instruction_seed stringlengths 5 2.9k | response_seed stringlengths 3 9.55k | input stringclasses 1
value | _source stringclasses 1
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|---|---|---|---|
Let l(a) = a + 18. Let k be l(-14). Let s = -64 - -29. Let v be 14/s + (-44)/(-10). Solve -v*r - q + k = 0, 0 = r + 3*r + 4*q - 16 for r.\n | 0\n | ibivibiv/math_instruct | |
What is next in 94, 87, 66, 25, -42, -141, -278, -459?\n | -690\n | ibivibiv/math_instruct | |
Let n(s) = -s + 4. Let x be n(2). Suppose -9 + 2 = -2*r - y, -2*r + 12 = x*y. Calculate the remainder when 23 is divided by 0/r + 24/2.\n | 11\n | ibivibiv/math_instruct | |
What is (-14*(-54)/(-24))/(-3)*42/(-392)*-96?\n | 108\n | ibivibiv/math_instruct | |
What is the nearest to 17812 in -8, 4, -214, -2?\n | 4\n | ibivibiv/math_instruct | |
Let h(f) = -f**2 + 3*f + 2. Let b be h(5). Let u = b + 14. Let r = u - 7. Sort r, 2, 3 in decreasing order.\n | 3, 2, r\n | ibivibiv/math_instruct | |
What is 1.59 times -199?\n | -316.41\n | ibivibiv/math_instruct | |
What is -1506288.29 rounded to the nearest ten thousand?\n | -1510000\n | ibivibiv/math_instruct | |
Calculate the lowest common multiple of 468303 and 38871.\n | 9834363\n | ibivibiv/math_instruct | |
What is the thousands digit of 1083?\n | 1\n | ibivibiv/math_instruct | |
Let n(b) = -10*b**3 - 3*b**2 - 2*b + b**2 - 1 + b**2. Let p be n(-1). Suppose 2*m + g = p + 3, 0 = -3*m - g + 18. Solve 0*q - m = q for q.\n | -5\n | ibivibiv/math_instruct | |
-1509 divided by -3\n | 503\n | ibivibiv/math_instruct | |
Is 1373305 composite?\n | True\n | ibivibiv/math_instruct | |
Let a(j) = j**3 - 8*j**2 - 8*j - 7. Let f be a(9). Let q be 32/20 + f/5. Let y(v) = 13*v - 8. Let h(o) = -7*o + 4. Let t(z) = 11*h(z) + 6*y(z). What is t(q)?\n | -2\n | ibivibiv/math_instruct | |
Which is the nearest to -0.1? (a) 3/5 (b) -3/4 (c) 1\n | b\n | ibivibiv/math_instruct | |
Is 147 a factor of 2125743039?\n | True\n | ibivibiv/math_instruct | |
Three letters picked without replacement from xxxxlxlyllxlyxyxxll. What is prob of sequence lyl?\n | 7/323\n | ibivibiv/math_instruct | |
Collect the terms in -96474963*j + 96474963*j + j**2.\n | j**2\n | ibivibiv/math_instruct | |
What is 1 divided by 60?\n | 1/60\n | ibivibiv/math_instruct | |
Let y = -6.46 - -6.56. What is the closest to 0 in y, -6/11, -4/15?\n | y\n | ibivibiv/math_instruct | |
In base 10, what is -3 - -422?\n | 419\n | ibivibiv/math_instruct | |
In base 7, what is -4 - 1134352451?\n | -1134352455\n | ibivibiv/math_instruct | |
Differentiate -2895*s + 6397 with respect to s.\n | -2895\n | ibivibiv/math_instruct | |
Let m = 37 - -20. Let z = m + -57. Solve z = -i - 1 - 4 for i.\n | -5\n | ibivibiv/math_instruct | |
Collect the terms in 401*j**2 + 393*j**2 - 1178*j**2 + 395*j**2 + 14*j.\n | 11*j**2 + 14*j\n | ibivibiv/math_instruct | |
Let m = -31 + 166. Calculate the greatest common divisor of m and 90.\n | 45\n | ibivibiv/math_instruct | |
