instruction_seed stringlengths 5 2.9k | response_seed stringlengths 3 9.55k | input stringclasses 1
value | _source stringclasses 1
value |
|---|---|---|---|
Four letters picked without replacement from nnnndnnd. Give prob of picking 2 n and 2 d.\n | 3/14\n | ibivibiv/math_instruct | |
Find w, given that 3*w**2 - 369*w - 1920 = 0.\n | -5, 128\n | ibivibiv/math_instruct | |
b"What is the gth term of 1300, 4972, 11020, 19444, 30244, 43420?\n" | 1188*g**2 + 108*g + 4\n | ibivibiv/math_instruct | |
Let i(t) = 3*t + t - t - 2*t. Let u(j) = -12*j. What is u(i(f))?\n | -12*f\n | ibivibiv/math_instruct | |
Let o(d) = 2*d**3 - 53*d**2 + 24*d + 55. Calculate o(26).\n | 3\n | ibivibiv/math_instruct | |
Find the common denominator of 113/7782 and 1/14.\n | 54474\n | ibivibiv/math_instruct | |
What is 1446.29 grams in micrograms?\n | 1446290000\n | ibivibiv/math_instruct | |
Simplify (p*p/p**0)**(-1/19)/(((p**(-8)/p)/p)/p**3) assuming p is positive.\n | p**(245/19)\n | ibivibiv/math_instruct | |
Write an educational piece suited for college students related to the following text snippet:
"# Expected value of random variable ($X$) that takes non-negative integer values.
We have to proof:
$$E[X] = \sum_{k=1}^{\infty} P(X \geq k).$$
We knew that: $$P(X \geq k)= \sum_{i=k}^{\infty} p_X(i)$$
$$\sum_{k=1}^{\infty}... | The equation you are trying to prove is a fundamental property of the expected value of a random variable that takes non-negative integer values. Let's break down the steps and clarify the rationale behind them.
First, recall that the probability mass function (pmf) of a discrete random variable $X$ is defined as:
$... | ibivibiv/math_instruct | |
(131 - -1) + (-9109 - -8867)\n | -110\n | ibivibiv/math_instruct | |
Let j = -28 - -80. Suppose -74*c - 27060 = -133*c - 73*c. What is the remainder when c is divided by j?\n | 49\n | ibivibiv/math_instruct | |
Calculate -1 - 216/(-63) - (-1)/((-7)/(-4)).\n | 3\n | ibivibiv/math_instruct | |
What is 576 minutes after 8:25 AM?\n | 6:01 PM\n | ibivibiv/math_instruct | |
Two letters picked without replacement from {d: 1, i: 6, x: 7}. Give prob of picking 2 x.\n | 3/13\n | ibivibiv/math_instruct | |
Suppose m - 4*o - 104 - 2772 = 0, 11444 = 4*m - 4*o. Does 28 divide m?\n | True\n | ibivibiv/math_instruct | |
Solve 3*r + 2*q = -26, 11 = -4*r - 2*q - 21 for r.\n | -6\n | ibivibiv/math_instruct | |
Let y(x) be the second derivative of -2*x**3/3 - 17*x**2/2 - 1931*x. Let t(o) = 11*o. Calculate y(t(l)).\n | -44*l - 17\n | ibivibiv/math_instruct | |
Let g(v) be the third derivative of 8*v**7/35 - 13*v**5/60 + v**3/6 + 59*v**2 - 2. What is the third derivative of g(r) wrt r?\n | 1152*r\n | ibivibiv/math_instruct | |
Calculate 32 divided by 8.\n | 4\n | ibivibiv/math_instruct | |
Let s = -20 - -28. Let n be -5*-2*s/20. Sort -4, 3, n in decreasing order.\n | n, 3, -4\n | ibivibiv/math_instruct | |
Let l(n) = -n**2 - 8*n - 5. Calculate the remainder when 38/(-2 - 0 - -3) is divided by l(-5).\n | 8\n | ibivibiv/math_instruct | |
Let y be ((-626)/10 - -6) + (21/35 - 1). Which is smaller: 19 or y?\n | y\n | ibivibiv/math_instruct | |
