instruction_seed stringlengths 5 2.9k | response_seed stringlengths 3 9.55k | input stringclasses 1
value | _source stringclasses 1
value |
|---|---|---|---|
Collect the terms in -19*c**2 + 3*c**2 - 21*c**2 - 19*c**2 + 70*c**2 - 17*c**2.\n | -3*c**2\n | ibivibiv/math_instruct | |
What is the next term in 70, 4, -60, -122, -182, -240, -296?\n | -350\n | ibivibiv/math_instruct | |
Round -2170.6 to the nearest one hundred.\n | -2200\n | ibivibiv/math_instruct | |
What is the highest common factor of 99 and 55?\n | 11\n | ibivibiv/math_instruct | |
What is the second smallest value in -3/2, 1, -88, -0.1, -1?\n | -3/2\n | ibivibiv/math_instruct | |
Let q be (-455)/(-130) - 2/(-4). What is the closest to 0 in -0.95, q, -0.7?\n | -0.7\n | ibivibiv/math_instruct | |
Which is the closest to -23? (a) -3/2 (b) 12 (c) 1.99 (d) -55/4 (e) 1\n | d\n | ibivibiv/math_instruct | |
What is 1 - (6 + -1 - (14 + 19 + -11 + 6))?\n | 24\n | ibivibiv/math_instruct | |
What is the greatest common factor of 262417 and 1588?\n | 397\n | ibivibiv/math_instruct | |
Suppose -y = -3*s + 17, 6*y - 3*y = -s - 61. Let t = -9 - y. Is t even?\n | False\n | ibivibiv/math_instruct | |
Which is the closest to -0.1? (a) -18 (b) 1/4 (c) 5\n | b\n | ibivibiv/math_instruct | |
Calculate -16717311 divided by -4927.\n | 3393\n | ibivibiv/math_instruct | |
Let g be 0/(-7) + (2/(-1) - -6). Suppose -3*p - 729 = -g*s, -2*s + 172 + 191 = -p. Suppose s = 7*b - 5*b. Does 9 divide b?\n | True\n | ibivibiv/math_instruct | |
Let l(u) be the third derivative of u**5/60 - u**4/24 - 260000*u**3/3 + 2*u**2. Let t = 14 - 14. Let w be l(t). Round w to the nearest 100000.\n | -500000\n | ibivibiv/math_instruct | |
What comes next: -164205, -164200, -164191, -164178, -164161?\n | -164140\n | ibivibiv/math_instruct | |
List the prime factors of 134118683.\n | 47, 113, 25253\n | ibivibiv/math_instruct | |
Round -46.63678 to two decimal places.\n | -46.64\n | ibivibiv/math_instruct | |
Let k = -67 - -41. Let g = 13183.114 + -13209. Let h = k - g. What is h rounded to 2 decimal places?\n | -0.11\n | ibivibiv/math_instruct | |
Let q = -296 - -303. Suppose q*v + v = 1640. What are the prime factors of v?\n | 5, 41\n | ibivibiv/math_instruct | |
Let z be 5/2*12/15. Let m(q) = -5*q - 33. Let v be m(-9). Solve z*x - v - 2 = 4*w, 5*x = -w - 20 for w.\n | -5\n | ibivibiv/math_instruct | |
What is (-138)/690*2*(-40)/(-18)?\n | -8/9\n | ibivibiv/math_instruct | |
Simplify ((h/h**(1/4))/(h**1*h))**(7/3) assuming h is positive.\n | h**(-35/12)\n | ibivibiv/math_instruct | |
Does 1 = 202/254993?\n | False\n | ibivibiv/math_instruct | |
Is -282 bigger than -282?\n | False\n | ibivibiv/math_instruct | |
In base 6, what is -12510515152 + -5?\n | -12510515201\n | ibivibiv/math_instruct | |
