instruction_seed stringlengths 5 2.9k | response_seed stringlengths 3 9.55k | input stringclasses 1
value | _source stringclasses 1
value |
|---|---|---|---|
Simplify (sqrt(18)*2)**2 + (sqrt(300) + sqrt(12))/sqrt(6).\n | 6*sqrt(2) + 72\n | ibivibiv/math_instruct | |
What are the prime factors of 3120857632?\n | 2, 311, 557, 563\n | ibivibiv/math_instruct | |
Let q = -66 - -37. Let c = q + -44. Let t = c + 166. What is the tens digit of t?\n | 9\n | ibivibiv/math_instruct | |
Let u be (-4)/(-6) + (-20)/39. Which is the smallest value? (a) u (b) -0.4 (c) 2\n | b\n | ibivibiv/math_instruct | |
Let z = -5011752.151077 - -5011747. Let i = z - -0.151637. Let w = 5 + i. Round w to four dps.\n | 0.0006\n | ibivibiv/math_instruct | |
Let t(y) = 2*y**2. Let h be 2*14/4 - -1. Suppose -h = -j - 3*j. Let a(g) = 0*g**j - g**2 - g**2. Determine t(a(i)).\n | 8*i**4\n | ibivibiv/math_instruct | |
Evaluate 1*(-35)/(650 + 15).\n | -1/19\n | ibivibiv/math_instruct | |
What is 42/7*-5*(-1)/6?\n | 5\n | ibivibiv/math_instruct | |
Multiply 0.4 and 6635.\n | 2654\n | ibivibiv/math_instruct | |
Simplify (sqrt(7) - sqrt(63))*4*4.\n | -32*sqrt(7)\n | ibivibiv/math_instruct | |
Let y = 20296 + -20298. What is the biggest value in 8/9, 0.4, -12, -2/3, y?\n | 8/9\n | ibivibiv/math_instruct | |
Let d(w) be the third derivative of -w**5/12 + 9*w**2 - 3*w. Let n(o) = 4*o**2 + 9*o. Let p(r) = 2*r**2 + 4*r. Let g(l) = 4*n(l) - 9*p(l). Determine d(g(j)).\n | -20*j**4\n | ibivibiv/math_instruct | |
b"What is the pth term of 13, 324, 1199, 2920, 5769?\n" | 47*p**3 - 18*p - 16\n | ibivibiv/math_instruct | |
Let z = -561 - -569. What is the closest to -1 in -9, 0.3, -0.5, z?\n | -0.5\n | ibivibiv/math_instruct | |
Is 273 a factor of 983327652?\n | False\n | ibivibiv/math_instruct | |
Calculate the remainder when 9 is divided by (-4)/5 + 98/35.\n | 1\n | ibivibiv/math_instruct | |
Evaluate -13 - (10 - (26 - 9)).\n | -6\n | ibivibiv/math_instruct | |
Differentiate -922*o**2 + 24*o + 125780 with respect to o.\n | -1844*o + 24\n | ibivibiv/math_instruct | |
Expand (-6 + 6 - 5*p**3)*(-2*p - p + 0*p)*(-p - 4*p - 7*p).\n | -180*p**5\n | ibivibiv/math_instruct | |
What is the result of the following expression?