What is nine tenths of a millennium in years?\n | 900\n | ibivibiv/math_instruct | |
Calculate prob of sequence inni when four letters picked without replacement from {i: 5, n: 4, q: 7}.\n | 1/182\n | ibivibiv/math_instruct | |
Let v(n) = 8*n - 104. Give v(-18).\n | -248\n | ibivibiv/math_instruct | |
Suppose 2*q - 71 = -r + 3, -r - 43 = -q. Is q composite?\n | True\n | ibivibiv/math_instruct | |
Round 0.00005438 to five dps.\n | 0.00005\n | ibivibiv/math_instruct | |
What are the prime factors of 104495954?\n | 2, 71, 761, 967\n | ibivibiv/math_instruct | |
Calculate the greatest common divisor of 1777136 and 88072.\n | 872\n | ibivibiv/math_instruct | |
Let g(d) = d + 10. Let s be g(0). Let c = s + -8. Solve 0 = c*p + p - 6 for p.\n | 2\n | ibivibiv/math_instruct | |
Simplify ((a*a**(-5))/a**(1/7))**10*(a**(-1/7)/a**(-3))/(a/(a*a**6)*a**(-2/9)) assuming a is positive.\n | a**(-2038/63)\n | ibivibiv/math_instruct | |
Let l(g) = g**2 - 10*g - 20. Give l(12).\n | 4\n | ibivibiv/math_instruct | |
Let v = 14 + 4. Let a = 10 - v. Let f = -7.99925 - a. What is f rounded to 4 dps?\n | 0.0008\n | ibivibiv/math_instruct | |
Amber is trying to decide if she wants to spend her $7 on candy or chips. She decides to buy the thing that she can get the most of. The bags of candy cost $1 and contain 12 ounces each. The bags of chips are $1.40 and contain 17 ounces each. How many ounces does she get if she buys the item that gives her the most? | If Amber buys candy, she can get 7/$1 = 7 bags of candy.
Each bag of candy contains 12 ounces, so she would get 7 x 12 = 84 ounces of candy.
If Amber buys chips, she can get 7/$1.40 = 5 bags of chips.
Each bag of chips contains 17 ounces, so she would get 5 x 17 = 85 ounces of chips.
Therefore, if Amber buys the item t... | ibivibiv/math_instruct | |
Evaluate -2 - (-480)/255 - (-1 - (-497)/544).\n | -1/32\n | ibivibiv/math_instruct | |
Expand 175827*t**3 + 5*t - 175697*t**3 + 5*t**2 - 4*t**2 + (0 + t + 0)*(3*t**2 - t**2 - 3*t**2) - 5*t**3 - 4*t**2 + 4*t**2.\n | 124*t**3 + t**2 + 5*t\n | ibivibiv/math_instruct | |
Let k be (-10)/(-25) + (-52)/5. Let n(m) = -m**3 - 9*m**2 + 9*m - 7. Let y be n(k). Find the first derivative of 315 - 6*j**y - 15*j**3 - 276 wrt j.\n | -63*j**2\n | ibivibiv/math_instruct | |
Which is the nearest to -3? (a) -2/3 (b) -0.2 (c) 4 (d) 72/5 (e) 2/7\n | a\n | ibivibiv/math_instruct | |
Suppose 4*f - 2*z - 24 = 0, -5*z + 36 = -0*f + 2*f. What is the units digit of f?\n | 8\n | ibivibiv/math_instruct | |
Suppose -23*o = -57*o + 170. Let f(p) = p**3 - 4*p**2 - 7*p + 4. What is f(o)?\n | -6\n | ibivibiv/math_instruct | |
Let u(m) = m**2 - 3*m + 7. What is u(3)?\n | 7\n | ibivibiv/math_instruct | |
Divide 42275 by -2225.\n | -19\n | ibivibiv/math_instruct | |
Let w = -137 + 135.13. Let k = -3448 - -3446. Do k and w have the same value?\n | False\n | ibivibiv/math_instruct | |
Suppose 0 = -5*j + 2*f + 5472, 4*j - 376 - 3999 = -f. What are the prime factors of j?\n | 2, 547\n | ibivibiv/math_instruct | |
What is the tens digit of 22406?\n | 0\n | ibivibiv/math_instruct | |