Solve -2018*i + 609*i + 5636 = 0 for i.\n | 4\n | ibivibiv/math_instruct | |
Let p = 511 + -512. Which is the closest to p? (a) -1 (b) -2 (c) 6\n | a\n | ibivibiv/math_instruct | |
What comes next: 8899, 17736, 26573, 35410, 44247?\n | 53084\n | ibivibiv/math_instruct | |
What is the next term in -5, 102, 289, 562, 927, 1390, 1957, 2634?\n | 3427\n | ibivibiv/math_instruct | |
Solve 77*h - 89*h - 19386 = 58*h + 289*h for h.\n | -54\n | ibivibiv/math_instruct | |
Suppose 0 = 2*w - 3*w. Find the common denominator of ((-2)/3)/((-80)/(-582)) and 2*(w - 339/108).\n | 180\n | ibivibiv/math_instruct | |
What is -66*(-46)/14168*-2?\n | -3/7\n | ibivibiv/math_instruct | |
Divide 207620 by 20.\n | 10381\n | ibivibiv/math_instruct | |
Rearrange -2 - 326*m**2 + 661*m**2 - 336*m**2 + 275*m + 0 to the form t + o*m + c*m**2 and give o.\n | 275\n | ibivibiv/math_instruct | |
Solve 90*z = 152 - 152 for z.\n | 0\n | ibivibiv/math_instruct | |
((4/(-12))/((-7)/((-2268)/30)))/((-552)/40)\n | 6/23\n | ibivibiv/math_instruct | |
Is 7636028783 composite?\n | True\n | ibivibiv/math_instruct | |
Let p = -1.02 - 19.48. Let b = -20 - p. Let h = 4.6 + 0.4. Sort h, -3, b in ascending order.\n | -3, b, h\n | ibivibiv/math_instruct | |
Express (u**2 + 5*u + 5*u**2 - 8*u**2 - 1)*(-2 + 2 + 2) in the form a*u**2 + k*u + n and give n.\n | -2\n | ibivibiv/math_instruct | |
What is the value of (-2 - -12)*11674/(-8980)?\n | -13\n | ibivibiv/math_instruct | |
Suppose 0 = 2*r, -2528 = -7*p + 3*p + 4*r. What is the units digit of p?\n | 2\n | ibivibiv/math_instruct | |
Simplify f*f/f**22*f**1 assuming f is positive.\n | f**(-19)\n | ibivibiv/math_instruct | |
Let w = 13 - -63. Suppose 57*u + 6384 = w*u. Is 12 a factor of u?\n | True\n | ibivibiv/math_instruct | |
Suppose 2769 = 2*q - 831. Calculate the remainder when 88 is divided by (1/(-5))/((-24)/q).\n | 13\n | ibivibiv/math_instruct | |
Suppose -40*r + 34 = -23*r. Sort -2, r, -55.\n | -55, -2, r\n | ibivibiv/math_instruct | |
What is the value of ((-6)/2)/((-2)/(-2))?\n | -3\n | ibivibiv/math_instruct | |
Differentiate -3*i**2*s*w - 3*i**2*s - 25*i**2*w - 30*i*s*w - 1773*i + 2*s wrt w.\n | -3*i**2*s - 25*i**2 - 30*i*s\n | ibivibiv/math_instruct | |
Let p(n) = n**3 - 261*n**2 + 14378*n - 24. Calculate p(79).\n | -24\n | ibivibiv/math_instruct | |
Is 79 a factor of 2035909?\n | True\n | ibivibiv/math_instruct | |
Let c(g) = g**3 - 7*g**2 + 6*g + 2. Let l be c(6). Let u be 2*(l + 3 - 3). Solve -2*m - 3*v - 3 = -10, -m = -u*v + 24 for m.\n | -4\n | ibivibiv/math_instruct | |
Let q(w) = -277*w**2. Let d(t) = -26*t**2 - 18*t - 9. Let m(c) = 12*c**2 + 8*c + 4. Let n(y) = 4*d(y) + 9*m(y). Determine n(q(g)).\n | 306916*g**4\n | ibivibiv/math_instruct | |
Is 8808277 composite?\n | True\n | ibivibiv/math_instruct | |