(-88.9663 * -23.632) / 89.5702 | 23.4727 | ibivibiv/math_instruct | |
Multiply 0.2 and 54743.489.\n | 10948.6978\n | ibivibiv/math_instruct | |
-10543504 (base 6) to base 2\n | -1001111010011100000\n | ibivibiv/math_instruct | |
Expand (-13 - q + 13)*(-101*q**2 - 10*q**2 + 289*q**2).\n | -178*q**3\n | ibivibiv/math_instruct | |
Let r(g) = 2*g**2. Let p(a) = 1. Let q = -1 + 0. Let z(n) = -5*n + 5. Let k(l) = q*z(l) + 5*p(l). Determine k(r(b)).\n | 10*b**2\n | ibivibiv/math_instruct | |
Which is the nearest to -0.02? (a) -7 (b) -1/4 (c) -1 (d) 0.02\n | d\n | ibivibiv/math_instruct | |
What is 710 minutes before 5:03 PM?\n | 5:13 AM\n | ibivibiv/math_instruct | |
Is 42827196 a multiple of 23?\n | True\n | ibivibiv/math_instruct | |
Suppose 0 = 7*j - 9 + 2. What is the tens digit of -9*(j - 189)*2/6?\n | 6\n | ibivibiv/math_instruct | |
Let v(c) = -c**3 - 7*c**2 - 6*c + 2. Let g be v(-6). Suppose 5*w = -5*d, -g*w - 2*w + 4*d + 32 = 0. Calculate the least common multiple of w and 6.\n | 12\n | ibivibiv/math_instruct | |
What is the hundreds digit of 480614?\n | 6\n | ibivibiv/math_instruct | |
Suppose 349 = 9*o - 650. Let j(z) = 5*z**3 - z**2 + 2. What is the remainder when o is divided by j(2)?\n | 35\n | ibivibiv/math_instruct | |
Suppose 4*r - 14 = 14. Calculate the remainder when r is divided by 3.\n | 1\n | ibivibiv/math_instruct | |
Do 1575 and 50 have the same value?\n | False\n | ibivibiv/math_instruct | |
Suppose -3*q + 4*q = 4. Let h(v) = v**2 - v - 5. Calculate the least common multiple of ((-2)/4)/(2/(-24)) and h(q).\n | 42\n | ibivibiv/math_instruct | |
Suppose 0 = w + 6*w - 1260. Does 15 divide w?\n | True\n | ibivibiv/math_instruct | |
Let y(i) = -i**3 - 2*i**2 + 5*i + 3. Let g be y(-4). Suppose 2*r - g + 1 = 0. Is 6 a factor of r?\n | False\n | ibivibiv/math_instruct | |
Suppose -100462 - 50948 = -490*y. What is the smallest common multiple of y and (-2)/4*(-9 + 1)?\n | 1236\n | ibivibiv/math_instruct | |
Let q(a) = -a**2 - 2*a. Let v be q(-2). Let t = 2 - v. Suppose t*u = -k - k + 28, 5*u = 5*k + 80. What are the prime factors of u?\n | 3, 5\n | ibivibiv/math_instruct | |
Round -0.070111592 to four dps.\n | -0.0701\n | ibivibiv/math_instruct | |
Is 127 composite?\n | False\n | ibivibiv/math_instruct | |
Solve the following system of linear equations for the values of x, y, and z:
3x + 2y - z = 5
2x - 3y + 4z = 7
6x + 4y - 2z = 10
Make sure to check if the matrix is singular and state whether a solution exists. | First, let's write the system of linear equations in matrix form:
A * X = B
where A is the matrix of coefficients, X is the column vector of variables (x, y, z), and B is the column vector of constants.
A = | 3 2 -1 |
| 2 -3 4 |
| 6 4 -2 |
X = | x |
| y |
| z |
B = | 5 |
| 7 |
| 10 |
... | ibivibiv/math_instruct | |
Solve -u + 42 = 3*i, -7*u - 8446*i + 8450*i = 56 for u.\n | 0\n | ibivibiv/math_instruct | |
What is next in -111, -108, -105?\n | -102\n | ibivibiv/math_instruct | |
Calculate (-12 - ((-57 - -15) + -3)) + 3 + 1.\n | 37\n | ibivibiv/math_instruct | |
What is the next term in -2907, -2987, -3139, -3375, -3707, -4147?\n | -4707\n | ibivibiv/math_instruct | |
Solve v = -d - 2*v + 11, -4*v = 2*d - 12 for d.\n | -4\n | ibivibiv/math_instruct | |