Calculate 1523 + 0.\n | 1523\n | ibivibiv/math_instruct | |
What are the prime factors of 61667609?\n | 4651, 13259\n | ibivibiv/math_instruct | |
Let h = 11 - 10.957. Let i = 25.957 + h. Let q = i + -26.0000105. Round q to six dps.\n | -0.000011\n | ibivibiv/math_instruct | |
Simplify ((u**(-1/4))**12*(u**(-2/5))**(2/121))/(u**(-3/4)*u*(u/(u/u**(3/5)))/u)**41 assuming u is positive.\n | u**(7607/2420)\n | ibivibiv/math_instruct | |
Sort 0.4, 0.5, -1/25, 0.6 in descending order.\n | 0.6, 0.5, 0.4, -1/25\n | ibivibiv/math_instruct | |
Suppose -35*q + 44*q - 1944 = 0. Calculate the least common multiple of q and 32.\n | 864\n | ibivibiv/math_instruct | |
Suppose 5*k - 2*s - 844 = k, 3*s = k - 221. Calculate the highest common divisor of k and 19.\n | 19\n | ibivibiv/math_instruct | |
Convert 51286.74l to millilitres.\n | 51286740\n | ibivibiv/math_instruct | |
-43 (base 5) to base 11\n | -21\n | ibivibiv/math_instruct | |
What is -764616 divided by -3?\n | 254872\n | ibivibiv/math_instruct | |
Let y(p) = -265*p**2 + 45*p + 45. Let q(s) be the third derivative of -s**5/5 + s**4/12 + s**3/3 - 13*s**2 + 3*s. Determine 45*q(t) - 2*y(t).\n | -10*t**2\n | ibivibiv/math_instruct | |
Let f(a) = -a. Let v(w) = 14*w + 9. Let h be v(4). Let n(x) = -13*x**2 - 65*x. Let s(m) = h*f(m) - n(m). Let l(q) = -2*q**2. Calculate s(l(k)).\n | 52*k**4\n | ibivibiv/math_instruct | |
Simplify ((d**(7/2)*d*(d**(-4)/d)/d*d*d**4*d**(2/19))**(-11))**(3/20) assuming d is positive.\n | d**(-4521/760)\n | ibivibiv/math_instruct | |
Let s(j) be the third derivative of -j**6/120 + 7*j**5/30 - 29*j**4/24 - 5*j**3/3 - 3*j**2 - 2. What is the hundreds digit of s(9)?\n | 1\n | ibivibiv/math_instruct | |
Two letters picked without replacement from {x: 7, b: 1, r: 12}. What is prob of picking 1 r and 1 b?\n | 6/95\n | ibivibiv/math_instruct | |
What is the third derivative of -69530*l**2*v**4 + 25*l**2*v**3 + 10*l**2*v**2 + 269*l**2 - 35*v**2 wrt v?\n | -1668720*l**2*v + 150*l**2\n | ibivibiv/math_instruct | |
What is the product of -15 and 0.12?\n | -1.8\n | ibivibiv/math_instruct | |
Simplify (sqrt(22)/sqrt(2)*-6 - (3*sqrt(891))**2) + -2*(-1*sqrt(297) - sqrt(297))/sqrt(3) + -1.\n | -8020 + 6*sqrt(11)\n | ibivibiv/math_instruct | |
Simplify (o*o**(3/5))**21 assuming o is positive.\n | o**(168/5)\n | ibivibiv/math_instruct | |
What is the next term in -81149, -162112, -243085, -324074, -405085, -486124?\n | -567197\n | ibivibiv/math_instruct | |
Let y(q) = 2*q**2. Suppose 4*s = 7*s. Let m(g) be the second derivative of s + 0*g**2 + 1/2*g**3 - 3*g. What is y(m(k))?\n | 18*k**2\n | ibivibiv/math_instruct | |
Round -197650.7 to the nearest one thousand.\n | -198000\n | ibivibiv/math_instruct | |
Let g = 26303 - 26390.065. Let b = -7405 - -7318. Let l = g - b. What is l rounded to 2 dps?\n | -0.07\n | ibivibiv/math_instruct | |
Calculate (-72)/112*(-392)/14.\n | 18\n | ibivibiv/math_instruct | |
Is 6343163 a prime number?\n | True\n | ibivibiv/math_instruct | |
