instruction_seed stringlengths 5 2.9k | response_seed stringlengths 3 9.55k | input stringclasses 1
value | _source stringclasses 1
value |
|---|---|---|---|
Suppose 30 - 373 = -49*f. Let y = 6 - 0. Calculate the smallest common multiple of f and y.\n | 42\n | ibivibiv/math_instruct | |
List the prime factors of 1569919241.\n | 11, 61, 2339671\n | ibivibiv/math_instruct | |
Put -5, 2, 0, 563, 38 in ascending order.\n | -5, 0, 2, 38, 563\n | ibivibiv/math_instruct | |
Let w = 0.02 - -33.28. Let c = -6.3 + w. Let g = 26 - c. Which is smaller: g or -23/5?\n | -23/5\n | ibivibiv/math_instruct | |
Differentiate -h*t**3 - 24*h - 146*t**4 - 34 with respect to t.\n | -3*h*t**2 - 584*t**3\n | ibivibiv/math_instruct | |
Suppose -3*l + 12 = -0*l, -3*l = 5*b - 187. List the prime factors of b.\n | 5, 7\n | ibivibiv/math_instruct | |
Calculate -37 - -38 - (-2 + 4).\n | -1\n | ibivibiv/math_instruct | |
Simplify ((((t/(t**(1/3)*t))/t)**(-45)*(t**(-1/3)/t)**5)**(-3/44))**(-9) assuming t is positive.\n | t**(360/11)\n | ibivibiv/math_instruct | |
What is the square root of 1784880071 to the nearest integer?\n | 42248\n | ibivibiv/math_instruct | |
Let i = -17 + 11. Let k be ((-40)/i)/((-2)/(-6)). Solve -k = 5*f, 3*g - 3*f = g + 8 for g.\n | -2\n | ibivibiv/math_instruct | |
Let c = -18 + 20. Let m(z) = -c*z + 0 + 17 - 42 + 5*z + 10*z**2 - z**3. List the prime factors of m(7).\n | 11, 13\n | ibivibiv/math_instruct | |
What comes next: -4, -85, -302, -721, -1408, -2429, -3850, -5737?\n | -8156\n | ibivibiv/math_instruct | |
What is 6 + 7 + (5 - 19)?\n | -1\n | ibivibiv/math_instruct | |
What is the value of (7/(-35)*5)/(-5)?\n | 1/5\n | ibivibiv/math_instruct | |
Let y be ((-15)/12)/(2/8). Let t(s) be the third derivative of s**6/120 + s**5/12 - s**4/24 - s**3/6 - 5*s**2. Let i be t(y). Solve i*f + 3 = -5 for f.\n | -2\n | ibivibiv/math_instruct | |
Expand (14*k**2 - 14*k**2 + 60*k**4)*(-4 + 4*k + 2*k + 5).\n | 360*k**5 + 60*k**4\n | ibivibiv/math_instruct | |
Let i(j) = -2*j**2 - 16*j - 31. Let t be i(-5). Are 20/209 and t nonequal?\n | True\n | ibivibiv/math_instruct | |
Suppose -2*q - 5*d + 31258 = 0, 5*d + 15629 = q + 3*d. Is q composite?\n | False\n | ibivibiv/math_instruct | |
Round -0.00015315055457 to 7 decimal places.\n | -0.0001532\n | ibivibiv/math_instruct | |
What is the highest common factor of 315 and 8971650?\n | 45\n | ibivibiv/math_instruct | |
Is -1/3442 < -1?\n | False\n | ibivibiv/math_instruct | |
Let l = 171 - 168. Let r(f) = 27*f - 2. What is r(l)?\n | 79\n | ibivibiv/math_instruct | |
Let r be ((-1978)/(-69))/(2/(-3)). Let u(z) = -z**3 - 43*z**2 - 8*z - 15. Calculate the remainder when u(r) is divided by 55.\n | 54\n | ibivibiv/math_instruct | |
Is 25 a factor of 15*(-1)/(-2)*10?\n | True\n | ibivibiv/math_instruct | |
What is fifty-two fifths of a litre in millilitres?\n | 10400\n | ibivibiv/math_instruct | |
Expand 516*y**2 + 2*y**4 + 518*y**2 + 87*y**3 - 1032*y**2 + (0*y**4 + 3*y**4 - 2*y**4)*(-5 + 4 + 2).\n | 3*y**4 + 87*y**3 + 2*y**2\n | ibivibiv/math_instruct | |
Collect the terms in m**2 + 193 + 0*m**2 - m**2 + 2*m**2.\n | 2*m**2 + 193\n | ibivibiv/math_instruct | |
Let f be (-3)/(-180)*-10*(0 + -3). Let x(k) be the second derivative of 0 - f*k**3 + 12*k - k**2. What is x(4)?\n | -14\n | ibivibiv/math_instruct | |