What is next in -448, -664, -880, -1096, -1312?\n | -1528\n | ibivibiv/math_instruct | |
Suppose -5*g = -10, -2*g + 60 = -d + 253. Let k = 339 - d. What are the prime factors of k?\n | 2, 71\n | ibivibiv/math_instruct | |
Let f be 8 + 36 + 4/(-2). Suppose -5*b + 58 = -f. Suppose 0 = 3*n - 5*q - b, -5*n - 2*q = -n - 44. Is 10 a factor of n?\n | True\n | ibivibiv/math_instruct | |
Let z = 10667 + -9455. Which is smaller: 3 or z?\n | 3\n | ibivibiv/math_instruct | |
Expand (-r**5 - 4*r + 4*r)*(0 + 0 + 1) + 3*r**5 + 2*r**5 - 6*r**5 + 52*r**5 - 151*r**5 - 183*r**5 + r.\n | -284*r**5 + r\n | ibivibiv/math_instruct | |
Let p(b) = b**2 + 17*b + 13. Give p(-14).\n | -29\n | ibivibiv/math_instruct | |
Let h(o) = -o**3 + 4*o**2 + 6*o + 4. Suppose 0 = 3*y + 3, m + 2*y + 7 = 3*y. Let b = m - -14. What is the remainder when h(5) is divided by b?\n | 3\n | ibivibiv/math_instruct | |
Suppose -2*v + 0*r + 3*r = -8, 3*v - 5*r = 14. What are the prime factors of (-2 - -8)*(-7)/v?\n | 3, 7\n | ibivibiv/math_instruct | |
What is thirteen fifths of a centimeter in micrometers?\n | 26000\n | ibivibiv/math_instruct | |
Rearrange (-3*q + 0*q + 4*q)*(-2 + 2 + 2 + (5 + 14 + 15)*(0 + 1 + 1))*(2 - 3 - 1) to the form k*q + x and give k.\n | -140\n | ibivibiv/math_instruct | |
Convert -33 (base 16) to base 9.\n | -56\n | ibivibiv/math_instruct | |
Let c be (2/4)/(1/4). Let g be (-2)/c*-2*1. Suppose 4*w = -g*p - 38, 49 = -4*p + 4*w - 3. Which is bigger: p or -1?\n | -1\n | ibivibiv/math_instruct | |
Solve -1337*n - 513*n + 22200 = 0 for n.\n | 12\n | ibivibiv/math_instruct | |
Simplify (n**(-3/25)/n)/(n**(-10)/n)*(n**(2/15))**(-41) assuming n is positive.\n | n**(331/75)\n | ibivibiv/math_instruct | |
Suppose 0 = -2*j - 4*q + 30, -2*q = 2*j - 0*q - 20. Determine x so that 0*x**4 - 2*x**3 + x**j - 3*x**4 + 2*x**4 + 2*x**2 + x - 1 = 0.\n | -1, 1\n | ibivibiv/math_instruct | |
Let -4*y**2 - 52/5*y + 4/5*y**3 - 28/5 = 0. What is y?\n | -1, 7\n | ibivibiv/math_instruct | |
What is the second biggest value in 0.1, 1216, -1531?\n | 0.1\n | ibivibiv/math_instruct | |
Solve 88*l = 127*l + 390 for l.\n | -10\n | ibivibiv/math_instruct | |
Solve -1362*f + 449*f + 13908 = -200*f - 469*f for f.\n | 57\n | ibivibiv/math_instruct | |
Suppose 39 = 5*g + 4. Suppose -g*n - 1 = -8. Let c(t) = t. What is c(n)?\n | 1\n | ibivibiv/math_instruct | |
Suppose 5*i + u - 39 = -23, -2*i - 2*u = 0. Let l be (59 - 1)*2/1. Calculate the highest common divisor of i and l.\n | 4\n | ibivibiv/math_instruct | |
What is the greatest common factor of 455568 and 1344?\n | 48\n | ibivibiv/math_instruct | |
608/(-9424)*(-31)/4\n | 1/2\n | ibivibiv/math_instruct | |
Let w = 1 - -3. Which is the smallest value? (a) 1 (b) -2/9 (c) w\n | b\n | ibivibiv/math_instruct | |
What is the greatest common divisor of 124 and 52483?\n | 31\n | ibivibiv/math_instruct | |
Let f = -3372121728 + 3372121893.9999917. Let c = -166.066 + 0.066. Let u = f + c. What is u rounded to six decimal places?\n | -0.000008\n | ibivibiv/math_instruct | |
Suppose 4*a + a - 367605 = 5*h, 0 = -5*a - 5*h + 367565. Is a prime?\n | True\n | ibivibiv/math_instruct | |
What is the second derivative of 51*p**3*z - 2*p**3 - 12061*p**2 + 1468829*p*z wrt p?\n | 306*p*z - 12*p - 24122\n | ibivibiv/math_instruct | |
