instruction_seed stringlengths 5 2.9k | response_seed stringlengths 3 9.55k | input stringclasses 1
value | _source stringclasses 1
value |
|---|---|---|---|
List the prime factors of 4294612.\n | 2, 7, 153379\n | ibivibiv/math_instruct | |
What is -13.79668 rounded to zero decimal places?\n | -14\n | ibivibiv/math_instruct | |
What is the common denominator of -11/30550 and 233/106882230?\n | 534411150\n | ibivibiv/math_instruct | |
Let c = 65 + -3. List the prime factors of c.\n | 2, 31\n | ibivibiv/math_instruct | |
Let o = 3 + 4. Suppose o*f - 2*f = -y + 15, 9 = y + 2*f. Solve 2*v = y + 3 for v.\n | 4\n | ibivibiv/math_instruct | |
-13 + (-7 - (-5 + -10))\n | -5\n | ibivibiv/math_instruct | |
What is the nearest to 0.15 in 3, -1, -2, 0.1?\n | 0.1\n | ibivibiv/math_instruct | |
What is the millions digit of 1755826?\n | 1\n | ibivibiv/math_instruct | |
Let k(s) = s**3 + 98*s**2 - 206*s - 560. Determine k(-100).\n | 40\n | ibivibiv/math_instruct | |
What is the nearest to 1/2 in -0.11, 3, -481?\n | -0.11\n | ibivibiv/math_instruct | |
Sort 3, 7, -20, -1 in increasing order.\n | -20, -1, 3, 7\n | ibivibiv/math_instruct | |
What is 23751 (base 8) in base 2?\n | 10011111101001\n | ibivibiv/math_instruct | |
Does 7 divide 1789?\n | False\n | ibivibiv/math_instruct | |
Simplify (y**1/((y**(-2/29)*y)/y)*y**(2/19)*y**14)**(-2/9) assuming y is positive.\n | y**(-1858/551)\n | ibivibiv/math_instruct | |
Let w(a) be the second derivative of -527*a**3/6 + 2*a - 630. Let b(t) = -t**2. Give w(b(l)).\n | 527*l**2\n | ibivibiv/math_instruct | |
How many minutes are there between 10:57 PM and 7:07 AM?\n | 490\n | ibivibiv/math_instruct | |
Is -270761 less than -270762?\n | False\n | ibivibiv/math_instruct | |
Which is the closest to -0.1? (a) -0.3 (b) -2 (c) 0.5 (d) 67\n | a\n | ibivibiv/math_instruct | |
Evaluate (55*(-21)/(-6930))/(2/(-12)).\n | -1\n | ibivibiv/math_instruct | |
Calculate prob of picking 1 f and 1 c when two letters picked without replacement from vvhvvcvvcvfvssvvvv.\n | 2/153\n | ibivibiv/math_instruct | |
Let t(w) = -17*w. Let r(m) be the second derivative of -m**3/3 + 6*m. Calculate r(t(u)).\n | 34*u\n | ibivibiv/math_instruct | |
Let s(f) = 4*f - 13. Let a(r) be the third derivative of -r**4/8 + 3*r**3/2 + 5358*r**2. Give 7*a(p) + 5*s(p).\n | -p - 2\n | ibivibiv/math_instruct | |
Let w = 14 + -14.3. Let n = 28.89 - -2.11. What is the third smallest value in n, w, -2/7?\n | n\n | ibivibiv/math_instruct | |
Calculate the smallest common multiple of 4105 and 456579.\n | 1874256795\n | ibivibiv/math_instruct | |
What is l in -27*l**3 - 372*l**2 - 1239*l + 294 = 0?\n | -7, 2/9\n | ibivibiv/math_instruct | |
What is (9*(-6)/(-567))/(1/(-7))?\n | -2/3\n | ibivibiv/math_instruct | |
Suppose -6*z + 40 = -5*z + 2*b, -4*z + 4*b = -196. Is 18 a factor of z?\n | False\n | ibivibiv/math_instruct | |
Divide -5 by -2805.\n | 1/561\n | ibivibiv/math_instruct | |
