instruction_seed stringlengths 5 2.9k | response_seed stringlengths 3 9.55k | input stringclasses 1
value | _source stringclasses 1
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|---|---|---|---|
Let i(d) = d**2 - 1. Let g(s) = -3 - 4 - 3*s**2 + 11*s**2. Let b(z) = -2*g(z) + 14*i(z). Let v(k) be the first derivative of k**2 + 1. Determine v(b(u)).\n | -4*u**2\n | ibivibiv/math_instruct | |
What are the prime factors of 421199398?\n | 2, 210599699\n | ibivibiv/math_instruct | |
What is 39279 to the power of 1/2, to the nearest integer?\n | 198\n | ibivibiv/math_instruct | |
Let v(b) = -b + 3. Let q(n) = 2*n - 7. Let k(m) = 3*q(m) + 7*v(m). Suppose -5*l = -113 + 28. Calculate the remainder when l is divided by k(-6).\n | 5\n | ibivibiv/math_instruct | |
Product of 2 and 1724.\n | 3448\n | ibivibiv/math_instruct | |
What is the biggest value in 0.06, 2/13, -0.1, -0.3, 7?\n | 7\n | ibivibiv/math_instruct | |
What is the value of 17 + ((40 - 21) + -4 - (-1 + 98))?\n | -65\n | ibivibiv/math_instruct | |
What is 303 minutes after 8:07 AM?\n | 1:10 PM\n | ibivibiv/math_instruct | |
What is the greatest common factor of 4144 and 7941680?\n | 592\n | ibivibiv/math_instruct | |
What is the hundreds digit of 287175572?\n | 5\n | ibivibiv/math_instruct | |
Product of 13085.264 and -0.3.\n | -3925.5792\n | ibivibiv/math_instruct | |
What is the cube root of 1263733323 to the nearest integer?\n | 1081\n | ibivibiv/math_instruct | |
What is the second derivative of -71*g*p**2 - 2*g*p + g - 2*p**2 - 49 wrt p?\n | -142*g - 4\n | ibivibiv/math_instruct | |
What is 18/552*(-1552)/(-194)?\n | 6/23\n | ibivibiv/math_instruct | |
Let i(p) = -31*p - 1. Let y be i(-1). Calculate the highest common factor of y and 75.\n | 15\n | ibivibiv/math_instruct | |
What is the square root of 2552759 to the nearest integer?\n | 1598\n | ibivibiv/math_instruct | |
Let i be (-360)/(4/(-1))*19. Suppose 0 = -11*o - 8*o + i. Is o a multiple of 3?\n | True\n | ibivibiv/math_instruct | |
Calculate prob of sequence spz when three letters picked without replacement from {p: 2, s: 12, z: 5}.\n | 20/969\n | ibivibiv/math_instruct | |
Calculate prob of sequence gi when two letters picked without replacement from {g: 12, i: 1}.\n | 1/13\n | ibivibiv/math_instruct | |
Work out 2 + -39933378.\n | -39933376\n | ibivibiv/math_instruct | |
Is 7 a factor of 19836487?\n | False\n | ibivibiv/math_instruct | |
What is -773794 rounded to the nearest 10000?\n | -770000\n | ibivibiv/math_instruct | |
Let a(o) = 4 - 64 - 43*o - 4. List the prime factors of a(-32).\n | 2, 41\n | ibivibiv/math_instruct | |
Let h be ((-8)/(-1))/((-6)/(-12)). Let l = h - 11. Suppose l*c - 4*c + 18300 = 0. Round c to the nearest 1000.\n | -18000\n | ibivibiv/math_instruct | |
Collect the terms in 84*g**2 - 33*g**2 + 33*g**2.\n | 84*g**2\n | ibivibiv/math_instruct | |