Let g(k) = -2*k**2 - 2*k + 1. Let y be g(1). Let s be 24 - y*(-1)/3. Suppose 5*l + s - 68 = 0. Calculate the remainder when 26 is divided by l.\n | 8\n | ibivibiv/math_instruct | |
Let i = -818 + 823. Solve -i*j + 5*j = 6*j for j.\n | 0\n | ibivibiv/math_instruct | |
What is the square root of 174318451 to the nearest integer?\n | 13203\n | ibivibiv/math_instruct | |
72309823 divided by 250207\n | 289\n | ibivibiv/math_instruct | |
Let t be 4/3*(186/12 - 8). Suppose t*p + 450 = 4000. What is the units digit of p?\n | 5\n | ibivibiv/math_instruct | |
List the prime factors of 286.\n | 2, 11, 13\n | ibivibiv/math_instruct | |
Let q(t) = t**3 - 6*t**2 + 7*t + 1. Let o be q(4). Let d(m) = -m**3 - 3*m**2 - 2*m. Let b be d(o). Solve -2*s = s - b for s.\n | 2\n | ibivibiv/math_instruct | |
What is the seventh smallest value in -0.25, 5, 3, 0.1, -6/11, -0.3, -9/5?\n | 5\n | ibivibiv/math_instruct | |
Solve 2*y + 4*z = 8 - 40, 73*z = 3*y - 268 for y.\n | -8\n | ibivibiv/math_instruct | |
What is the product of -2 and -756?\n | 1512\n | ibivibiv/math_instruct | |
What is 1b4a (base 13) in base 9?\n | 5575\n | ibivibiv/math_instruct | |
Let u = -599 + 600. What is the closest to u in -3/2, 0, 1?\n | 1\n | ibivibiv/math_instruct | |
Let s(b) be the first derivative of 14*b**5/5 - 2*b**3/3 - 172*b - 7. Find the first derivative of s(d) wrt d.\n | 56*d**3 - 4*d\n | ibivibiv/math_instruct | |
Does 7 divide 350719?\n | False\n | ibivibiv/math_instruct | |
What is prob of sequence azaz when four letters picked without replacement from zzaakzzazzkz?\n | 7/330\n | ibivibiv/math_instruct | |
b"What is the vth term of 5, -100, -405, -1018, -2047, -3600, -5785, -8710?\n" | -18*v**3 + 8*v**2 - 3*v + 18\n | ibivibiv/math_instruct | |
Let s(l) = 9*l - 3. Let r be s(3). Let q = -22 - -49. Suppose 17 = -2*i + q. Solve 2*n + 2*j = -0*j, 0 = i*n - j - r for n.\n | 4\n | ibivibiv/math_instruct | |
Four letters picked without replacement from {r: 1, n: 1, i: 7, d: 6}. Give prob of picking 2 i, 1 d, and 1 r.\n | 6/65\n | ibivibiv/math_instruct | |
Let r = -655 - -459. Let s be (108/(-162))/(r/(-6)). Suppose 0 = 5*t + 3*o + 14 - 0, -3 = o. Which is bigger: t or s?\n | s\n | ibivibiv/math_instruct | |
Calculate ((-108)/60)/((-3)/5).\n | 3\n | ibivibiv/math_instruct | |
Let q = -0.202 + -0.09. Let d = -0.008 + q. What is the fourth biggest value in 2, 1/4, 0.4, d?\n | d\n | ibivibiv/math_instruct | |
Express (5 - 7 + 1)*(-101 - 7 - 76)*(2*j - 2*j - 3*j) in the form f*j + d and give f.\n | -552\n | ibivibiv/math_instruct | |
Let l = 122 + -49. What is the units digit of l?\n | 3\n | ibivibiv/math_instruct | |
Let z(w) = 5*w**2 - 5. Let k(o) = -35*o + 44*o + 5049 - 5048. Calculate z(k(r)).\n | 405*r**2 + 90*r\n | ibivibiv/math_instruct | |
Let g(p) = -87*p**3 - 5*p**2 + 8*p + 44. Is 146 a factor of g(-4)?\n | False\n | ibivibiv/math_instruct | |
Expand ((-4 - 2*w**3 + 4)*(0 - 3 + 2) - w**3 - 2208456*w**2 + 0*w**3 + 2209440*w**2)*(0*w - w + 0*w).\n | -w**4 - 984*w**3\n | ibivibiv/math_instruct | |
Which is the third smallest value? (a) -1/5 (b) 17.7 (c) -4 (d) 10/7 (e) 1\n | e\n | ibivibiv/math_instruct | |