Solve -1724*n - 13*k + 56 = -1728*n - k, k - 2*k = -4 for n.\n | -2\n | ibivibiv/math_instruct | |
Simplify ((x*x*x*x**2*x*x*x*x)**3)**22/((x*(x/x**(-2/5))/x)**(-4/7)/((x/x**5)/(x**(-2/25)*x))) assuming x is positive.\n | x**(14747/25)\n | ibivibiv/math_instruct | |
Solve -5*y - t = 25, -t - 11 + 6 = 0 for y.\n | -4\n | ibivibiv/math_instruct | |
What is 469.3172 centuries in years?\n | 46931.72\n | ibivibiv/math_instruct | |
Suppose 4*h + 4*l = -4 - 0, -20 = 4*l. Let y(z) be the first derivative of -1/6*z**3 + h + 3/4*z**2 - z. Factor y(x).\n | -(x - 2)*(x - 1)/2\n | ibivibiv/math_instruct | |
Suppose -4*j - 44 = -2*d, -2*d + 5*j = -5*d + 121. What is the greatest common factor of d and 48?\n | 16\n | ibivibiv/math_instruct | |
Express -1245*r**2 + 626*r**2 + 2*r + 105*r**4 - 646*r**4 - 2*r**3 + 1 + 621*r**2 in the form o*r**4 + t*r**2 + m*r + v + y*r**3 and give m.\n | 2\n | ibivibiv/math_instruct | |
Solve 332*r + 10410 - 2442 = -3320 for r.\n | -34\n | ibivibiv/math_instruct | |
Simplify sqrt(77)/(1*sqrt(176)).\n | sqrt(7)/4\n | ibivibiv/math_instruct | |
Let c be 4/16 + (10/(-8) - 2). Let t be (-22)/12 - -2 - 0/c. What is the closest to t in -5/3, -1, -1/5?\n | -1/5\n | ibivibiv/math_instruct | |
What is the third derivative of 85191201*l**3 - 31473849*l**2 wrt l?\n | 511147206\n | ibivibiv/math_instruct | |
Which is the nearest to -1? (a) -5 (b) 0.027 (c) 0.5 (d) 1/75 (e) 0\n | e\n | ibivibiv/math_instruct | |
Convert 0.8132457 grams to micrograms.\n | 813245.7\n | ibivibiv/math_instruct | |
Let s be (5 - 5)/(1 + 1). Suppose 5*l = -s*l + 10. Solve b + 12 = -l*b for b.\n | -4\n | ibivibiv/math_instruct | |
Calculate 1084616759586 + 23.\n | 1084616759609\n | ibivibiv/math_instruct | |
What is the square root of 1181 to the nearest integer?\n | 34\n | ibivibiv/math_instruct | |
What is next in 6, 31, 90, 201, 382, 651, 1026, 1525?\n | 2166\n | ibivibiv/math_instruct | |
Simplify h**(-1/2)*h**17*h**(5/3)/h**(-26/5) assuming h is positive.\n | h**(701/30)\n | ibivibiv/math_instruct | |
What is the closest to -4 in 5, 3, -79.8?\n | 3\n | ibivibiv/math_instruct | |
Suppose 11*m - 116 = -1073. Let h be 7*-37*(-3)/(-9). Let n = h - m. Which is the fourth smallest value? (a) -1/4 (b) n (c) -2/11 (d) -0.5\n | b\n | ibivibiv/math_instruct | |
Let w = 8/7 + -1. Let b be (-16)/(-42) + ((-187)/51 - -3). Sort 1, -3, w, b in decreasing order.\n | 1, w, b, -3\n | ibivibiv/math_instruct | |
Solve 0 = 849*c - 1820*c + 10681 for c.\n | 11\n | ibivibiv/math_instruct | |
Simplify (z**(3/19)*z*z**9)/(z*z/z**(1/7))**(10/9) assuming z is positive.\n | z**(9689/1197)\n | ibivibiv/math_instruct | |
Let c(i) = 4*i - 11. Let z(m) = m - 3. Let v(h) = 6*c(h) - 22*z(h). Let j(q) = -91*q**2. Give j(v(p)).\n | -364*p**2\n | ibivibiv/math_instruct | |
Differentiate -80*x**2 + 7*x + 127173 with respect to x.\n | -160*x + 7\n | ibivibiv/math_instruct | |