What is 185 minutes after 6:20 AM?\n | 9:25 AM\n | ibivibiv/math_instruct | |
Rearrange -12197*t**2 + 12209*t**2 - 5*t + 31*t to the form a*t**2 + l + p*t and give a.\n | 12\n | ibivibiv/math_instruct | |
What is 9 divided by -1486568?\n | -9/1486568\n | ibivibiv/math_instruct | |
Suppose -5*p - 6 - 9 = 0. Let c be (-11)/2 + p/6. List the prime factors of (-15)/c*8/5.\n | 2\n | ibivibiv/math_instruct | |
Let k be (-2 + 221)*24/9. Let l = k + 1352. What are the prime factors of l/32 + (-2)/4?\n | 2, 3, 5\n | ibivibiv/math_instruct | |
What is the tens digit of 443916?\n | 1\n | ibivibiv/math_instruct | |
Convert -314a2 (base 16) to base 12.\n | -98a02\n | ibivibiv/math_instruct | |
Let x = 63 + -64.98. Let d = -0.02 + x. Which is the closest to d? (a) -3 (b) 0.1 (c) -2\n | c\n | ibivibiv/math_instruct | |
Collect the terms in 4 + 2635*n - 4 + 0.\n | 2635*n\n | ibivibiv/math_instruct | |
Let z be (-126)/(-28) + 2/4. Suppose -z*w = -36 + 16. What is the first derivative of 3 + 3 + 1 + 6*g**w wrt g?\n | 24*g**3\n | ibivibiv/math_instruct | |
Is 545739 composite?\n | True\n | ibivibiv/math_instruct | |
Let q = -54.4 - -54.39558. What is q rounded to four dps?\n | -0.0044\n | ibivibiv/math_instruct | |
What is the units digit of 19718?\n | 8\n | ibivibiv/math_instruct | |
What is (27/22)/3*7128/(-16038)?\n | -2/11\n | ibivibiv/math_instruct | |
Evaluate -42 - -15 - (-105 - (49 + 18)).\n | 145\n | ibivibiv/math_instruct | |
Let j(i) = i**3 + 24*i**2 + 29*i - 11. Let v = 38 - 60. Let m be j(v). Suppose 4*l + 4*r - m = 209, -2*r - 653 = -5*l. What are the prime factors of l?\n | 131\n | ibivibiv/math_instruct | |
Simplify (h/(h**(-8)*h))**(-3)/((h/h**(1/4))/h*h/(h**0*h)) assuming h is positive.\n | h**(-95/4)\n | ibivibiv/math_instruct | |
What is the value of (5 - 10) + -3 + 15?\n | 7\n | ibivibiv/math_instruct | |
What is the value of (-15 - (30 + -60)) + -31?\n | -16\n | ibivibiv/math_instruct | |
0 * 6.1\n | 0\n | ibivibiv/math_instruct | |
Collect the terms in 7230*u**2 + 60*u**3 - 14423*u**2 + 7203*u**2.\n | 60*u**3 + 10*u**2\n | ibivibiv/math_instruct | |
List the prime factors of 1181259978.\n | 2, 3, 557, 353459\n | ibivibiv/math_instruct | |
What is the millions digit of 207847876?\n | 7\n | ibivibiv/math_instruct | |
What is the next term in 31, 94, 169, 262, 379, 526?\n | 709\n | ibivibiv/math_instruct | |
Simplify ((sqrt(63) + 0 + sqrt(7))**2 - -5*sqrt(42)/sqrt(6)) + (sqrt(28)/(sqrt(12)/sqrt(3)) + -1)*3.\n | 8*sqrt(7) + 109\n | ibivibiv/math_instruct | |
Let o(d) = -8*d**3 + 73*d**2 + 3*d - 103. Let v be o(9). Solve v*r + 20 = 0, -2*r - 16 = 5*c + 2*r for c.\n | 0\n | ibivibiv/math_instruct | |
Three letters picked without replacement from xafxa. Give prob of picking 2 a and 1 f.\n | 1/10\n | ibivibiv/math_instruct | |
Calculate 54 - ((18 - 25) + 43).\n | 18\n | ibivibiv/math_instruct | |
Which is the nearest to 2? (a) -0.4 (b) 2236 (c) 1\n | c\n | ibivibiv/math_instruct | |