Let y(s) = -s**3 + 25*s**2 + 156*s - 180. Let m be y(30). Is -18/403 greater than or equal to m?\n | False\n | ibivibiv/math_instruct | |
Which is greater: -1 or -1/568?\n | -1/568\n | ibivibiv/math_instruct | |
Let y = -326 - -6196/19. Put 2, y, 5 in ascending order.\n | y, 2, 5\n | ibivibiv/math_instruct | |
What is 10362078 divided by -34?\n | -304767\n | ibivibiv/math_instruct | |
Four letters picked without replacement from wfff. Give prob of sequence ffwf.\n | 1/4\n | ibivibiv/math_instruct | |
Let i = 6 + -6. Let n(t) = -4 + 0*t - 4*t + i. What is the units digit of n(-3)?\n | 8\n | ibivibiv/math_instruct | |
Put 2/7, 0.06, -31/26 in decreasing order.\n | 2/7, 0.06, -31/26\n | ibivibiv/math_instruct | |
Calculate the smallest common multiple of 4488 and 5202.\n | 228888\n | ibivibiv/math_instruct | |
Express -18*w**4 - 22*w**4 - w - w**2 + 19*w**3 - 23*w**4 + 62*w**4 as q*w**4 + p*w**2 + r*w + l + z*w**3 and give p.\n | -1\n | ibivibiv/math_instruct | |
What is the value of ((-1)/25)/(((-20)/1050)/(4/28))?\n | 3/10\n | ibivibiv/math_instruct | |
What is the derivative of -2620*w**3*z + 6*w**3 + w**2 + 2*w*z - z + 2341 wrt z?\n | -2620*w**3 + 2*w - 1\n | ibivibiv/math_instruct | |
Let y = 1438 - 1368. What is the remainder when y is divided by 6?\n | 4\n | ibivibiv/math_instruct | |
Does 29 divide 29?\n | True\n | ibivibiv/math_instruct | |
Simplify (6*(-2 + sqrt(1008) + 0 + sqrt(1008)))**2 + sqrt(49)/((sqrt(112)/sqrt(2))/sqrt(8)) + -4.\n | -3455*sqrt(7) + 145292\n | ibivibiv/math_instruct | |
Solve -j + 53*j + 104*j = 15*j + 14382 for j.\n | 102\n | ibivibiv/math_instruct | |
Divide -6 by 280.\n | -3/140\n | ibivibiv/math_instruct | |
Let j(d) be the first derivative of d**5 + 5*d**4/4 - 20*d**3/3 - 10*d**2 + 186. Factor j(v).\n | 5*v*(v - 2)*(v + 1)*(v + 2)\n | ibivibiv/math_instruct | |
Suppose 11*b = 9*b + 4570. Suppose -2*a = -3*f - 1522, a - b = -2*a + 4*f. Is a composite?\n | True\n | ibivibiv/math_instruct | |
Let i(m) be the first derivative of -m**2/2 + 10. Let x(z) = 36*z. Calculate x(i(n)).\n | -36*n\n | ibivibiv/math_instruct | |
What is the value of 10 - (19 + -38 - -25)?\n | 4\n | ibivibiv/math_instruct | |
Suppose -16 = 2*p - 6*p. Suppose t = w, p - 24 = -5*w. List the prime factors of t.\n | 2\n | ibivibiv/math_instruct | |
Let q(o) = -11339818*o**2 + o. Let t be q(-1). Let h = -1247390513/110 - t. Let i = h - -903/10. Calculate the common denominator of i and -25/3.\n | 33\n | ibivibiv/math_instruct | |
Let s(b) = -b**3 - 20*b**2 - 41. Suppose 0 = -11*g + 6*g - 105. Is s(g) a multiple of 32?\n | False\n | ibivibiv/math_instruct | |
Let g(f) = -2*f**2 + 114*f - 3011. Calculate g(46).\n | -1999\n | ibivibiv/math_instruct | |
Does 177 divide 2105370?\n | False\n | ibivibiv/math_instruct | |
What is -3 take away -5388475795.12?\n | 5388475792.12\n | ibivibiv/math_instruct | |
Let f(z) = 1408*z - 43633. Give f(31).\n | 15\n | ibivibiv/math_instruct | |
Let q = -134 + 138. Let k(g) = 2*g - 3*g + 0*g. Let w be k(-2). Solve -6*x = -q*x - w for x.\n | 1\n | ibivibiv/math_instruct |
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