instruction_seed stringlengths 5 2.9k | response_seed stringlengths 3 9.55k | input stringclasses 1
value | _source stringclasses 1
value |
|---|---|---|---|
Evaluate 2*1 + (-23 - 3906/(-189)).\n | -1/3\n | ibivibiv/math_instruct | |
Solve -341*v - 2940 = 1152 for v.\n | -12\n | ibivibiv/math_instruct | |
Calculate the remainder when 50260 is divided by 541.\n | 488\n | ibivibiv/math_instruct | |
Let l = 7 + -2. Let f = -9 + 5. What is the least common multiple of l and 12/(1/(-2)*f)?\n | 30\n | ibivibiv/math_instruct | |
Calculate prob of sequence jjs when three letters picked without replacement from jsjssssssss.\n | 1/55\n | ibivibiv/math_instruct | |
Is 16 a factor of 1312?\n | True\n | ibivibiv/math_instruct | |
In base 13, what is -2 + 10a0?\n | 109b\n | ibivibiv/math_instruct | |
Calculate the common denominator of -99/386780 and 1/14110.\n | 6575260\n | ibivibiv/math_instruct | |
What is (9 + -7)*(-5 - -3)/((-12)/(-9))?\n | -3\n | ibivibiv/math_instruct | |
Let t(k) = -7*k - 58. Let i be t(-8). Let b(y) = -y**2 - 2*y - 3. Determine b(i).\n | -3\n | ibivibiv/math_instruct | |
Let f = -16 - -23. Let w be 20/(-1)*(138/24 + -6). Solve -f = -w*b - 2 for b.\n | 1\n | ibivibiv/math_instruct | |
Let i(d) = 6*d**2. Let b(h) = -h**2 - 7*h - 1. Let l = -9 - -3. Let g be b(l). Let q(z) = 5*z + z - g*z. What is i(q(r))?\n | 6*r**2\n | ibivibiv/math_instruct | |
Let v(c) = c. Let a(z) = 29*z**2. What is a(v(y))?\n | 29*y**2\n | ibivibiv/math_instruct | |
Let d = -145 - -143. Sort d, -4, -10 in increasing order.\n | -10, -4, d\n | ibivibiv/math_instruct | |
Is 1.3 equal to -397?\n | False\n | ibivibiv/math_instruct | |
Let n = -0.02 + -0.38. Let v = n + -3.6. What is the second smallest value in 1/2, 0.2, v?\n | 0.2\n | ibivibiv/math_instruct | |
Let y(x) = -192*x + 1809. Does 33 divide y(-32)?\n | True\n | ibivibiv/math_instruct | |
Suppose -52 = -5*p - 0*l + l, -5*l - 10 = 0. Suppose -74*a + 76*a - p = 0. Is (12/(-15))/(a/(925/(-2))) composite?\n | True\n | ibivibiv/math_instruct | |
What is -10310 (base 4) in base 11?\n | -260\n | ibivibiv/math_instruct | |
Let b = 221 - 86. Let d = 236 + b. Is d composite?\n | True\n | ibivibiv/math_instruct | |
What is the result of the following expression?