Suppose -n = -33*n - 96. Let y be 6255/81 - 4/18. Suppose -5*k = -y + 22. Sort n, -2, k, 0.3 in descending order.\n | k, 0.3, -2, n\n | ibivibiv/math_instruct | |
Suppose -4*v - 9 = 5*l, 2*l + 3*v = -0*v + 2. Let x = 30 + -41. Let w(h) = -2*h. Let j be w(-2). Sort l, j, x in decreasing order.\n | j, l, x\n | ibivibiv/math_instruct | |
Suppose -3*q = 24, 78*d - 76*d + 24 = -4*q. Solve -198 = d*t - 226 for t.\n | 7\n | ibivibiv/math_instruct | |
Let x = 9 + -11. Let o = 11779 - 235471/20. Calculate the common denominator of (1/20)/(x/188) and o.\n | 20\n | ibivibiv/math_instruct | |
Is 536639 composite?\n | True\n | ibivibiv/math_instruct | |
Let g(z) = 3*z + 3. Let p(j) = -j + 11. Let q be p(10). Suppose s - d = q, 4*s = -d + 6*d + 7. What is g(s)?\n | -3\n | ibivibiv/math_instruct | |
What are the prime factors of 1309?\n | 7, 11, 17\n | ibivibiv/math_instruct | |
Round 0.000081048 to five dps.\n | 0.00008\n | ibivibiv/math_instruct | |
What is -7*14/(-931)*(-3)/(-3)?\n | 2/19\n | ibivibiv/math_instruct | |
Let g = -6 + 5. Which is the nearest to -1? (a) g (b) -2 (c) 3\n | a\n | ibivibiv/math_instruct | |
Simplify (((d**(3/7)*d)/d)**(2/137)/((d/(d**(4/3)/d))/d**(-1)))**24 assuming d is positive.\n | d**(-38216/959)\n | ibivibiv/math_instruct | |
What is the result of the following expression?
-10.9892 - (93.0764 - 86.6628) | -17.4028 | ibivibiv/math_instruct | |
Express 3*x**2 - 4*x**2 - 6*x**2 + (-x**2 - 4*x**2 + 2*x**2)*(-53 + 25 + 29) in the form c*x + b + j*x**2 and give j.\n | -10\n | ibivibiv/math_instruct | |
Let x(y) = -1678*y**2 - y - 23. Let i be x(-21). What is i rounded to the nearest 100000?\n | -700000\n | ibivibiv/math_instruct | |
What is the hundreds digit of 6079?\n | 0\n | ibivibiv/math_instruct | |
Calculate prob of picking 1 c, 1 a, and 1 y when three letters picked without replacement from yayccayyc.\n | 2/7\n | ibivibiv/math_instruct | |
What is the lowest common multiple of 21 + -11 + 11324 + 8*(-1)/(-1) and 2?\n | 11342\n | ibivibiv/math_instruct | |
Collect the terms in 434*s**2 - 427*s**2 + 10*s - 12*s.\n | 7*s**2 - 2*s\n | ibivibiv/math_instruct | |
Put 5, 32/9, 0, 87, 0.2, -1 in decreasing order.\n | 87, 5, 32/9, 0.2, 0, -1\n | ibivibiv/math_instruct | |
Suppose -3*k + 4990 = -3*m - 1391, -3*m = 15. What is the thousands digit of k?\n | 2\n | ibivibiv/math_instruct | |
What is the sixth root of 774138430 to the nearest integer?\n | 30\n | ibivibiv/math_instruct | |
Simplify (((g*g**(-1/4)/g)/g)/(((g*g*g*(g**(-5/2)*g*g)/g*g)/g*g)/g)*g**(-1/5)*g**(2/15))**10 assuming g is positive.\n | g**(-169/6)\n | ibivibiv/math_instruct | |
Let v(a) be the third derivative of -a**5/15 + 7*a**4/24 - 314*a**2. What is v(2)?\n | -2\n | ibivibiv/math_instruct | |
Write an educational piece suited for college students related to the following text snippet:
"# Joint PDF of two random variables and their sum
What is the joint PDF of two uniformly distributed random variables and their sum?