What are the prime factors of 1877834?\n | 2, 7, 113, 1187\n | ibivibiv/math_instruct | |
Let i = 478/3 - 161. Which is smaller: -2 or i?\n | -2\n | ibivibiv/math_instruct | |
Solve -4*l - 4 = q, 24*q + 20 = 19*q for l.\n | 0\n | ibivibiv/math_instruct | |
Which is the third smallest value? (a) 3 (b) 0.1 (c) -2/191\n | a\n | ibivibiv/math_instruct | |
Is 17423 a multiple of 19?\n | True\n | ibivibiv/math_instruct | |
Write an educational piece suited for college students related to the following text snippet:
"Finding eigenvalues and eigenvectors
Let $v=(3 ,1 ,3 ,-4)$ and $A=v^t\cdot v$. Find the eigenvalues and eigenvectors of $A$ without calculating the whole matrix $A$
$Rank(AB) \leq min((Rank(A),Rank(B))$ so $Rank(A)\leq 1$ b... | To understand the problem of finding eigenvalues and eigenvectors of a given matrix A, let us first define what eigenvalues and eigenvectors are. An eigenvector of a square matrix A is a nonzero vector v such that when A is multiplied by v, the result is a scalar multiple of v. This scalar is known as the eigenvalue c... | ibivibiv/math_instruct | |
Let u(j) = j**3 + 27*j**2 + 22*j - 43. Let o be u(-26). Differentiate -25 - 9 + 78*n - 17 + o*n - 40*n with respect to n.\n | 99\n | ibivibiv/math_instruct | |
Let r = 12 + -20. Let h be (-4)/(-6) - r/6. Suppose -2*w - 3*p + 6 = 0, -4*w + 4 = -2*w + h*p. Solve 0 = -w*v - v + 4 for v.\n | 4\n | ibivibiv/math_instruct | |
-772 divided by -5\n | 772/5\n | ibivibiv/math_instruct | |
What is 351054 to the power of 1/3, to the nearest integer?\n | 71\n | ibivibiv/math_instruct | |
Find the second derivative of 2*i**4 - 15315*i**3 - 11*i**2 + i - 25698.\n | 24*i**2 - 91890*i - 22\n | ibivibiv/math_instruct | |
Solve -50*g = -24*g - 130 for g.\n | 5\n | ibivibiv/math_instruct | |
Suppose -4*p - 3*z + 102 = 0, p + 15*z - 10*z = 34. Solve -p + 26 = 2*x for x.\n | 1\n | ibivibiv/math_instruct | |
Suppose 3*w - 907 - 4811 = 0. List the prime factors of w.\n | 2, 953\n | ibivibiv/math_instruct | |
Divide -7410 by 38.\n | -195\n | ibivibiv/math_instruct | |
What is 11181317 to the power of 1/2, to the nearest integer?\n | 3344\n | ibivibiv/math_instruct | |
Simplify (-5*(sqrt(7)*2*2*-1 + sqrt(42)/sqrt(54) + -1))**2.\n | 550*sqrt(7)/3 + 21400/9\n | ibivibiv/math_instruct | |
Calculate (2*3/(-63))/((-6)/(-14)).\n | -2/9\n | ibivibiv/math_instruct | |
Solve -3 = -14*d + 11 for d.\n | 1\n | ibivibiv/math_instruct | |
Let p(t) = -t**2 - 61*t + 2732. Let r be p(30). Solve -v - r*x = 7, -4*v = v + 2*x - 5 for v.\n | 3\n | ibivibiv/math_instruct | |
Calculate the remainder when 208 is divided by 42.\n | 40\n | ibivibiv/math_instruct | |
Solve -18 = 2*j - 152*y + 156*y, -4*y - 17 = 3*j for j.\n | 1\n | ibivibiv/math_instruct | |
Suppose 0 = -w + 2. What is the remainder when 2 is divided by w?\n | 0\n | ibivibiv/math_instruct | |