In base 8, what is -22021 - 0?\n | -22021\n | ibivibiv/math_instruct | |
Let z = 11 - 8. Suppose -3*s + s = -i, 5*s = z*i. Let l be (i*1/3)/(-2). Sort 2, -1, l.\n | -1, l, 2\n | ibivibiv/math_instruct | |
What is the thousands digit of 167533?\n | 7\n | ibivibiv/math_instruct | |
Suppose 29*i + 84 = 41*i. Let p be (-2)/3*9/12. Which is the third biggest value? (a) p (b) i (c) 0.5\n | a\n | ibivibiv/math_instruct | |
What is the smallest common multiple of 2198 and 7528150?\n | 7528150\n | ibivibiv/math_instruct | |
Find the second derivative of -11126*f**4 + 4*f**3 + 15672*f wrt f.\n | -133512*f**2 + 24*f\n | ibivibiv/math_instruct | |
Simplify (0 + sqrt(117) + 3)**2 - ((-2*sqrt(325))**2 + 4).\n | -1178 + 18*sqrt(13)\n | ibivibiv/math_instruct | |
What is the least common multiple of 424 and 64?\n | 3392\n | ibivibiv/math_instruct | |
Solve -2*i - 59 + 46 = -n, -5 = 5*n + 4*i for n.\n | 3\n | ibivibiv/math_instruct | |
Let c = -3.5 - 1.5. What is the second biggest value in -1/9, c, 0?\n | -1/9\n | ibivibiv/math_instruct | |
What is 10/7*(-54)/1620*-2604*-1?\n | -124\n | ibivibiv/math_instruct | |
How many millimeters are there in seventy-three fifths of a centimeter?\n | 146\n | ibivibiv/math_instruct | |
Find the common denominator of 1/48*146*-4 and 14/(-1617)*501 - (-8)/(-14).\n | 66\n | ibivibiv/math_instruct | |
Let q be -2*(2 - 3)*-1. Let a(r) = 32876*r**3 + 3*r**2 + 4*r + 4. Let w be a(q). Round w to the nearest ten thousand.\n | -260000\n | ibivibiv/math_instruct | |
b"What is the hth term of 5781, 12865, 19949, 27033, 34117?\n" | 7084*h - 1303\n | ibivibiv/math_instruct | |
Simplify (m*m**(-35)*m**8*m**(9/5)*m/((m**(-14)*m)/m))**(-25) assuming m is positive.\n | m**230\n | ibivibiv/math_instruct | |
Suppose 0 = f - 4*a - 314, 3*f + f = a + 1271. Let r be 3/((-3)/f*-3). Let y = -47 + r. Is y composite?\n | False\n | ibivibiv/math_instruct | |
Let u(b) = -33. Let r(c) = -c - 31. Let k(p) = 7*r(p) - 6*u(p). Let n be k(-11). Suppose -4*d = 4*m - 100, -3*m = -3*d - 23 - n. Does 6 divide m?\n | False\n | ibivibiv/math_instruct | |
Let m = 16 - 22. Let h(n) = -2*n**3 - 2*n**2 + 7. Suppose 56*q = 541 - 597. Let g(f) = -11. Let l(k) = -5. Let t(a) = 6*g(a) - 13*l(a). Give m*t(v) + q*h(v).\n | 2*v**3 + 2*v**2 - 1\n | ibivibiv/math_instruct | |
Is 690 at most 693?\n | True\n | ibivibiv/math_instruct | |
Expand (-6*t**2 + 2*t**2 + 3*t**2 + (-3*t + 4*t + 0*t)*(t + 0*t - 2*t) - 6*t - t**2 + 6*t)*(0 + 2 - 3).\n | 3*t**2\n | ibivibiv/math_instruct | |
How many minutes are there between 12:34 PM and 8:59 PM?\n | 505\n | ibivibiv/math_instruct | |
Suppose 7*a = -4*a + 33. Solve n - 5*i = -5, -5*i - 1 + 26 = a*n for n.\n | 5\n | ibivibiv/math_instruct | |
Write an educational piece suited for college students related to the following text snippet:
"# How to calculate likelihood from Bayes' theorem without the normalisation?
