instruction_seed stringlengths 5 2.9k | response_seed stringlengths 3 9.55k | input stringclasses 1
value | _source stringclasses 1
value |
|---|---|---|---|
Solve -4*u - 517 = 5*n - 520, 2*u = 8*n + 12 for u.\n | 2\n | ibivibiv/math_instruct | |
What is -799 divided by -17?\n | 47\n | ibivibiv/math_instruct | |
Evaluate ((0 - 1) + 0)/(-36 + 16709/465).\n | 15\n | ibivibiv/math_instruct | |
List the prime factors of 50901.\n | 3, 19, 47\n | ibivibiv/math_instruct | |
What is 130813917 to the power of 1/5, to the nearest integer?\n | 42\n | ibivibiv/math_instruct | |
1555 (base 6) to base 10\n | 431\n | ibivibiv/math_instruct | |
Factor 4*w**2 - 40*w - 224.\n | 4*(w - 14)*(w + 4)\n | ibivibiv/math_instruct | |
Collect the terms in 8*q**2 + 11*q**2 - 17*q**2.\n | 2*q**2\n | ibivibiv/math_instruct | |
Let h = -49.978 + -0.022. Which is the closest to 2/3? (a) -1 (b) h (c) -1/2\n | c\n | ibivibiv/math_instruct | |
Simplify ((c/(c/(c*c*c*c/(c*c**(2/7)/c))))**(-36)/(c**(-1/3)/c)**(-31/3))**(-46) assuming c is positive.\n | c**(427432/63)\n | ibivibiv/math_instruct | |
Let j(n) = 3*n - 13. Let q be j(5). Let g(i) = 7*i**2 - q*i - 3*i**2 + 5*i**2. List the prime factors of g(2).\n | 2\n | ibivibiv/math_instruct | |
Sort 3, -3, -6, 0 in ascending order.\n | -6, -3, 0, 3\n | ibivibiv/math_instruct | |
What is the nearest to -8 in 7, -2/27, 3, 1, -4?\n | -4\n | ibivibiv/math_instruct | |
Let w = 422 + -423. Let a = 23 + -19. Suppose o = 4*o + 4*t, t = -a*o. Which is greater: w or o?\n | o\n | ibivibiv/math_instruct | |
b"What is the zth term of -109, -494, -1145, -2062, -3245, -4694?\n" | -133*z**2 + 14*z + 10\n | ibivibiv/math_instruct | |
Suppose 4*x - 6*n + 2*n = 14916, 3733 = x - 3*n. Let c = -2549 + x. List the prime factors of c.\n | 2, 19, 31\n | ibivibiv/math_instruct | |
Suppose -2*s - 16 = -4*u, -3*s - 3*u = -0*s - 12. Suppose -3*o + 16 + 29 = s. Suppose -4*j + o = 4*x - x, 5*j = 3*x + 12. What is the units digit of x?\n | 1\n | ibivibiv/math_instruct | |
Which is smaller: -375 or -325?\n | -375\n | ibivibiv/math_instruct | |
Simplify ((j/(j/j**(-27))*(j*j*j/j**(4/15)*j)/j)/(j/(j/(j*j**(-13))))**(-2/19))**(1/14) assuming j is positive.\n | j**(-3638/1995)\n | ibivibiv/math_instruct | |
Simplify -2 + ((-2*sqrt(242))**2 + -3 - (6*-1*(1 + sqrt(2)))**2).\n | -72*sqrt(2) + 855\n | ibivibiv/math_instruct | |
What are the prime factors of 646226?\n | 2, 7, 31, 1489\n | ibivibiv/math_instruct | |
-11384 divided by 2\n | -5692\n | ibivibiv/math_instruct | |
Let s(j) be the third derivative of -j**4/24 - j**3 - j**2. Let y be s(-6). Suppose y = -n - 2*n - z + 255, -z = 4*n - 341. Is n a multiple of 43?\n | True\n | ibivibiv/math_instruct | |
Factor -4*f**2 + 19524*f.\n | -4*f*(f - 4881)\n | ibivibiv/math_instruct | |
Round -2.73510919 to one dp.\n | -2.7\n | ibivibiv/math_instruct | |
Suppose 5*f - 8 = 42. Calculate the lowest common multiple of f and 6.\n | 30\n | ibivibiv/math_instruct | |