(43.111 / -85.654) + (-6.801 - -65.467) | 58.1627 | ibivibiv/math_instruct | |
Solve 0 = -377*b + 376*b + 2*f - 11, -6 = -4*b + 2*f - 26 for b.\n | -3\n | ibivibiv/math_instruct | |
What is the units digit of (5 - 8)*3579/(-9)?\n | 3\n | ibivibiv/math_instruct | |
Let v(c) = -c**2 - 3*c + 1. Calculate v(-4).\n | -3\n | ibivibiv/math_instruct | |
b"What is the rth term of 249227, 996345, 2241551, 3984851, 6226251, 8965757, 12203375?\n" | r**3 + 249038*r**2 - 3*r + 191\n | ibivibiv/math_instruct | |
Let o = 12519 + -12671. Which is smaller: o or -38?\n | o\n | ibivibiv/math_instruct | |
In base 9, what is -686 - -7255?\n | 6458\n | ibivibiv/math_instruct | |
Calculate the remainder when 153087 is divided by 126.\n | 123\n | ibivibiv/math_instruct | |
Which is the nearest to 1/5? (a) 129 (b) 2/15 (c) -0.4 (d) -5 (e) -1.2\n | b\n | ibivibiv/math_instruct | |
Let f = -405 - -730. What is the greatest common divisor of 39 and f?\n | 13\n | ibivibiv/math_instruct | |
Let u be (1/12)/(6/12). Let c = -15 + 8. Let o = 10 + c. What is the biggest value in -0.1, u, o?\n | o\n | ibivibiv/math_instruct | |
Divide -3 by 82631.\n | -3/82631\n | ibivibiv/math_instruct | |
b"What is the vth term of -106, -208, -310, -412, -514?\n" | -102*v - 4\n | ibivibiv/math_instruct | |
-2222200 (base 3) to base 16\n | -882\n | ibivibiv/math_instruct | |
Divide -8 by 5267.\n | -8/5267\n | ibivibiv/math_instruct | |
Does -2 = -6548882.73?\n | False\n | ibivibiv/math_instruct | |
Let u be 4/(-10) + (-304)/(-860). Let a be (-3 - (-78)/18) + 7/(-3). Which is smaller: a or u?\n | a\n | ibivibiv/math_instruct | |
b"What is the sth term of 5655, 5668, 5703, 5772, 5887?\n" | 2*s**3 - s**2 + 2*s + 5652\n | ibivibiv/math_instruct | |
Let x(q) = -q**2 - 358 + 680 - 350 - 21*q. Suppose -3*g - 2*g = 85. What is the units digit of x(g)?\n | 0\n | ibivibiv/math_instruct | |
Divide -41468 by 2962.\n | -14\n | ibivibiv/math_instruct | |
Write an educational piece suited for college students related to the following text snippet:
"# What is the intuition behind $\Delta_1^0$ sets and $\Delta_1^1$ sets?
In the context of first-order arithmetic, if $\phi$ is a formula with only bounded quantifiers, then if you put existential quantifiers in front it beco... | Now, let's delve into the world of logic, mathematics, and computability theory to understand the concept of $\Delta\_1^0$ and $\Delta\_1^1$ sets. We will begin by explaining some fundamental ideas and gradually build up to these terms. This should provide you with a solid foundation while fostering engagement through... | ibivibiv/math_instruct | |
Is 12063 a multiple of 15?\n | False\n | ibivibiv/math_instruct | |
Let j(x) = -2*x + 1. Let h be j(-2). Suppose h*d = 195 + 230. Is d a composite number?\n | True\n | ibivibiv/math_instruct | |
Which is the second biggest value? (a) -5.4 (b) 4 (c) 1488\n | b\n | ibivibiv/math_instruct | |
Simplify (sqrt(135)/sqrt(144))/(sqrt(3) + (sqrt(15)/sqrt(5)*-1 - sqrt(3)) + sqrt(3) + sqrt(3)).\n | sqrt(5)/4\n | ibivibiv/math_instruct | |
Round 4413300 to the nearest one hundred thousand.\n | 4400000\n | ibivibiv/math_instruct | |
Calculate the common denominator of 29/150018 and 131/1500180.\n | 1500180\n | ibivibiv/math_instruct | |
