b + 105)\n | ibivibiv/math_instruct | |
Let v be 3/7 + 73/(-7). Let y(o) = -o**2 - 10*o. Let g be y(v). Let h = 71 + -73. Which is the nearest to g? (a) 0.4 (b) 4 (c) h\n | a\n | ibivibiv/math_instruct | |
Find c, given that -17035*c**2 - 10*c = 0.\n | -2/3407, 0\n | ibivibiv/math_instruct | |
What is the nearest to -4 in -0.4, 2/9, 0.3, 5?\n | -0.4\n | ibivibiv/math_instruct | |
Solve 4*v = -4*u, -3*v - 661*u - 2 = -660*u for v.\n | -1\n | ibivibiv/math_instruct | |
Convert 12217.392 months to years.\n | 1018.116\n | ibivibiv/math_instruct | |
Let x(s) = -6*s**2. Let c(p) = 5*p + 8. Let q(u) = -4*u - 7. Let z(n) = 3*c(n) + 4*q(n). Let k be z(-5). Determine x(k).\n | -6\n | ibivibiv/math_instruct | |
What is (-6)/1*3/5*5150/412?\n | -45\n | ibivibiv/math_instruct | |
Is 36312 a multiple of 26?\n | False\n | ibivibiv/math_instruct | |
Is 4701 composite?\n | True\n | ibivibiv/math_instruct | |
What is the value of ((-1)/14)/((-28)/(-336))?\n | -6/7\n | ibivibiv/math_instruct | |
Evaluate 19 + -18 + -27 - -12 - -11.\n | -3\n | ibivibiv/math_instruct | |
What is the units digit of 882?\n | 2\n | ibivibiv/math_instruct | |
Write an educational piece suited for college students related to the following text snippet:
"I would like to find the adjoint operator in the Hilbertspace $L^2(0,\infty)$ of the operator $$(Ax)(t)=x(at), x\in L^2(0,\infty), a>0.$$
My calculation is the following; I use the substitution $u=at$.
$$\langle Ax,y\rangle... | To begin, lets establish some necessary background information. The concept of an adjoint operator arises from functional analysis, which studies vector spaces equipped with a topology, allowing for the notion of continuity. Specifically, within this context, we consider Hilbert spaces - complete inner product spaces,... | ibivibiv/math_instruct | |
What is -147111445000 rounded to the nearest one million?\n | -147111000000\n | ibivibiv/math_instruct | |
Let o = 0 - -26. Let t be o*3/378 - (-6)/(-14). Sort 6, -4, t in decreasing order.\n | 6, t, -4\n | ibivibiv/math_instruct | |
Two letters picked without replacement from csccnen. Give prob of sequence ns.\n | 1/21\n | ibivibiv/math_instruct | |
Let u be (-508)/(-12) + 4/(-3). Let f = -22 + u. What is the units digit of f?\n | 9\n | ibivibiv/math_instruct | |
Let w(v) = -3*v**3 + 15*v**2 + 4*v + 5. Let g(y) = -4*y**3 + 22*y**2 + 6*y + 7. Give 5*g(c) - 7*w(c).\n | c**3 + 5*c**2 + 2*c\n | ibivibiv/math_instruct | |
Suppose 0 = 2*n - 6 - 26. Suppose 0 = 2*u, 4*m - 4*u - n = 8. Calculate the greatest common factor of m and 12.\n | 6\n | ibivibiv/math_instruct | |
Let s(z) be the first derivative of z**6/30 + z**5/25 - z**4/10 - 4. Determine j, given that s(j) = 0.\n | -2, 0, 1\n | ibivibiv/math_instruct | |
Let j = -224 - -224.2. Suppose -3*y - 3 = -v + 6, 2*y + 3*v = -6. Which is the closest to 1? (a) -0.5 (b) y (c) j\n | c\n | ibivibiv/math_instruct | |
Differentiate -132*c**2 + c - 3 wrt c.\n | -264*c + 1\n | ibivibiv/math_instruct | |
Suppose 3*r = -5*h + 63, h + 72 - 87 = -3*r. What is the highest common divisor of h and 180?\n | 12\n | ibivibiv/math_instruct | |
Which is the closest to -2? (a) 0.5 (b) 3 (c) -0.034\n | c\n | ibivibiv/math_instruct | |