Suppose 5 + 21 = 3*j + b, 0 = -5*j - 3*b + 46. Let t = 8 + j. Calculate the smallest common multiple of t and 2.\n | 16\n | ibivibiv/math_instruct | |
Calculate (10/6)/(2*1/(-6)).\n | -5\n | ibivibiv/math_instruct | |
What are the prime factors of 25504?\n | 2, 797\n | ibivibiv/math_instruct | |
Round 2530.206 to the nearest integer.\n | 2530\n | ibivibiv/math_instruct | |
Let p(o) = 59*o**2 + o + 13. Give p(0).\n | 13\n | ibivibiv/math_instruct | |
Solve -13*v = -3*f - 124, -38*v + 0*f = 5*f + 339 - 729 for v.\n | 10\n | ibivibiv/math_instruct | |
Let q = -3573 + 25010/7. Let s be ((-1)/(-5))/(2 - 1). What is the nearest to s in -4, -5/4, q?\n | q\n | ibivibiv/math_instruct | |
Suppose -2 = -j + 4. Let v be 1*-1*3/j. Which is the nearest to v? (a) -1/6 (b) -2 (c) 1/2\n | a\n | ibivibiv/math_instruct | |
Let r(q) = -640*q. Let u(z) = 1206*z**2. Give r(u(v)).\n | -771840*v**2\n | ibivibiv/math_instruct | |
Let o = 10.76 - -0.24. Let k = o - 11.9. Let w = k + 1.1. What is the third biggest value in -1/2, 5, w?\n | -1/2\n | ibivibiv/math_instruct | |
Express 0*b**2 - 3*b**2 - 2*b**3 + 160 + 2*b**2 - 845 + b**3 + 2*b in the form f*b + n*b**2 + s + g*b**3 and give n.\n | -1\n | ibivibiv/math_instruct | |
Let o = 4938 - 2323. Calculate the greatest common factor of o and 5.\n | 5\n | ibivibiv/math_instruct | |
Suppose -21*v = 19138 - 199087. List the prime factors of v.\n | 11, 19, 41\n | ibivibiv/math_instruct | |
Factor m**5/3 - 6*m**4 + 4*m**3 + 584*m**2/3 + 512*m + 384.\n | (m - 12)**2*(m + 2)**3/3\n | ibivibiv/math_instruct | |
Let c = 621 + -324. Let i = -1627 + 1632. Suppose -1037 = -i*n - c. Is n a multiple of 23?\n | False\n | ibivibiv/math_instruct | |
Is 507536/22 - 4*36/(-792) a multiple of 43?\n | False\n | ibivibiv/math_instruct | |
What is 122057 divided by 5?\n | 122057/5\n | ibivibiv/math_instruct | |
Which is greater: -315563 or -315468?\n | -315468\n | ibivibiv/math_instruct | |
Solve -45 = -5*j - 130*m + 128*m, -2*j + 4*m - 30 = 0 for j.\n | 5\n | ibivibiv/math_instruct | |
Which is the fourth smallest value? (a) 0.152 (b) 1 (c) -50 (d) -2/3 (e) -5\n | a\n | ibivibiv/math_instruct | |
Simplify (3*sqrt(342))/sqrt(2).\n | 9*sqrt(19)\n | ibivibiv/math_instruct | |
Calculate prob of sequence qo when two letters picked without replacement from {q: 1, o: 1, l: 2, u: 1, p: 3, e: 4}.\n | 1/132\n | ibivibiv/math_instruct | |
What is the nearest to 1 in 13, -1/4, -3?\n | -1/4\n | ibivibiv/math_instruct | |
Calculate prob of picking 1 f and 2 o when three letters picked without replacement from {y: 2, i: 1, q: 1, f: 1, h: 3, o: 4}.\n | 3/110\n | ibivibiv/math_instruct | |
Factor 2*p**4 - 964*p**3 - 5846*p**2 - 4880*p.\n | 2*p*(p - 488)*(p + 1)*(p + 5)\n | ibivibiv/math_instruct |
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