instruction_seed stringlengths 5 2.9k | response_seed stringlengths 3 9.55k | input stringclasses 1
value | _source stringclasses 1
value |
|---|---|---|---|
Does 25 divide 991528?\n | False\n | ibivibiv/math_instruct | |
Let i(z) = -3211*z + 72. List the prime factors of i(-3).\n | 3, 5, 647\n | ibivibiv/math_instruct | |
Convert 62 (base 8) to base 10.\n | 50\n | ibivibiv/math_instruct | |
Let g(l) = 6*l**3 - 7*l**2 + 7. Let h(i) be the third derivative of -i**6/120 + i**5/60 - i**3/6 + 297*i**2. Determine 5*g(y) + 35*h(y).\n | -5*y**3\n | ibivibiv/math_instruct | |
Calculate the greatest common divisor of 47 and 2550643.\n | 47\n | ibivibiv/math_instruct | |
Let z(a) be the second derivative of a**4/2 + a**2/2 + a. Let o(h) = h**3 - 5*h**2 + 7*h - 16. Calculate the remainder when o(5) is divided by z(1).\n | 5\n | ibivibiv/math_instruct | |
Suppose 4*w + 3*h + 16 = 0, w - 3*w + 10 = -3*h. Sort -2, w, -9 in increasing order.\n | -9, -2, w\n | ibivibiv/math_instruct | |
Let c(t) = -t**2 - 22*t + 42. Let w be c(-23). Which is smaller: 17 or w?\n | 17\n | ibivibiv/math_instruct | |
Suppose 0 = -v - 5*f + 55, v - 2*f - 40 = 22. Is 10 a factor of v?\n | True\n | ibivibiv/math_instruct | |
Work out -391.55 * -29.5.\n | 11550.725\n | ibivibiv/math_instruct | |
Let x be ((-1576)/(-4) - -3)/(1/3). Is 1188 > x?\n | False\n | ibivibiv/math_instruct | |
Let w be 10/3 - (-4 + 120/36). What is the second derivative of 183*r**5 - w - 3*r - 435*r**2 + 435*r**2 wrt r?\n | 3660*r**3\n | ibivibiv/math_instruct | |
What is (-2)/(1/1)*1874/2811?\n | -4/3\n | ibivibiv/math_instruct | |
Find s, given that s**3/4 - 171*s**2/4 - 349*s/4 + 519/4 = 0.\n | -3, 1, 173\n | ibivibiv/math_instruct | |
Let u = -30 - -14. Let z = -16 - u. Suppose z = -34*f + 36*f - 32. Is 4 a factor of f?\n | True\n | ibivibiv/math_instruct | |
What is (-6)/(-165)*(29 - 209)/36?\n | -2/11\n | ibivibiv/math_instruct | |
What is the ten millions digit of 1846411401?\n | 4\n | ibivibiv/math_instruct | |
Let r(z) = -475*z - 163141. Calculate r(-343).\n | -216\n | ibivibiv/math_instruct | |
Express 580109 - 580109 + 229*a as i*a + l and give i.\n | 229\n | ibivibiv/math_instruct | |
Collect the terms in 3*f - 59 + 9 + 42 + 8.\n | 3*f\n | ibivibiv/math_instruct | |
Let b(j) = j**3 - j**2 + 4*j - 5. Let u be b(2). Suppose 0 = -u*h + 2172 - 37. Let r = h + -177. Is r a multiple of 32?\n | True\n | ibivibiv/math_instruct | |
Let i = 157 - 156.99767. Round i to four dps.\n | 0.0023\n | ibivibiv/math_instruct | |
Let y(q) = -2*q**2 - 159*q - 58. Determine y(-37).\n | 3087\n | ibivibiv/math_instruct | |
Let m(s) = 31*s**2 - 2. Let q(a) = -3 + 5117308*a + 32*a**2 - 5117308*a. Calculate 3*m(n) - 2*q(n).\n | 29*n**2\n | ibivibiv/math_instruct | |
Expand -50*a**2 - 3*a**2 - 4 + 7*a**2 + (0*a + 0*a + a)*(a + a - a) - 8 - 5*a**2 + 8 - 3*a + 3*a + 2*a**2.\n | -48*a**2 - 4\n | ibivibiv/math_instruct | |
Suppose 2*r + 8 = 6*r. Suppose 0 = r*f - 69 + 7. Is 21 a factor of f?\n | False\n | ibivibiv/math_instruct | |
Evaluate (-456)/4320 + (-25)/(-500).\n | -1/18\n | ibivibiv/math_instruct | |
Let z = 1.71 + -1.65. Which is smaller: z or 28?\n | z\n | ibivibiv/math_instruct | |
