instruction_seed stringlengths 5 2.9k | response_seed stringlengths 3 9.55k | input stringclasses 1
value | _source stringclasses 1
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|---|---|---|---|
Let a = -0.0615 - -0.1315. Let r = 2 - -1. Let l = 38.7 + -39. What is the closest to a in r, -4, l?\n | l\n | ibivibiv/math_instruct | |
Simplify (((f*((f/f**(-2/5))/f*f)/f)/f)**(-6)*(f/((f*f/(f*f*f**(-8)))/f))/f*f**(1/5)*f)**(1/51) assuming f is positive.\n | f**(-41/255)\n | ibivibiv/math_instruct | |
Find the third derivative of -6*q**2*v + 2*q**2*y**3 + 3*q**2*y - 691922*q*v*y**3 + 152*q*v*y - q*v + q*y - 2*v*y**4 - 4*y**2 wrt y.\n | 12*q**2 - 4151532*q*v - 48*v*y\n | ibivibiv/math_instruct | |
0.2581 * 1214\n | 313.3334\n | ibivibiv/math_instruct | |
Write an educational piece suited for college students related to the following text snippet:
"how to show that this expectation is infinite
Suppose we are give $X$ which is normally distributed with mean $\mu$ and variance $\sigma^2$. How do I show that
$$E[e^{e^X}]=\infty$$
Of course I wanted to find a lower bound... | To begin, let's define what it means for an expectation to be infinite. In probability theory, the expected value or expectation of a random variable is the sum (or integral) of all possible values it can take, weighted by their respective probabilities. When the sum or integral does not converge, then we say that the... | ibivibiv/math_instruct | |
Round -2646.9 to the nearest 100.\n | -2600\n | ibivibiv/math_instruct | |
In base 11, what is 73 + 4?\n | 77\n | ibivibiv/math_instruct | |
What is the next term in -80, -128, -176, -224?\n | -272\n | ibivibiv/math_instruct | |
Let m(b) = 30*b. Let i(p) = p - 4. Let n be i(6). Let k(h) = -5*h + n*h + h. Determine k(m(f)).\n | -60*f\n | ibivibiv/math_instruct | |
Which is the fourth smallest value? (a) -6 (b) 1/60 (c) 0 (d) -33\n | b\n | ibivibiv/math_instruct | |
Let j(i) = -768*i - 20. Let p(v) = -256*v - 7. Calculate 6*j(g) - 17*p(g).\n | -256*g - 1\n | ibivibiv/math_instruct | |
Let n = -200 + 203. Which is the closest to n? (a) 1 (b) -8/11 (c) -0.3\n | a\n | ibivibiv/math_instruct | |
Let u(o) = 7*o + 224. Let r(s) = -4*s. Give r(u(p)).\n | -28*p - 896\n | ibivibiv/math_instruct | |
Factor -2*k**2/11 - 9664*k/11 - 19320/11.\n | -2*(k + 2)*(k + 4830)/11\n | ibivibiv/math_instruct | |
Let y = 24 - 23. Let l = 0.3 + 0.2. Which is the closest to -2? (a) y (b) l (c) 0\n | c\n | ibivibiv/math_instruct | |
Round -9.88493368 to two dps.\n | -9.88\n | ibivibiv/math_instruct | |
Calculate the remainder when 25563 is divided by 107.\n | 97\n | ibivibiv/math_instruct | |
Calculate 35 + (-5 - (-19 - -37)) - -16.\n | 28\n | ibivibiv/math_instruct | |
Suppose 2*n = -8, 0*n - 25 = -x + 4*n. Let l(h) = -h**2 - 7*h - 4. Let t be l(-7). Let y be (-202)/(-28) - t/14. Is x at least as big as y?\n | True\n | ibivibiv/math_instruct | |
What is -2004.48079 rounded to the nearest 10?\n | -2000\n | ibivibiv/math_instruct | |