I often see in the books that the Bayes theorem is used without the normalisation denominator as: $$P(A\mid B)\propto P(A)\cdot P(B\mid A)$$ While ... | Yes, your approach to computing the likelihood $P(B|A)$ from the given posterior probabilities using proportionality is correct. This method is commonly employed when dealing with problems where the computation of the normalization factor is difficult or time-consuming. By utilizing proportionalities, you focus only o... | ibivibiv/math_instruct | |
What is 11.04993 months in millennia?\n | 0.0009208275\n | ibivibiv/math_instruct | |
Is 75984401767 prime?\n | True\n | ibivibiv/math_instruct | |
Let n(d) be the third derivative of 3*d**5/20 - 43*d**4/24 - 13*d**3/6 + 13516*d**2. What is n(5)?\n | -3\n | ibivibiv/math_instruct | |
What is fifty-one quarters of a week in hours?\n | 2142\n | ibivibiv/math_instruct | |
Suppose -3*r + 9 = 0, -2 + 0 = -z + 3*r. Suppose 2*n = 2*j + 352, -z*n - j + 516 = -8*n. What is the units digit of n?\n | 3\n | ibivibiv/math_instruct | |
What is 31/2 of a litre in millilitres?\n | 15500\n | ibivibiv/math_instruct | |
What is 3791974 to the power of 1/4, to the nearest integer?\n | 44\n | ibivibiv/math_instruct | |
Let p be (-2)/56 + (-2)/(-7). Let r(f) = -f**2 + 15*f + 39. Let q be r(19). Let h = 34 + q. Put h, 1, p in descending order.\n | 1, p, h\n | ibivibiv/math_instruct | |
Calculate 661 divided by -2810.\n | -661/2810\n | ibivibiv/math_instruct | |
Let g(x) = -x. Let k(u) = -3*u + 2. Suppose -2*b = -q - 13, -31 - 1 = -3*b + 4*q. Suppose 1 = 2*p - s, 7*p + 19 = 3*p - 5*s. Give b*g(j) + p*k(j).\n | -j - 2\n | ibivibiv/math_instruct | |
Calculate the remainder when 1428 is divided by 245.\n | 203\n | ibivibiv/math_instruct | |
What is the third smallest value in -0.2, 3/8, -67?\n | 3/8\n | ibivibiv/math_instruct | |
Let u(w) = -w**3 + w**2 + w - 173. Let v be u(0). Let i = v - -264. Let q = i - 53. List the prime factors of q.\n | 2, 19\n | ibivibiv/math_instruct | |
Simplify sqrt(36)/(sqrt(72)/sqrt(6)*-3).\n | -sqrt(3)/3\n | ibivibiv/math_instruct | |
What is 1/64 of a gram in micrograms?\n | 15625\n | ibivibiv/math_instruct | |
Round 0.003067494 to 5 dps.\n | 0.00307\n | ibivibiv/math_instruct | |
What is the third biggest value in 0, -3/10, 1?\n | -3/10\n | ibivibiv/math_instruct | |
What is next in -2884793, -2884806, -2884819, -2884832?\n | -2884845\n | ibivibiv/math_instruct | |
What is the derivative of 776*c*f**2*v**2 - 853*c*f**2 - 4*f**2*v + 654350*f*v**2 wrt c?\n | 776*f**2*v**2 - 853*f**2\n | ibivibiv/math_instruct | |
Expand (-2*q**2 + 0 + 0)*(-6*q - 2*q + 2*q) + (-q**2 - 3*q + 3*q)*(q - 3*q + 4*q) + 0*q**3 + 6*q**3 - 3*q**3.\n | 13*q**3\n | ibivibiv/math_instruct | |
Calculate the lowest common multiple of 600 and 28500.\n | 57000\n | ibivibiv/math_instruct | |
What is the tens digit of 26190?\n | 9\n | ibivibiv/math_instruct | |
b"What is the dth term of 127, 232, 515, 1066, 1975, 3332, 5227?\n" | 15*d**3 - d**2 + 3*d + 110\n | ibivibiv/math_instruct |
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