Simplify ((1*sqrt(180))/sqrt(5))/(sqrt(1728)*2).\n | sqrt(3)/24\n | ibivibiv/math_instruct | |
Express -6 - 4*k**2 - 5 + k**2 + k**2 in the form q + u*k + v*k**2 and give v.\n | -2\n | ibivibiv/math_instruct | |
Suppose 13*q = 6*q + 14. Solve -2 = -3*r + u + q, r + u = 0 for r.\n | 1\n | ibivibiv/math_instruct | |
Calculate prob of picking 3 i when three letters picked without replacement from {x: 1, i: 3}.\n | 1/4\n | ibivibiv/math_instruct | |
Suppose 128 = -3*i - 5*x + 376, -i - x + 86 = 0. Suppose 0 = -i*f + 96*f - 160. What is the remainder when 57 is divided by f?\n | 25\n | ibivibiv/math_instruct | |
Round -0.00115748 to 7 decimal places.\n | -0.0011575\n | ibivibiv/math_instruct | |
Suppose -516*c + 505*c + 13739 = 0. List the prime factors of c.\n | 1249\n | ibivibiv/math_instruct | |
Calculate prob of sequence ka when two letters picked without replacement from {x: 2, a: 3, h: 2, u: 6, k: 1}.\n | 3/182\n | ibivibiv/math_instruct | |
How many decades are there in one twentieth of a millennium?\n | 5\n | ibivibiv/math_instruct | |
What is 3802328 divided by 39?\n | 3802328/39\n | ibivibiv/math_instruct | |
Let f be ((-2)/4*0)/(-2). Suppose 2*m - 10 = -f*m. Solve 0*b + 31 = 2*b + m*z, -2*z = 2*b - 16 for b.\n | 3\n | ibivibiv/math_instruct | |
What is the value of 20/6 - (-3 + -3 + 9)?\n | 1/3\n | ibivibiv/math_instruct | |
A florist is making bouquets for the weekend. The florist uses red, yellow, orange, and purple flowers, and each bouquet contains 9 flowers of any color combinations. This week he planted 125 seeds for each color of flower. Unfortunately, a fungus killed 45 red flowers, 61 yellow, 30 orange, and 40 purple flowers. How ... | The florist planted 125 seeds for each color, so he had a total of 125 x 4 = 500 flowers.
However, some flowers died due to the fungus, so the florist has 500 - 45 - 61 - 30 - 40 = 324 flowers left.
Each bouquet contains 9 flowers, so the florist can make 324 / 9 = 36 bouquets.
#### 36
The answer is: 36 | ibivibiv/math_instruct | |
Two letters picked without replacement from sqqsuqaqqacqsat. What is prob of sequence ca?\n | 1/70\n | ibivibiv/math_instruct | |
Simplify ((g**(2/15)/g)/(g/((g**(1/5)*g)/g)))**32 assuming g is positive.\n | g**(-160/3)\n | ibivibiv/math_instruct | |
What is the units digit of 1771?\n | 1\n | ibivibiv/math_instruct | |
Let o(w) = -15*w + 6. Suppose 0*k = -4*k - 12. Is o(k) a prime number?\n | False\n | ibivibiv/math_instruct | |
Determine a so that -3*a**3 - 37494*a**2 + 5192577*a - 5155080 = 0.\n | -12635, 1, 136\n | ibivibiv/math_instruct | |
Expand -q**2 - 2*q**2 + 2*q**2 + (1 - 2*q - 1)*(4*q - q - 4*q) + (41 - 70 + 504)*(-2*q**2 + 3*q**2 + q**2).\n | 951*q**2\n | ibivibiv/math_instruct | |
Sort -5, 4, -2, -12, 3, -4 in ascending order.\n | -12, -5, -4, -2, 3, 4\n | ibivibiv/math_instruct | |
Calculate -9084 + 0.1.\n | -9083.9\n | ibivibiv/math_instruct | |
Let g(b) = 15*b. Let v(i) = -240*i + 2. Determine v(g(t)).\n | -3600*t + 2\n | ibivibiv/math_instruct | |
Let y(s) be the first derivative of 1779*s**4/4 - 2*s**3/3 + s**2/2 + 1423*s + 7696. Find the second derivative of y(h) wrt h.\n | 10674*h - 4\n | ibivibiv/math_instruct | |