Collect the terms in 58*r**2 - 5*r**2 - 56*r**2.\n | -3*r**2\n | ibivibiv/math_instruct | |
In base 16, what is 2acb38 + 2?\n | 2acb3a\n | ibivibiv/math_instruct | |
Let s = -0.72 - -0.671. What is s rounded to two dps?\n | -0.05\n | ibivibiv/math_instruct | |
Let j = -56 + 91. What is the least common multiple of (14/5)/(7/j) and 18?\n | 126\n | ibivibiv/math_instruct | |
Let a = -336 + 330. Calculate the remainder when 257 is divided by (-1200)/(-210)*((-27)/a - 1).\n | 17\n | ibivibiv/math_instruct | |
Is 987653 composite?\n | True\n | ibivibiv/math_instruct | |
What is 56792130 rounded to the nearest one hundred thousand?\n | 56800000\n | ibivibiv/math_instruct | |
What is the units digit of 51358?\n | 8\n | ibivibiv/math_instruct | |
Let u be (-208)/240 + (-2)/15. Sort 5, 1866, u in descending order.\n | 1866, 5, u\n | ibivibiv/math_instruct | |
Let o be 680/(-2282) + 374/1309. What is the nearest to 2 in -2/3, 4, o?\n | 4\n | ibivibiv/math_instruct | |
Which is the closest to 1/2? (a) 2/15 (b) 0.1 (c) -6921/4\n | a\n | ibivibiv/math_instruct | |
Let b = -2 - -1/3. Let w be 4/12 - 6/9. What is the nearest to w in b, 0, 3?\n | 0\n | ibivibiv/math_instruct | |
Solve -43 = 13*s + 2*a, 5*s - 10*a + 8*a = -8*a - 163 for s.\n | 1\n | ibivibiv/math_instruct | |
Let v be -1 + 0 + -276 + 3 - -3. Let w = 540 + v. Is w a composite number?\n | False\n | ibivibiv/math_instruct | |
Is 18713 a composite number?\n | False\n | ibivibiv/math_instruct | |
What is the result of the following expression?
(-55.3492 - -9.6319) / (-79.6966 * -18.7247) | -0.0306 | ibivibiv/math_instruct | |
What is the greatest common factor of 8269422 and 336?\n | 42\n | ibivibiv/math_instruct | |
Let o(u) = 42*u + 2. Let w be o(2). Let q = w + -56. Let p = q - 14. Calculate the remainder when 46 is divided by p.\n | 14\n | ibivibiv/math_instruct | |
Rearrange 2*d - 2*d + 5*d**2 + (d + 4*d - 4*d)*(-4*d + 3*d + 3*d) - 3 + 11*d**2 - 12*d**2 + 47 to u*d + a + o*d**2 and give a.\n | 44\n | ibivibiv/math_instruct | |
Let m(g) = -g**3 - 7*g**2 + 7*g - 9. Let j be m(-8). Let v(u) = 2*u**2 + 12*u + 5. Let b be v(-5). Put 5, b, j in decreasing order.\n | 5, j, b\n | ibivibiv/math_instruct | |
Simplify u*u/u**(-8)*u*u/u**9*u*u*u**3*u*u/(u/((u*u*u/((u/u**(1/6)*u)/u)*u)/u*u*u)) assuming u is positive.\n | u**(79/6)\n | ibivibiv/math_instruct | |
Suppose 21*i - 6 = -8 - 19. Let t = -6 - -111/19. Is t at least i?\n | True\n | ibivibiv/math_instruct | |
What is 1512 (base 11) in base 8?\n | 3635\n | ibivibiv/math_instruct | |
Suppose -2*f + 103 - 163 = 0. Let z = 40 + f. Calculate the lowest common multiple of 12 and z.\n | 60\n | ibivibiv/math_instruct | |
Let s(y) = 2*y - 8. Let p be s(7). Suppose t - 3*t = -p*t. Let d(c) = -c - 11. Let w be d(-10). Put -5, -2, t, w in ascending order.\n | -5, -2, w, t\n | ibivibiv/math_instruct | |
b"What is the xth term of 2991, 5989, 8987, 11985, 14983, 17981?\n" | 2998*x - 7\n | ibivibiv/math_instruct | |