Calculate prob of picking 1 n, 1 h, and 1 w when three letters picked without replacement from tphnwtmn.\n | 1/28\n | ibivibiv/math_instruct | |
Calculate the highest common divisor of 13560192 and 2.\n | 2\n | ibivibiv/math_instruct | |
What is 117 (base 9) in base 12?\n | 81\n | ibivibiv/math_instruct | |
Let -5*c**4 - 775*c**3 + 32595*c**2 - 338045*c + 551990 = 0. Calculate c.\n | -191, 2, 17\n | ibivibiv/math_instruct | |
What comes next: -7812, -31150, -70052, -124524, -194572, -280202, -381420, -498232?\n | -630644\n | ibivibiv/math_instruct | |
Calculate the common denominator of -70/183 and 45/41.\n | 7503\n | ibivibiv/math_instruct | |
Collect the terms in 451*p + 5*p**3 - 451*p.\n | 5*p**3\n | ibivibiv/math_instruct | |
Which is bigger: -31 or 1777.9?\n | 1777.9\n | ibivibiv/math_instruct | |
What is the product of 0.0446 and 0.5?\n | 0.0223\n | ibivibiv/math_instruct | |
Let j = -0.15 + 0.2. Suppose -2*q - 2*k = -4, -19*k + 20*k = 5. Let l be (q/((-84)/8))/((-10)/(-28)). Which is the biggest value? (a) -1 (b) 2 (c) j (d) l\n | b\n | ibivibiv/math_instruct | |
Is 42323363 a prime number?\n | True\n | ibivibiv/math_instruct | |
Let f be (((-246)/5)/(-1))/(58/(-290)). Let l = -245 - f. Suppose -2*u - 1 = -7. Solve -4*y + 7 = -u*p, 22 - l = 3*p + 3*y for p.\n | 3\n | ibivibiv/math_instruct | |
Calculate the highest common factor of 2739 and 9324469.\n | 913\n | ibivibiv/math_instruct | |
Is 106 a factor of 4209578?\n | True\n | ibivibiv/math_instruct | |
Solve 538 = r + 547 for r.\n | -9\n | ibivibiv/math_instruct | |
What is the second derivative of -27*b - 6*b**3 - 703 + 4*b**3 + 702 wrt b?\n | -12*b\n | ibivibiv/math_instruct | |
Express (-4 + 1 + 1)*(10 - 18 + 11)*(0*o**4 - o**4 + 4*o**4 + (-2*o**3 - 2*o**3 + 6*o**3)*(-6*o - 13*o + 0*o)) as y*o**3 + u*o**4 + k*o**2 + c*o + j and give u.\n | 210\n | ibivibiv/math_instruct | |
What is prob of picking 1 v and 2 h when three letters picked without replacement from {h: 11, v: 9}?\n | 33/76\n | ibivibiv/math_instruct | |
What is the result of the following expression?
91.043 - (-36.352 / -23.518) | 89.4973 | ibivibiv/math_instruct | |
What is the third biggest value in -18, -3, 1.086?\n | -18\n | ibivibiv/math_instruct | |
Solve -16104*w - 962772 + 302508 = 0 for w.\n | -41\n | ibivibiv/math_instruct | |
Let a(k) = -k**3 + 2*k**2. Let g(m) = -2*m**3 + 3*m**2. Let l be -1*0/(0 - -2). Suppose -6*h + 2*h + 8 = l. What is h*g(z) - 3*a(z)?\n | -z**3\n | ibivibiv/math_instruct | |
What is 58 (base 16) in base 7?\n | 154\n | ibivibiv/math_instruct | |
Let w = 839670.462 + -837662.04799808. Let z = w - 2004.514. Let h = z - 3.9. Round h to 7 dps.\n | 0.0000019\n | ibivibiv/math_instruct | |
Expand (2*h + 0*h + 0*h)*(-1 + 5 - 3 + (2 + 1 - 1)*(-1 + 3 + 6)).\n | 34*h\n | ibivibiv/math_instruct | |
Suppose 4 = -f + 7. Suppose 0 = 2*g + 1 - f. Sort g, -0.2, -5 in descending order.\n | g, -0.2, -5\n | ibivibiv/math_instruct | |
Let m(j) be the second derivative of -j**7/84 + 2*j**6/15 - 5*j**5/8 + 19*j**4/12 - 7*j**3/3 + 2*j**2 - 20*j. Factor m(t).\n | -(t - 2)**3*(t - 1)**2/2\n | ibivibiv/math_instruct | |