Let m(q) be the first derivative of q**7/280 + q**5/24 - q**3/3 - 1. Let f(y) be the third derivative of m(y). What is the second derivative of f(j) wrt j?\n | 18*j\n | ibivibiv/math_instruct | |
Simplify ((((w*w**(-2/17))/(w**(4/7)*w))**42)**(-1/8))**(1/41) assuming w is positive.\n | w**(3/34)\n | ibivibiv/math_instruct | |
Let q = 1 - 2. Let z = q + 5. Sort -2/9, z, -0.1 in ascending order.\n | -2/9, -0.1, z\n | ibivibiv/math_instruct | |
Let x be ((-2)/6)/((-3)/45). Let p(g) = g**2 + 4. Let o(v) = -v**2 - 5. What is x*p(t) + 4*o(t)?\n | t**2\n | ibivibiv/math_instruct | |
Let i = -5 - -7. Let u be (0 - -1)*(1 + i). Suppose u*f - 101 = 40. What is f rounded to the nearest 10?\n | 50\n | ibivibiv/math_instruct | |
-1876050 divided by 165\n | -11370\n | ibivibiv/math_instruct | |
Let c(p) = p**3 - 11*p**2 - 31*p + 327. Let y be c(12). Let u = 48 - 143/3. What is the closest to y in -0.5, 0.3, u?\n | u\n | ibivibiv/math_instruct | |
What is next in 300974, 300968, 300962, 300956, 300950, 300944?\n | 300938\n | ibivibiv/math_instruct | |
Two letters picked without replacement from hgphppchhhhcdhdhdj. What is prob of sequence hp?\n | 4/51\n | ibivibiv/math_instruct | |
Let m = 127 - 124. Is m + 139 + (-3)/3 + 4 prime?\n | False\n | ibivibiv/math_instruct | |
Let p(x) = 160*x + 145. What is p(-2)?\n | -175\n | ibivibiv/math_instruct | |
What is prob of picking 3 l and 1 f when four letters picked without replacement from zlehlefrhlehllh?\n | 2/273\n | ibivibiv/math_instruct | |
Let h = 892141 + -4422141. Round h to the nearest 1000000.\n | -4000000\n | ibivibiv/math_instruct | |
Let f = 4 - 2. Suppose -t + f*l = -1, -5*t - l + 0*l - 6 = 0. Put 5, 0, t in increasing order.\n | t, 0, 5\n | ibivibiv/math_instruct | |
What is the derivative of -100951862*d**2 - 174385921?\n | -201903724*d\n | ibivibiv/math_instruct | |
Calculate the remainder when 236247 is divided by 114.\n | 39\n | ibivibiv/math_instruct | |
Expand (-u + 15*u - 4*u)*(u + u - 3*u + (0 - 1 + 4)*(4*u - 3*u + u)).\n | 50*u**2\n | ibivibiv/math_instruct | |
Sort 2/7, 1, -2/5, -4, -23, -3/631.\n | -23, -4, -2/5, -3/631, 2/7, 1\n | ibivibiv/math_instruct | |
Simplify ((d*d/(d*d/d**(-1/4))*d)/d)**(-16)*d*d**0*d*d**4 assuming d is positive.\n | d**10\n | ibivibiv/math_instruct | |
Let g(q) = 2*q**2 - 14*q + 30. Calculate g(6).\n | 18\n | ibivibiv/math_instruct | |
Let m be ((-6)/(-15))/(4/360). Suppose m = 2*b + 5*v, 3*b - 79 = -0*b + 5*v. Suppose -4*s + r + b = 0, -s - 5*r = 4*s - 35. Solve 3*n - s*n = 9 for n.\n | -3\n | ibivibiv/math_instruct | |
Collect the terms in -31 - 20440*x + 31 + 19938*x.\n | -502*x\n | ibivibiv/math_instruct | |
What is -10362.21999 rounded to zero dps?\n | -10362\n | ibivibiv/math_instruct | |
Put -8, -9, 1, 4 in decreasing order.\n | 4, 1, -8, -9\n | ibivibiv/math_instruct | |
What is 320 minutes before 3:37 PM?\n | 10:17 AM\n | ibivibiv/math_instruct | |
Let c = 0.13 - -0.07. What is the closest to -0.1 in c, -5, 1/2?\n | c\n | ibivibiv/math_instruct | |
Let t = 183 - 19. Suppose 4*p + 4*k = t, 3*p - 2*k - 113 = -3*k. Suppose -p = -4*d - 2*h, -18 - 15 = -3*d - 3*h. List the prime factors of d.\n | 7\n | ibivibiv/math_instruct | |