Let j = -7 + 36. What are the prime factors of j?\n | 29\n | ibivibiv/math_instruct | |
Two letters picked without replacement from {o: 5, y: 2}. What is prob of sequence oo?\n | 10/21\n | ibivibiv/math_instruct | |
Suppose -2*p = 4*p. Suppose -5*g = 2*z - 369 + 22, p = -5*g + z + 359. List the prime factors of g.\n | 71\n | ibivibiv/math_instruct | |
Is 247025767 a composite number?\n | False\n | ibivibiv/math_instruct | |
Does 13 divide 35558?\n | False\n | ibivibiv/math_instruct | |
Expand (2 + 1 - 1)*(-77 - 53 + 229)*(1 + 0 + 2)*(0*r - r + 2*r).\n | 594*r\n | ibivibiv/math_instruct | |
Which is the nearest to -2/15? (a) -132 (b) -1 (c) -0.1 (d) 3 (e) 0.01\n | c\n | ibivibiv/math_instruct | |
Simplify (sqrt(7) - (5 + sqrt(21)/sqrt(3))) + -2.\n | -7\n | ibivibiv/math_instruct | |
Let r = -88/515 + -3/103. Let g = -9 + 8.5. Which is the closest to r? (a) 4 (b) -0.2 (c) g\n | b\n | ibivibiv/math_instruct | |
What is the ninth root of 3127903 to the nearest integer?\n | 5\n | ibivibiv/math_instruct | |
Find the second derivative of -7*m*n**4 + m*n**3 - m*n + m + 3*n**4 + 18 wrt n.\n | -84*m*n**2 + 6*m*n + 36*n**2\n | ibivibiv/math_instruct | |
Suppose 147*w**5/5 + 12264*w**4/5 - 113472*w**3/5 + 224112*w**2/5 - 101424*w/5 + 13248/5 = 0. Calculate w.\n | -92, 2/7, 2, 6\n | ibivibiv/math_instruct | |
What comes next: -45, -50, -57, -66?\n | -77\n | ibivibiv/math_instruct | |
Round 0.0000007549 to 7 decimal places.\n | 0.0000008\n | ibivibiv/math_instruct | |
What is next in -939, -941, -943?\n | -945\n | ibivibiv/math_instruct | |
Let l = -22 - -36. Let o = -297.9 - -284. Let p = l + o. Sort 2/3, p, 4.\n | p, 2/3, 4\n | ibivibiv/math_instruct | |
Write an educational piece suited for college students related to the following text snippet:
"An effective method to estimate parameters in a model with latent variables is the Estimation and Maximization algorithm (EM algorithm). In the example states that we have the record set of heads and tails from a couple of co... | The Expectation-Maximization (EM) algorithm is a powerful statistical technique used when dealing with models containing unobserved or "latent" variables. These algorithms are particularly useful in situations where you want to estimate the parameters of a probability distribution based on incomplete data. A classic e... | ibivibiv/math_instruct | |
Rearrange (2*p**2 - 3*p**2 - p**2)*(2*p**2 - p**2 + p**2 + (-16*p - 105 + 105)*(-17*p - 20 + 20)) to k*p + t + o*p**3 + q*p**4 + u*p**2 and give t.\n | 0\n | ibivibiv/math_instruct | |
Let q(r) = r**3 + 2*r**2 + 7*r + 32. What is q(-4)?\n | -28\n | ibivibiv/math_instruct | |
Evaluate $2000^3-1999\cdot 2000^2-1999^2\cdot 2000+1999^3$ | We can factor out $2000^2$ from the first two terms and $1999^2$ from the last two terms to get \[2000^2(2000-1999)-1999^2(2000-1999).\]
Simplifying, we have \[2000^2(1)-1999^2(1).\] Notice that this expression is a difference of squares, so we can factor further to get \[(2000+1999)(2000-1999).\] Evaluating this expre... | ibivibiv/math_instruct | |
Which is the fourth smallest value? (a) -2/7 (b) -1 (c) 204 (d) 4 (e) 0.2 (f) 2\n | f\n | ibivibiv/math_instruct | |