What is the fourth smallest value in -2/11, -1, 0.06, 2/7?\n | 2/7\n | ibivibiv/math_instruct | |
Let p be 3 + -3 + 5 - 0. Suppose 3*l + p = -4. Let i(n) = -24 - 30 - 23 - 4*n + 75. What is i(l)?\n | 10\n | ibivibiv/math_instruct | |
What is the closest to 0 in 2/5, -1/12, 2/7?\n | -1/12\n | ibivibiv/math_instruct | |
How many minutes are there between 11:11 AM and 9:06 PM?\n | 595\n | ibivibiv/math_instruct | |
0.5 + 78319970153125\n | 78319970153125.5\n | ibivibiv/math_instruct | |
What are the prime factors of (-15 - (-92)/8)/((-1)/128)?\n | 2, 7\n | ibivibiv/math_instruct | |
Factor 4*z**4 + 16*z**3 - 84*z**2 + 16*z + 112.\n | 4*(z - 2)**2*(z + 1)*(z + 7)\n | ibivibiv/math_instruct | |
What is the next term in 729617, 729550, 729483?\n | 729416\n | ibivibiv/math_instruct | |
Let m(d) = -2*d**2 - 2*d. Let b(h) = -h**2 - 10*h + 14. Give b(a) - 5*m(a).\n | 9*a**2 + 14\n | ibivibiv/math_instruct | |
Solve 424*q - 149*q - 714 = 173*q for q.\n | 7\n | ibivibiv/math_instruct | |
What comes next: -48, -95, -142, -189, -236, -283?\n | -330\n | ibivibiv/math_instruct | |
Let h(z) = -30*z + 58. Let r be h(2). Let k(c) = 14*c**2 - 6*c - 8. What is the smallest common multiple of 60 and k(r)?\n | 60\n | ibivibiv/math_instruct | |
Suppose -3*h - 4*u = -4, -4*u = 10468*h - 10466*h. Let r = 6 - 3. Solve -3*l = h*p - 29, 3*l + 0*p + r*p - 24 = 0 for l.\n | 3\n | ibivibiv/math_instruct | |
Collect the terms in 13*g + 95*g**3 + 149*g - 187*g**3 + 94*g**3.\n | 2*g**3 + 162*g\n | ibivibiv/math_instruct | |
Put -4, 1, -3, 9, -2, 1229 in descending order.\n | 1229, 9, 1, -2, -3, -4\n | ibivibiv/math_instruct | |
Let d(o) = -o + 6. Let t be d(3). Suppose -h - t*h = -4. What is the units digit of (4*2)/(h - 0)?\n | 8\n | ibivibiv/math_instruct | |
Suppose 0 = 3*g - 53*g + 600. Let p be (-2)/7 + (-26)/7. Let v(l) = -8*l + 3. What is the remainder when v(p) is divided by g?\n | 11\n | ibivibiv/math_instruct | |
What is the next term in -414139, -828383, -1242627, -1656871?\n | -2071115\n | ibivibiv/math_instruct | |
Let a = 9/5 - 11/5. Let k = 19.3 - 2.3. Let d = k + -20. What is the closest to -2/7 in d, a, -1/4?\n | -1/4\n | ibivibiv/math_instruct | |
What is 468 minutes before 1:21 AM?\n | 5:33 PM\n | ibivibiv/math_instruct | |
Solve 453*v - 21894 = 12634 + 12584 for v.\n | 104\n | ibivibiv/math_instruct | |
What is the cube root of 4335067 to the nearest integer?\n | 163\n | ibivibiv/math_instruct | |
Is 106 a factor of 82150?\n | True\n | ibivibiv/math_instruct | |
What are the prime factors of 6134?\n | 2, 3067\n | ibivibiv/math_instruct | |
Expand 121*j**4 - 35*j**5 - 121*j**4 + (2*j**2 - 2*j**2 - 2*j**2)*(3 - 3*j**3 - 3)*(3 - 3 - 1).\n | -41*j**5\n | ibivibiv/math_instruct | |
Let v = -2 - -6. Let n = -18 + 55. Let l = n - 41. What is the nearest to -1 in v, -0.1, l?\n | -0.1\n | ibivibiv/math_instruct | |
Three letters picked without replacement from {g: 4, s: 5, a: 3, z: 1}. What is prob of picking 3 a?\n | 1/286\n | ibivibiv/math_instruct | |
What is -1 + 0 - 52 - (-796 - -798)?\n | -55\n | ibivibiv/math_instruct | |
Which is the closest to -2? (a) -0.4 (b) 3 (c) -1/7 (d) 9\n | a\n | ibivibiv/math_instruct | |