Let w(b) = 3*b**2 - b. Let p(f) = -5*f**2 + 9*f + 5. Let g(t) = 6*t**2 - 8*t - 4. Let a(q) = -5*g(q) - 4*p(q). Give -2*a(d) - 7*w(d).\n | -d**2 - d\n | ibivibiv/math_instruct | |
Is 28 a factor of 31698?\n | False\n | ibivibiv/math_instruct | |
Find the third derivative of -37*d**3*q**3 - 47*d**3 + 11893*d**2*q**3 wrt d.\n | -222*q**3 - 282\n | ibivibiv/math_instruct | |
What is the value of (1080/126)/((-415)/(-1743))?\n | 36\n | ibivibiv/math_instruct | |
Calculate the common denominator of 41/41841 and -67/1539.\n | 7154811\n | ibivibiv/math_instruct | |
Suppose 2*j - 24 = 36. Let n be 6/4*25*(0 + 2). What is the greatest common factor of j and n?\n | 15\n | ibivibiv/math_instruct | |
Suppose 0 = n + 3*v - 5*v + 1, 0 = -3*n - 4*v + 17. Let p be 36/(-270) - 424/(-30). Let u(j) = -111*j**3 + p*j + 2 - 15*j + 110*j**3 + 4*j**2. Give u(n).\n | 8\n | ibivibiv/math_instruct | |
Calculate 416*-14.\n | -5824\n | ibivibiv/math_instruct | |
Write an educational piece suited for college students related to the following text snippet:
"# Write down what metric this transformation preserves based on animation
https://www.desmos.com/calculator/u5qpd135uc
I made it because I wanted to compare and contrast it with the Lorentz boost.
The transformation should... | Let us begin by describing the given transformation in more detail. The provided Desmos link contains a graph with two sets of curves: green and red. It appears that there is a family of green hyperbolas, where each branch can be described by the equation xy = c for some constant c > 0. Additionally, there are red par... | ibivibiv/math_instruct | |
Suppose -22*f - 6*p - 229 = -24*f - 3, 0 = 3*p. Let z(t) = t**3 + 49. Let v be z(0). Let c = v + f. What is the units digit of c?\n | 2\n | ibivibiv/math_instruct | |
Let i = -1.3 + 6.3. Let m = 23.6 - 40.5. Let c = m - -20.9. Put -2/15, i, c in descending order.\n | i, c, -2/15\n | ibivibiv/math_instruct | |
Calculate the highest common divisor of 6 and 11301.\n | 3\n | ibivibiv/math_instruct | |
What is the thousands digit of 4430?\n | 4\n | ibivibiv/math_instruct | |
Let a(c) = -1875*c + 10. Let g(w) = -46*w + 1. What is -2*a(t) + 18*g(t)?\n | 2922*t - 2\n | ibivibiv/math_instruct | |
Let k = -1.5 + 1. Let p be 3/9 + (-1)/21. Put k, p, -1/7 in decreasing order.\n | p, -1/7, k\n | ibivibiv/math_instruct | |
Let v = -2/11745 - -67862/11745. Calculate the common denominator of v and (-498)/(-102) - 5 - 750/561.\n | 99\n | ibivibiv/math_instruct | |
List the prime factors of 539228.\n | 2, 134807\n | ibivibiv/math_instruct | |
Simplify (t/(t*t**(-4))*t/(t/(t/(t*t*(t/t**(2/7))/t*t))))/(t**3*t/(t/(t*t**(-3/8))))*((((t*t**(-2/5))/t)/t)/t*t/(t**(-2)/t))**(-32) assuming t is positive.\n | t**(-14711/280)\n | ibivibiv/math_instruct | |
How many minutes are there between 12:49 AM and 3:29 AM?\n | 160\n | ibivibiv/math_instruct | |
Sort -7, 0, -1, 0.3.\n | -7, -1, 0, 0.3\n | ibivibiv/math_instruct | |
What is -479.39 rounded to the nearest ten?\n | -480\n | ibivibiv/math_instruct | |
Let v = -10 - -15. Suppose -k - 191 = -v*r, -3*r + 2*r - 5*k = -59. Is 17 a factor of r?\n | False\n | ibivibiv/math_instruct |
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