Let b(y) be the second derivative of 4427*y**6/30 - 5605*y**4/12 - 5231*y. What is the third derivative of b(c) wrt c?\n | 106248*c\n | ibivibiv/math_instruct | |
-1 (base 10) to base 4\n | -1\n | ibivibiv/math_instruct | |
Let a(z) = -15*z - 4. Let m be a(-4). Suppose 5*x + i - 34 = 0, 0*x + 4*i + 11 = x. Calculate the greatest common factor of x and m.\n | 7\n | ibivibiv/math_instruct | |
Let m = -0.57 + -2.43. Let t = -0.2 + 0.2. What is the second smallest value in m, 2, t?\n | t\n | ibivibiv/math_instruct | |
What is the value of 102*(-3)/54*-2*(-3)/2?\n | -17\n | ibivibiv/math_instruct | |
Let w be ((-10)/160*12)/(6/(-4952)). Suppose -35*d - k = -31*d - w, 0 = 2*d + 2*k - 302. Is 7 a factor of d?\n | False\n | ibivibiv/math_instruct | |
What is the second derivative of 3*n**4 + 49890*n**3 + 62*n**2 - 125528860*n?\n | 36*n**2 + 299340*n + 124\n | ibivibiv/math_instruct | |
Solve 3*q = -10*q + 329687 - 329544 for q.\n | 11\n | ibivibiv/math_instruct | |
Suppose -219 - 732 = -q. Is q a prime number?\n | False\n | ibivibiv/math_instruct | |
2569.12*0\n | 0\n | ibivibiv/math_instruct | |
Four letters picked without replacement from wwwzwwwwwwwwzwwwww. What is prob of sequence zzww?\n | 1/153\n | ibivibiv/math_instruct | |
What are the prime factors of 606?\n | 2, 3, 101\n | ibivibiv/math_instruct | |
Simplify (sqrt(63) + (sqrt(504)/sqrt(128) + sqrt(63) - sqrt(63)) + sqrt(63)*-2*1)/(1*sqrt(441)*1).\n | -3*sqrt(7)/28\n | ibivibiv/math_instruct | |
-8a3612 (base 12) to base 8\n | -10320656\n | ibivibiv/math_instruct | |
Calculate 32830848 divided by -5.\n | -32830848/5\n | ibivibiv/math_instruct | |
Calculate prob of picking 2 x and 2 v when four letters picked without replacement from {h: 1, t: 6, j: 7, v: 2, x: 2, m: 1}.\n | 1/3876\n | ibivibiv/math_instruct | |
Let m(c) = 13*c + 3. Let b be m(1). Solve 0 = -w + 6*w + 20, 2*x + 3*w + b = 0 for x.\n | -2\n | ibivibiv/math_instruct | |
Three letters picked without replacement from kkkskkkkkkss. Give prob of picking 2 s and 1 k.\n | 27/220\n | ibivibiv/math_instruct | |
What is 527882785 to the power of 1/2, to the nearest integer?\n | 22976\n | ibivibiv/math_instruct | |
Simplify -5 + 4*(sqrt(1224) + (sqrt(1224) - (sqrt(1224) - -2*sqrt(1224))) - sqrt(34))/(1*sqrt(2)*-5) + -3.\n | -8 + 28*sqrt(17)/5\n | ibivibiv/math_instruct | |
Are -1621 and -1622 non-equal?\n | True\n | ibivibiv/math_instruct | |
What is the closest to 20 in -1/15, 3/8, -3, -0.1, -1, -19/3?\n | 3/8\n | ibivibiv/math_instruct | |
Let c be (-1 + 3 + -12)*(-6)/3. Which is bigger: c or 23?\n | 23\n | ibivibiv/math_instruct | |
Four letters picked without replacement from hxxxxhxxxhxxxxxxxx. Give prob of sequence xhxh.\n | 7/408\n | ibivibiv/math_instruct | |
Four letters picked without replacement from nlnelllnngeynlgnl. What is prob of picking 2 g and 2 l?\n | 3/476\n | ibivibiv/math_instruct | |
Let p be 23/(-5) + (-9)/(-15). Let t be 1 + 0 + -1 + -5. Is t greater than or equal to p?\n | False\n | ibivibiv/math_instruct | |
What is the ten thousands digit of 289442?\n | 8\n | ibivibiv/math_instruct | |
What is the tens digit of 51?\n | 5\n | ibivibiv/math_instruct |
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