Suppose 4*a = -2*g + 26, 8*g = 3*g + 25. Solve a*t - 3*t - 5*h = -12, h + 6 = 3*t for t.\n | 3\n | ibivibiv/math_instruct | |
Suppose -2*u**5/13 - 2242*u**4/13 - 1544*u**3 - 62344*u**2/13 - 80096*u/13 - 35584/13 = 0. Calculate u.\n | -1112, -4, -2, -1\n | ibivibiv/math_instruct | |
b"What is the lth term of 1441, 1443, 1437, 1417, 1377, 1311, 1213, 1077?\n" | -l**3 + 2*l**2 + 3*l + 1437\n | ibivibiv/math_instruct | |
Is 1102357698 a multiple of 33?\n | False\n | ibivibiv/math_instruct | |
Solve 326 = 4*c - 5*h + 317, -2*c + 2 = -2*h for c.\n | -4\n | ibivibiv/math_instruct | |
Rearrange (-102 + 160 - 97)*(24 + 41 + 3 - 3*u**4) to c*u + l*u**4 + w + i*u**3 + r*u**2 and give w.\n | -2652\n | ibivibiv/math_instruct | |
What is 130 minutes before 7:00 AM?\n | 4:50 AM\n | ibivibiv/math_instruct | |
What comes next: 6, -174, -692, -1716, -3414, -5954, -9504, -14232?\n | -20306\n | ibivibiv/math_instruct | |
Suppose 3*u - 36 = -u. What is the common denominator of 3 and 69/u*(-18)/(-4)?\n | 2\n | ibivibiv/math_instruct | |
What is the third derivative of -793986*d*w**3 - d*w**2 - d*w + 97*d - 203*w**2 wrt w?\n | -4763916*d\n | ibivibiv/math_instruct | |
How many minutes are there between 2:56 PM and 9:07 PM?\n | 371\n | ibivibiv/math_instruct | |
What is -499b55 (base 13) in base 12?\n | -710957\n | ibivibiv/math_instruct | |
Which is the closest to 0.1? (a) 2798 (b) -4 (c) -2/5\n | c\n | ibivibiv/math_instruct | |
Let o(k) = -k + k - k**3 + 10*k**2 - 7*k + 7 - 2*k. What is the units digit of o(9)?\n | 7\n | ibivibiv/math_instruct | |
Let l(j) = -j**2 - j**2 - j**2. Let m(q) = 8 + 0 - 45*q + 50*q + 0 - 3. Calculate m(l(x)).\n | -15*x**2 + 5\n | ibivibiv/math_instruct | |
Let k = 41 - 37. Suppose -3*v = -4 - 11, k*g + 3*v - 19 = 0. Solve -g - 5 = -2*a for a.\n | 3\n | ibivibiv/math_instruct | |
Suppose -2*i + 10 + 28 = 0. Let o = -24 - -31. What is the remainder when i is divided by o?\n | 5\n | ibivibiv/math_instruct | |
Let q = -40 + 66. Let y = q + -10. What is the lowest common multiple of y and 20?\n | 80\n | ibivibiv/math_instruct | |
Suppose -i = 4*i + 90. Let g = 3 - i. Calculate the remainder when g is divided by ((-39)/(-3) + -2)*1.\n | 10\n | ibivibiv/math_instruct | |
Solve -67 = g + 16*q, 214*g - 5 = 213*g + 2*q for g.\n | -3\n | ibivibiv/math_instruct | |
What is 111991 to the power of 1/10, to the nearest integer?\n | 3\n | ibivibiv/math_instruct | |
What is the biggest value in 0, -22, 8, 0.18, -0.016, -7, 0.1?\n | 8\n | ibivibiv/math_instruct | |
Simplify (sqrt(110)/(2*sqrt(275) + sqrt(275)))/((sqrt(2) - sqrt(32))*-2*-3).\n | -sqrt(5)/270\n | ibivibiv/math_instruct | |
Let w be (10/(-4))/(2/4). Let s(p) = 7*p**2 - 66. Let j(y) = 2*y**2 - 2*y - 24. Let r(n) = -3*j(n) + s(n). Give r(w).\n | 1\n | ibivibiv/math_instruct | |
What is 0.0000479 rounded to six dps?\n | 0.000048\n | ibivibiv/math_instruct | |