Solve -2*k + 3*u = -35, 3*k + 7499*u - 54 = 7504*u for k.\n | 13\n | ibivibiv/math_instruct | |
What is the second derivative of -4273359*i**2 - 234765*i?\n | -8546718\n | ibivibiv/math_instruct | |
What comes next: 755, 953, 1283, 1745?\n | 2339\n | ibivibiv/math_instruct | |
Simplify (1 + sqrt(1053) + sqrt(1053)*-3 + (sqrt(208) - -6*sqrt(208)*3))**2.\n | 116*sqrt(13) + 43733\n | ibivibiv/math_instruct | |
Let l be (-10 - -13) + (678 - -9). Is l < 690?\n | False\n | ibivibiv/math_instruct | |
What is the third root of 7915 to the nearest integer?\n | 20\n | ibivibiv/math_instruct | |
Is 4 a factor of 7180124?\n | True\n | ibivibiv/math_instruct | |
Is 1070579 composite?\n | False\n | ibivibiv/math_instruct | |
Is 1805188339 a composite number?\n | False\n | ibivibiv/math_instruct | |
Write an educational piece suited for college students related to the following text snippet:
"# How many injective functions $f:[1,…,m]\to{[1,…,n]}$ has no fixed point? $(m\le n)$
How many injective functions $f:[1,...,m]\to{[1,...,n]}$ has no fixed point? $(m\le n)$
I thought about the next thing:
$f(x_1)\neq x_1$... | Let us consider the problem of finding the number of injective functions from a set $[1, ..., m]$ to a set $[1, ..., m] o [1, ..., a]$ such that none of these functions maps any element to itself, where $a$ is a nonnegative integer. For convenience, we will refer to such functions as "no-fixed-point-injections." The ... | ibivibiv/math_instruct | |
In base 5, what is -120 - 34?\n | -204\n | ibivibiv/math_instruct | |
Expand -6*r**2 + 4*r**2 + r**2 + (-2*r + 2*r - 4*r)*(7*r - 13*r - 9*r) + (-3*r - 2*r + 4*r)*(-r - 2 + 2).\n | 60*r**2\n | ibivibiv/math_instruct | |
Let p(i) be the second derivative of -2*i**6/5 - 17*i**2 - 34*i. Differentiate p(n) with respect to n.\n | -48*n**3\n | ibivibiv/math_instruct | |
Let f be (0 + 15/6)/(6/(-12)). Which is the closest to 0.1? (a) f (b) -1 (c) -2.2\n | b\n | ibivibiv/math_instruct | |
Evaluate -2*(-5)/(-4)*(-19)/(-95).\n | -1/2\n | ibivibiv/math_instruct | |
What is the units digit of 8120425?\n | 5\n | ibivibiv/math_instruct | |
Put -11/2, -2/5, 5, -2/7 in ascending order.\n | -11/2, -2/5, -2/7, 5\n | ibivibiv/math_instruct | |
Rearrange (-14 - 12 + 11)*(-2*w - w + w) to the form z + s*w and give z.\n | 0\n | ibivibiv/math_instruct | |
Expand (43 + 5*f - 11 - 21)*(f + 5*f - 5*f) + 4*f**2 - 3*f**2 - 2*f**2 + (-3 + 2 - 1)*(-3*f**2 + 2*f**2 + 2*f**2).\n | 2*f**2 + 11*f\n | ibivibiv/math_instruct | |
Let v(a) = a**3 + 10*a**2 + 9*a + 1. Let q be v(-9). Let u(n) = n**2 + n - 1. Give u(q).\n | 1\n | ibivibiv/math_instruct | |
Let g = -2.453 + 3.453. What is the smallest value in g, -1/2, -1, -0.1?\n | -1\n | ibivibiv/math_instruct | |
80 (base 9) to base 15\n | 4c\n | ibivibiv/math_instruct | |
Let q = -0.4 - -0.2. Let l = 4.8 - q. Which is the second smallest value? (a) -0.5 (b) 0.4 (c) l\n | b\n | ibivibiv/math_instruct | |
Suppose 3 = b + 6, -3*b + 39 = -3*o. Let t be (-81)/(-4) - 12/o. Suppose -y - t = -4*y. Is y a composite number?\n | False\n | ibivibiv/math_instruct | |