Suppose -2*z + 5*h = 39, -3*z = z - 2*h + 70. Let l be 2 + 0 + z/7. Let n = 7 - 11. What is the closest to -1 in l, n, -0.5?\n | -0.5\n | ibivibiv/math_instruct | |
Let d = -24 - -23. Let z = 0.06 + -0.01. Let b = z + -0.1. Is d less than b?\n | True\n | ibivibiv/math_instruct | |
Let k be (-105)/80*(-4)/6. What is the nearest to 0.1 in 0.3, 0.1, k?\n | 0.1\n | ibivibiv/math_instruct | |
Let g(q) = 3*q + 24*q**2 + 8*q + 17 + 6 - 9*q**2. Let i(b) = -5*b**2 - 4*b - 8. Let m(z) = -4*g(z) - 11*i(z). What is the first derivative of m(l) wrt l?\n | -10*l\n | ibivibiv/math_instruct | |
Simplify (p**(-5/2)/(p*p*p/((p*p*p**(-6/5))/p)))**(-1/3) assuming p is positive.\n | p**(19/10)\n | ibivibiv/math_instruct | |
What is the highest common divisor of 317835 and 7665?\n | 105\n | ibivibiv/math_instruct | |
Express (-38*g + 103 - 103)*(8 + 4 + 0) + (3 - 3 - 2*g)*(0 + 0 + 1) as q*g + t and give q.\n | -458\n | ibivibiv/math_instruct | |
Let p(h) = -48*h**3 - 3*h**2 - 7*h - 2. Let g(b) = -47*b**3 - 2*b**2 - 6*b - 1. Let q(z) = -4*g(z) + 3*p(z). List the prime factors of q(1).\n | 2, 11\n | ibivibiv/math_instruct | |
Let x(c) = 8*c + 28. Give x(-3).\n | 4\n | ibivibiv/math_instruct | |
What is the value of 3*1 + 15/(450/(-84))?\n | 1/5\n | ibivibiv/math_instruct | |
Calculate the smallest common multiple of (954/1749)/(4/154) and 2652.\n | 18564\n | ibivibiv/math_instruct | |
Let j = -1108607 - -1108610. Factor 5/3*m**j + 2/3*m**2 - m + 0.\n | m*(m + 1)*(5*m - 3)/3\n | ibivibiv/math_instruct | |
Factor 3*n**2/4 - 687*n/2 - 68400.\n | 3*(n - 608)*(n + 150)/4\n | ibivibiv/math_instruct | |
What is the length of the Peano curve of order 3, where each successive iteration increases the number of line segments by a factor of 9? | The Peano curve is a space-filling curve, which means that it fills the entire 2D space within a square. In this case, we are asked to find the length of the Peano curve of order 3.
For the Peano curve, the length of the curve at each iteration is multiplied by a factor of 3. This is because the curve is divided into ... | ibivibiv/math_instruct | |
What is 3/32 of a meter in micrometers?\n | 93750\n | ibivibiv/math_instruct | |
Let f = -111 + 113. Suppose -f*p + 11 = -r, -5*r - 1 - 14 = 0. Solve 7 + 1 = -p*s for s.\n | -2\n | ibivibiv/math_instruct | |
What is the highest common factor of 36 and 1152?\n | 36\n | ibivibiv/math_instruct | |
Let y = 53/39 + -9/13. Let k = 0.24 - -0.06. Let l = 163/22 - 54/11. Which is the biggest value? (a) l (b) y (c) k\n | a\n | ibivibiv/math_instruct | |
Suppose -2*r = -45 - 77. Let z = -60 + r. Let k = -0.1 + 0.2. Which is the closest to k? (a) -0.1 (b) z (c) 0\n | c\n | ibivibiv/math_instruct | |
What is 28681540 rounded to the nearest 1000000?\n | 29000000\n | ibivibiv/math_instruct | |
Let j be (90/(-21))/(2/(-28)). Suppose 0*n + 3*n = -j. Let i = 23 + n. Sort -2/7, 0.3, i in ascending order.\n | -2/7, 0.3, i\n | ibivibiv/math_instruct | |
Let -3*f**5 - 468*f**4 + 480*f**3 + 1410*f**2 - 477*f - 942 = 0. Calculate f.\n | -157, -1, 1, 2\n | ibivibiv/math_instruct | |
Let v(p) = -144*p**2 - 18428*p + 524. Calculate v(-128).\n | 12\n | ibivibiv/math_instruct | |
What is 921836 to the power of 1/9, to the nearest integer?\n | 5\n | ibivibiv/math_instruct |
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