-
What would you like it to be? The marginal pdfs do not, in general, determine the joint ... | In probability theory, a common task is to find the joint probability density function (PDF) or the marginal distributions of certain random variables (RVs), often based on information about their individual properties or relationships with other RVs. This discussion will focus on the problem posed by user "em70," who... | ibivibiv/math_instruct | |
Four letters picked without replacement from ohhhmhcmmmmmmmm. What is prob of sequence ooho?\n | 0\n | ibivibiv/math_instruct | |
What is the smallest common multiple of 10 and 34?\n | 170\n | ibivibiv/math_instruct | |
Does 1033 = -40638?\n | False\n | ibivibiv/math_instruct | |
Suppose -6*o - 48 = -72. Let y(s) = -2. Let m(g) = g**2 - 8. Let l(i) = o*y(i) - m(i). Let u(v) be the first derivative of -v**3 - 5*v + 2. Determine u(l(h)).\n | -3*h**4 - 5\n | ibivibiv/math_instruct | |
What is the ten thousands digit of 378622836?\n | 2\n | ibivibiv/math_instruct | |
What is the third biggest value in -49832, 19, -0.1?\n | -49832\n | ibivibiv/math_instruct | |
Suppose 17*n = 8*n + 378. Let c(l) = -n*l**2 - 2*l + 0*l + 1 + 5*l + 41*l**2. Suppose 2*g - 20 = 5*t, -2*g = -g + t - 3. Determine c(g).\n | -9\n | ibivibiv/math_instruct | |
What is -117588 divided by -717?\n | 164\n | ibivibiv/math_instruct | |
What is the distance between -67 and -0.4?\n | 66.6\n | ibivibiv/math_instruct | |
Let b = -79.460581 - -79.0606. Let l = 0.2 - 0.6. Let n = l - b. Round n to 5 decimal places.\n | -0.00002\n | ibivibiv/math_instruct | |
Let n(y) be the third derivative of y**6/120 + 3*y**5/20 - 3*y**4/8 + 5*y**3/2 + 1550*y**2. Let m = 2 - 12. List the prime factors of n(m).\n | 5\n | ibivibiv/math_instruct | |
Let h = -10 + 31. Let y = -43417 + 43456. Calculate the remainder when y is divided by h.\n | 18\n | ibivibiv/math_instruct | |
Suppose -77*t = -84*t + 7. Which is the third smallest value? (a) 3/2 (b) 15/8 (c) t\n | b\n | ibivibiv/math_instruct | |
Solve 8*g - 10 = 4*k + 10*g, 5*k + 5 = 5*g for k.\n | -2\n | ibivibiv/math_instruct | |
Is 3173/132 less than or equal to 24?\n | False\n | ibivibiv/math_instruct | |
Expand (0 + 0 - 3*g)*(-35*g - 2375 + 66*g - 18*g - 17*g).\n | 12*g**2 + 7125*g\n | ibivibiv/math_instruct | |
What is the square root of 189 to the nearest integer?\n | 14\n | ibivibiv/math_instruct | |
-3437 (base 8) to base 3\n | -2111112\n | ibivibiv/math_instruct | |
Let r = -305 + 18604/61. Let w = -78275087/259093779 + 2/606777. Let m = r - w. Sort 2, m, -0.2.\n | -0.2, m, 2\n | ibivibiv/math_instruct | |
What is the nearest to 1/4 in -417, -0.2, -1.2, -3?\n | -0.2\n | ibivibiv/math_instruct | |
Let d(x) = x**2 - 2*x - 2. Let t(u) = 2*u + 2. Give -5*d(l) - 6*t(l).\n | -5*l**2 - 2*l - 2\n | ibivibiv/math_instruct | |
Simplify ((sqrt(153) + 1 + sqrt(153) + sqrt(153))*2 + -1)**2.\n | 36*sqrt(17) + 5509\n | ibivibiv/math_instruct | |
Suppose -3*d + 0*d - 3249 = 0. Let c = d + 1633. What is c rounded to the nearest one hundred?\n | 600\n | ibivibiv/math_instruct | |
How many distinct positive factors does 32 have? | The prime factorization of 32 is $2^5$.
A positive factor of 32 must be of the form $2^a$, where $0 \le a \le 5$.
Thus, there are $\boxed{6}$ distinct positive factors of 32: 1, 2, 4, 8, 16, and 32.