Express (2 + 2*c - 2)*(6*c - 2*c - 2*c) - 4*c**2 + 5*c**2 - 3*c**2 - c**2 + 33*c**2 + 14*c**2 in the form x*c + j + d*c**2 and give j.\n | 0\n | ibivibiv/math_instruct | |
Let k = 0.62 + -0.42. What is the closest to k in 0.4, 4, 0.11?\n | 0.11\n | ibivibiv/math_instruct | |
Let y = 2 - 3. Let h = 14.3 - 14. What is the nearest to -1 in y, h, -4/7?\n | y\n | ibivibiv/math_instruct | |
Factor 3*k**5/8 + 9*k**4/8 + 9*k**3/8 + 3*k**2/8.\n | 3*k**2*(k + 1)**3/8\n | ibivibiv/math_instruct | |
Expand (-9*w + 14*w + w**2 - w)*(5*w**2 - 14*w**2 - 11*w**2).\n | -20*w**4 - 80*w**3\n | ibivibiv/math_instruct | |
Let c(i) be the first derivative of -i**2 - 2*i - 58. Let f(b) = -1 - b + 1. Suppose 0 = -2*h + v, -1 - 9 = -5*v. Determine h*c(k) - 3*f(k).\n | k - 2\n | ibivibiv/math_instruct | |
List the prime factors of 311167.\n | 23, 83, 163\n | ibivibiv/math_instruct | |
Is 1139 bigger than 1138?\n | True\n | ibivibiv/math_instruct | |
What is 706 minutes before 5:06 AM?\n | 5:20 PM\n | ibivibiv/math_instruct | |
What is prob of sequence zz when two letters picked without replacement from rzrlzulkarar?\n | 1/66\n | ibivibiv/math_instruct | |
Calculate the remainder when 5687 is divided by 2732.\n | 223\n | ibivibiv/math_instruct | |
Round -2220.0623 to the nearest 100.\n | -2200\n | ibivibiv/math_instruct | |
Solve 0 = -68*v + 157*v + 121*v - 4410 for v.\n | 21\n | ibivibiv/math_instruct | |
Let z(m) = -2629*m + 202405. What is z(77)?\n | -28\n | ibivibiv/math_instruct | |
Convert 100112102 (base 3) to base 6.\n | 52102\n | ibivibiv/math_instruct | |
What is 155203658 to the power of 1/2, to the nearest integer?\n | 12458\n | ibivibiv/math_instruct | |
Round -74590 to the nearest one thousand.\n | -75000\n | ibivibiv/math_instruct | |
What is the value of -11 - (-2 + (20 - (-7 + 26)))?\n | -10\n | ibivibiv/math_instruct | |
What is the ten thousands digit of 448350768?\n | 5\n | ibivibiv/math_instruct | |
Write an educational piece suited for college students related to the following text snippet:
"# Unique Existential Quantifier Domain Definition
I am trying to convert the unique existential quantifier into plain logic. I have two statements with different placements of the 'for all' quantifier.
∃x ∀y, $(P(y) ∧ P(x))... | In order to understand the difference between the two statements provided, it is important to first clarify their proper formulation using appropriate parentheses. The corrected versions are as follows:
1. ∃x ∀y [(P(y) ∧ P(x)) → (y=x)]
2. ∃x [P(x) ∧ ∀y (P(y) → (y=x))]
Next, we need to define the relevant logical sym... | ibivibiv/math_instruct | |
What is the value of (((-2040)/(-15))/34)/(4/6)?\n | 6\n | ibivibiv/math_instruct | |
What is the distance between 308622 and -44?\n | 308666\n | ibivibiv/math_instruct | |
What is the fifth root of 1362 to the nearest integer?\n | 4\n | ibivibiv/math_instruct |
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