Suppose 0*w + 12 = w. Let d be (-3)/(-6)*(18 + 6 + -2). Suppose -5*x = -i + 12, 3*i - 69 = 4*x - d. What is the lowest common multiple of i and w?\n | 132\n | ibivibiv/math_instruct | |
Suppose 5*l + 2*i - 20 = -78, -2*l = -3*i + 27. Let c be ((-12)/9)/(l/54). Let o be c/15 - (123/420 - 0). Which is bigger: -1 or o?\n | o\n | ibivibiv/math_instruct | |
Let i(c) = -c**3 + 6*c**2 + 5*c - 3. Let d be i(6). Let h = -31022 - -31026. Solve -d = 5*j - 2, h*u - 13 = j for u.\n | 2\n | ibivibiv/math_instruct | |
What is the derivative of -280511691*i**3 + 139730957?\n | -841535073*i**2\n | ibivibiv/math_instruct | |
Let o be 9 + 23/(138/(-36)). Sort -0.5, 0.05, o, -5 in decreasing order.\n | o, 0.05, -0.5, -5\n | ibivibiv/math_instruct | |
Which is the closest to -2/5? (a) -9 (b) 4/9 (c) 2/3 (d) -6\n | b\n | ibivibiv/math_instruct | |
Let w(g) = -8*g**3 + 6*g**2 + 418*g + 2048. Calculate w(-5).\n | 1108\n | ibivibiv/math_instruct | |
Evaluate (20 - 11) + 11 + 10 + -22.\n | 8\n | ibivibiv/math_instruct | |
Convert 653.7538 meters to micrometers.\n | 653753800\n | ibivibiv/math_instruct | |
In base 4, what is 12300123 + -301321?\n | 11332202\n | ibivibiv/math_instruct | |
Does 212 divide 1111079704?\n | True\n | ibivibiv/math_instruct | |
What is the cube root of 7627437 to the nearest integer?\n | 197\n | ibivibiv/math_instruct | |
Let z(x) be the third derivative of x**8/1120 - x**7/630 - x**4/24 + x**2. Let i(f) be the second derivative of z(f). Factor i(u).\n | 2*u**2*(3*u - 2)\n | ibivibiv/math_instruct | |
Suppose 2*m = -5*o - 300, -7*o = -9*o. Let f = m + 353. What is the tens digit of f?\n | 0\n | ibivibiv/math_instruct | |
What is 10/21 of a week in minutes?\n | 4800\n | ibivibiv/math_instruct | |
What are the prime factors of 2312?\n | 2, 17\n | ibivibiv/math_instruct | |
Simplify (sqrt(85)*-2*-4 + 4*1*sqrt(85))/(-1*sqrt(605)*4 - (sqrt(605) + 1*(sqrt(605) - sqrt(605)*1 - sqrt(605)))).\n | -3*sqrt(17)/11\n | ibivibiv/math_instruct | |
What is the next term in 3641, 14579, 32809, 58331, 91145, 131251?\n | 178649\n | ibivibiv/math_instruct | |
Solve 230 = -4*j - 22*n, 5*n - 5 - 18 = -41 - 37 for j.\n | 3\n | ibivibiv/math_instruct | |
List the prime factors of 915.\n | 3, 5, 61\n | ibivibiv/math_instruct | |
Let r = 20 - 88. Let w be 2/14 - 15/((-1050)/(-4910)). Which is smaller: w or r?\n | w\n | ibivibiv/math_instruct | |
Put 1/7, 2/5, 1316.71, -3 in decreasing order.\n | 1316.71, 2/5, 1/7, -3\n | ibivibiv/math_instruct | |
Let f be ((-5)/(-4))/(7/(-28)). Let g be 2/f + (-4)/15. What is the nearest to 0.2 in 0, g, 0.3?\n | 0.3\n | ibivibiv/math_instruct | |
if g is the smallest positive integer such that 3150 multiplied by g is the square of an integer , then g must be | To find the smallest positive integer g such that 3150 multiplied by g is the square of an integer, we need to prime factorize 3150 and then determine what factors are needed to make it a perfect square.
Lets prime factorize 3150:
3150 = 2 × 3 × 3 × 5 × 5 × 7
3150 = 2 × 3^2 × 5^2 × 7
For a number to be a perfect squ... | ibivibiv/math_instruct | |
In base 3, what is 110022201202 - -2002?\n | 110022210211\n | ibivibiv/math_instruct | |
Let t(p) = -552*p. Let i(y) = 8*y. Give t(i(k)).\n | -4416*k\n | ibivibiv/math_instruct |
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