The answer is: 6 | ibivibiv/math_instruct | |
466 (base 7) to base 5\n | 1434\n | ibivibiv/math_instruct | |
Let y(o) = -o**2 - 14*o + 54. What is y(-23)?\n | -153\n | ibivibiv/math_instruct | |
Which is smaller: -193/1901399 or 1?\n | -193/1901399\n | ibivibiv/math_instruct | |
Put -1044, 0, 4/7, -275 in ascending order.\n | -1044, -275, 0, 4/7\n | ibivibiv/math_instruct | |
What is j in -2*j**3/5 - 8*j**2/5 - 2*j/5 + 12/5 = 0?\n | -3, -2, 1\n | ibivibiv/math_instruct | |
Sort 2/21, 14/577, -2/11 in decreasing order.\n | 2/21, 14/577, -2/11\n | ibivibiv/math_instruct | |
What is the result of the following expression?
-21.4408 - -29.7332 | 8.2924 | ibivibiv/math_instruct | |
What is the product of 0 and 3856?\n | 0\n | ibivibiv/math_instruct | |
Expand (-16*s - 29*s**2 + 16*s)*(-384*s**2 + 67*s**2 + s + 3*s - 4*s)*(s + 0*s + s).\n | 18386*s**5\n | ibivibiv/math_instruct | |
What is 0.2235016 micrometers in millimeters?\n | 0.0002235016\n | ibivibiv/math_instruct | |
Evaluate ((392/(-35))/(-1))/(10*15/(-375)).\n | -28\n | ibivibiv/math_instruct | |
Which is the fourth smallest value? (a) -281.3 (b) -2 (c) 4/29 (d) 1/7\n | d\n | ibivibiv/math_instruct | |
Solve -5*v - 138 = -236*c - 390*c + 622*c, 2*v + 5*c = -42 for v.\n | -26\n | ibivibiv/math_instruct | |
Sort -0.41, -3, 1/213, 1, -8, 3, -1 in increasing order.\n | -8, -3, -1, -0.41, 1/213, 1, 3\n | ibivibiv/math_instruct | |
What is the sixth root of 1432 to the nearest integer?\n | 3\n | ibivibiv/math_instruct | |
What is the third derivative of 4*j**4 - 6*j**4 + 2*j**4 - 5*j**2 + 101*j**2 - 108*j**5 wrt j?\n | -6480*j**2\n | ibivibiv/math_instruct | |
Simplify 4*((5 + (sqrt(272) + sqrt(17))**2 - ((1*sqrt(1088))**2 + sqrt(17))) + -5*((sqrt(17) - sqrt(51)/sqrt(3)) + -3)*3).\n | -2452 - 4*sqrt(17)\n | ibivibiv/math_instruct | |
What is 42.98766ms in microseconds?\n | 42987.66\n | ibivibiv/math_instruct | |
Calculate (-23310)/(-19980)*(4/30)/(2/18).\n | 7/5\n | ibivibiv/math_instruct | |
Sort 7, 32, -4, -3 in decreasing order.\n | 32, 7, -3, -4\n | ibivibiv/math_instruct | |
Let j(x) = -3*x - 1. Let f(l) = l**3 + 19*l**2 + 21*l + 54. Let z be f(-18). Suppose 15*a - 22 - 38 = z. Determine j(a).\n | -13\n | ibivibiv/math_instruct | |
Let t be 2/3 - (-4)/3 - -4. Let g(h) = h**3 + h**2 - 7*h + 4. Let y be g(2). Suppose -y*l + 7*b - 2*b = -27, -4*b = 3*l + 17. Put t, l, 0 in descending order.\n | t, l, 0\n | ibivibiv/math_instruct | |
Let k(m) = 5*m - 6. Let i(w) = 3 - 4*w + 6 - 4. Suppose 0 = 5*v + 10, -u + v - 2 = -0. Calculate u*i(d) - 3*k(d).\n | d - 2\n | ibivibiv/math_instruct | |
Let c = -222 - -171. Let r be (15 + c)/(6/(-4)). Solve 0 = 4*a + 4*a - r for a.\n | 3\n | ibivibiv/math_instruct | |
Suppose -73 = -27*j + 386. Let r(k) = 0 - 18 + 2 - k**2 + j. Let z(l) = 4*l**2 - 8. What is -6*r(w) - z(w)?\n | 2*w**2 + 2\n | ibivibiv/math_instruct | |
What is the thousands digit of 399219?\n | 9\n | ibivibiv/math_instruct | |
Solve 4*n + 3 = -5*c, 0 = -4*n - 13*n + 11*n + 18 for c.\n | -3\n | ibivibiv/math_instruct |
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