Let b = 612 - 384. Suppose -24*d - b = -28*d. Does 14 divide d?\n | False\n | ibivibiv/math_instruct | |
Which is bigger: -2/7747 or 1?\n | 1\n | ibivibiv/math_instruct | |
What is the value of 1/((-9)/72)*(-2 + 1)?\n | 8\n | ibivibiv/math_instruct | |
Let p = 0.08 + -0.84. Let d = p - -0.56. What is the smallest value in d, -0.3, -20?\n | -20\n | ibivibiv/math_instruct | |
Which is smaller: -315 or 171983?\n | -315\n | ibivibiv/math_instruct | |
What is -2.7234 times -2?\n | 5.4468\n | ibivibiv/math_instruct | |
What is 0.0000290674 rounded to 5 dps?\n | 0.00003\n | ibivibiv/math_instruct | |
Let v = -257996637 - -131926637. What is v rounded to the nearest one million?\n | -126000000\n | ibivibiv/math_instruct | |
What is the product of 1 and -0.35192?\n | -0.35192\n | ibivibiv/math_instruct | |
What is the next term in -55335, -110663, -165991, -221319, -276647, -331975?\n | -387303\n | ibivibiv/math_instruct | |
Let q = 11029298/209 - 52772. Calculate the common denominator of q and 7/88.\n | 1672\n | ibivibiv/math_instruct | |
Solve -1200*p = -13478 - 3322 for p.\n | 14\n | ibivibiv/math_instruct | |
Let s(o) = -o. Let p(d) be the second derivative of -1/3*d**3 + 0*d**2 - 4*d + 0. Determine p(s(b)).\n | 2*b\n | ibivibiv/math_instruct | |
Let f(l) = 2*l + 6. Let g be f(0). Let v(k) = -23*k + 46*k + 18 - 13 - 25*k. Determine v(g).\n | -7\n | ibivibiv/math_instruct | |
What is 3013 (base 7) in base 6?\n | 4451\n | ibivibiv/math_instruct | |
Suppose -n = -p - 6, 5*n + 24 = -2*p + 26. Solve -a - 12 = -4*z, -10 = -4*z - 4*a + n for z.\n | 3\n | ibivibiv/math_instruct | |
Let j = 9396 + -4340. What is the hundreds digit of j?\n | 0\n | ibivibiv/math_instruct | |
Sort 6, -13, 156 in increasing order.\n | -13, 6, 156\n | ibivibiv/math_instruct | |
Simplify (x*x**2*x/((x/(x**0*x))/x))**(1/16)*((x*x/(x/((x/x**1)/x)))/x)**(-7/5)/(x/(x/(x/x**(1/4)*x*x)))**40 assuming x is positive.\n | x**(-8663/80)\n | ibivibiv/math_instruct | |
Work out -23596 * 8.\n | -188768\n | ibivibiv/math_instruct | |
Let k(c) = c**2 - 15*c - 15. Let d be k(-4). Suppose 75*m - 2716 = d*m. List the prime factors of m.\n | 2, 97\n | ibivibiv/math_instruct | |
Let a(v) = -v**3 - 19*v**2 + 20*v + 5. Calculate a(-20).\n | 5\n | ibivibiv/math_instruct | |
Suppose -45 = -4*m + 35. Let v be (-2)/5 + (-92)/m. Let c be (6 + -8)*(v - -1). Solve -c = 3*o - 20 for o.\n | 4\n | ibivibiv/math_instruct | |
Suppose 99 = 3*t + 6*t. Calculate the least common multiple of 9 and t.\n | 99\n | ibivibiv/math_instruct | |
What is the second biggest value in -5/36, 24, -0.01792?\n | -0.01792\n | ibivibiv/math_instruct | |
Which is greater: 521 or 522?\n | 522\n | ibivibiv/math_instruct | |
Calculate prob of picking 1 v and 1 s when two letters picked without replacement from avnsaabmvaavsbs.\n | 3/35\n | ibivibiv/math_instruct | |
Solve 18*k - 62*k - 778 - 574 = 232 for k.\n | -36\n | ibivibiv/math_instruct | |
Does 61 divide 1417091?\n | True\n | ibivibiv/math_instruct |
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