Let x(w) = -w**2 - 6*w - 5. Let u be x(-5). Let b be (1 - 0 - 1) + 1. Differentiate -3 + 7 + u*m**2 - 2*m**2 - b wrt m.\n | -4*m\n | ibivibiv/math_instruct | |
Suppose 2*j - 2*o + 11 = 3*j, 4*o = 12. Let v = -8 - -12. Suppose 3*m + 0*m = 4*g + 83, -v*m - j*g + 90 = 0. Is 6 a factor of m?\n | False\n | ibivibiv/math_instruct | |
Multiply -0.3 and -7688.\n | 2306.4\n | ibivibiv/math_instruct | |
What is prob of picking 1 m and 3 o when four letters picked without replacement from {s: 2, m: 7, o: 3}?\n | 7/495\n | ibivibiv/math_instruct | |
What is prob of sequence ri when two letters picked without replacement from {r: 3, i: 1, p: 1, m: 2, f: 3}?\n | 1/30\n | ibivibiv/math_instruct | |
Suppose -f - 2*i + 67 = 0, 0 = -5*f - i + 39 + 287. What is the tens digit of f?\n | 6\n | ibivibiv/math_instruct | |
Factor 2*l**2/7 + 10366*l/7 - 31116/7.\n | 2*(l - 3)*(l + 5186)/7\n | ibivibiv/math_instruct | |
Suppose -5 = 5*b, -83*b = t - 84*b - 2. What is the greatest common divisor of 4823 and t?\n | 1\n | ibivibiv/math_instruct | |
Let o = 120 - 118. Suppose 0 = 3*c + 24 - 6. Let i = -1 - c. Sort o, -5, i in ascending order.\n | -5, o, i\n | ibivibiv/math_instruct | |
What is 0 + 6 + -34 + 23 - 4?\n | -9\n | ibivibiv/math_instruct | |
What is the second smallest value in 22, -3/5, 2225, 0.4, 1/126?\n | 1/126\n | ibivibiv/math_instruct | |
Let m(v) = -3*v - 2. Let d(c) = -1. Let h(a) = -a - 2. Let n(j) = -2*d(j) + 2*h(j). Give 3*m(f) - 4*n(f).\n | -f + 2\n | ibivibiv/math_instruct | |
What are the prime factors of 590669609?\n | 137, 1009, 4273\n | ibivibiv/math_instruct | |
Suppose -2261*s - 179630000 = -2250*s. Round s to the nearest one hundred thousand.\n | -16300000\n | ibivibiv/math_instruct | |
Expand (-4*n + 4*n + 2*n)*(-3 - 3 + 7) + 0 + n + 0 - 2*n + 56 - 56 + (2 - 5 + 2)*(-3*n + 2*n + 0*n).\n | 2*n\n | ibivibiv/math_instruct | |
Express 0*o**2 - 2*o**2 - o**2 + (4*o - 2*o + 0*o)*(2*o + 0*o - 4*o) + 344*o**2 + 1603 - 1603 as y*o + c + v*o**2 and give v.\n | 337\n | ibivibiv/math_instruct | |
Let p(t) = 5*t**2 + 7*t - 10*t - 3*t + t**3 + 3. Let w be p(-6). Solve -k = w*k for k.\n | 0\n | ibivibiv/math_instruct | |
In base 13, what is 4b + -5?\n | 46\n | ibivibiv/math_instruct | |
In base 6, what is 1403 + -3?\n | 1400\n | ibivibiv/math_instruct | |
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"Technical Article
# The Cumulative Distribution Function in Normally Distributed Data
August 19, 2020 by Robert Keim
## This article explains how we obtain the Gaussian cumulative distribution function and why it is useful... | In statistics, when dealing with normally distributed data, we often rely on two essential functions: the probability density function (PDF) and the cumulative distribution function (CDF). While the PDF allows us to determine the likelihood of a particular value occurring within our dataset, the CDF provides the overa... | ibivibiv/math_instruct |
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