Suppose 3*y - 150 = -5*m, 4*y - 15 = -4*m + 97. Calculate the remainder when 73 is divided by m.\n | 7\n | ibivibiv/math_instruct | |
Two letters picked without replacement from fvfffvvvfffyffffvfy. What is prob of picking 2 v?\n | 10/171\n | ibivibiv/math_instruct | |
Let f(l) = -2*l**2 + 5*l - 5. Let v be f(7). What is the units digit of (-2)/(-8) + (-1479)/v?\n | 2\n | ibivibiv/math_instruct | |
Subtract -9933129050 from -42.9.\n | 9933129007.1\n | ibivibiv/math_instruct | |
Find w such that -62*w**5/5 - 492*w**4/5 + 32*w**3/5 = 0.\n | -8, 0, 2/31\n | ibivibiv/math_instruct | |
What is the second derivative of -5*j*u**3 - j*u**2 - 6*j*u - 67*j - 100*u**3 - 12*u**2 - 48*u - 1 wrt u?\n | -30*j*u - 2*j - 600*u - 24\n | ibivibiv/math_instruct | |
Solve 0 = 9694*z - 9688*z - 4*p + 68, 4*z + z - 35 = -5*p for z.\n | -4\n | ibivibiv/math_instruct | |
Is 92753 a multiple of 40?\n | False\n | ibivibiv/math_instruct | |
Round 0.00012192 to five decimal places.\n | 0.00012\n | ibivibiv/math_instruct | |
Round 0.07993 to 1 decimal place.\n | 0.1\n | ibivibiv/math_instruct | |
Is 292307563 composite?\n | False\n | ibivibiv/math_instruct | |
Suppose -4*n + 8 = 0, -3*r - 5*n + 1910 = r. What are the prime factors of r?\n | 5, 19\n | ibivibiv/math_instruct | |
Let g = 0.9794 - -0.6306. What is g rounded to the nearest one hundred?\n | 0\n | ibivibiv/math_instruct | |
Simplify (-6*(1 + sqrt(12)/sqrt(6) + -4 - (0 + -6*sqrt(22)/sqrt(11)))*-3)**2.\n | -13608*sqrt(2) + 34668\n | ibivibiv/math_instruct | |
What is the smallest value in 11, -14, 0?\n | -14\n | ibivibiv/math_instruct | |
Let r = -63.907 - -64. Round r to two dps.\n | 0.09\n | ibivibiv/math_instruct | |
What is -7.47 take away 0.16?\n | -7.63\n | ibivibiv/math_instruct | |
Let i(k) = -7*k. Suppose 4*x - 1 = 7. Let c(h) = 46*h - 46*h + 3*h**x. Calculate i(c(o)).\n | -21*o**2\n | ibivibiv/math_instruct | |
Collect the terms in 95*r**2 - 381*r**2 - 304*r**2.\n | -590*r**2\n | ibivibiv/math_instruct | |
Calculate the remainder when 1859 is divided by 306.\n | 23\n | ibivibiv/math_instruct | |
Let i = -22 + 14. Let m be (2/i*2)/((-3)/30). Solve 4*t - 37 = m*f, f - 3*t + 11 = -3 for f.\n | -5\n | ibivibiv/math_instruct | |
Does 465 = 485?\n | False\n | ibivibiv/math_instruct | |
What is prob of sequence oe when two letters picked without replacement from ffiiiiiiiofiifeooii?\n | 1/114\n | ibivibiv/math_instruct | |
Is 163577 a composite number?\n | True\n | ibivibiv/math_instruct | |
How many minutes are there between 10:37 AM and 9:59 PM?\n | 682\n | ibivibiv/math_instruct | |
Suppose 3*c + 6 = -3*a - 0, -2*c + 21 = -3*a. Let l(w) = -8 + 8 + c*w - 6*w. Let u(s) = -5*s**2. What is u(l(p))?\n | -45*p**2\n | ibivibiv/math_instruct | |
What is 80 (base 10) in base 6?\n | 212\n | ibivibiv/math_instruct | |
Let q(c) = 20*c**2 - 17*c**2 - 3 - 2*c**2. Let l be q(2). Suppose -5*k + 35 = 4*g - 0*g, 0 = 5*k - 3*g. Which is bigger: k or l?\n | k\n | ibivibiv/math_instruct | |
How many minutes are there between 1:26 AM and 12:54 PM?\n | 688\n | ibivibiv/math_instruct | |
Collect the terms in -841 - 775 - 845 - 12*h - 841 + 3302.\n | -12*h\n | ibivibiv/math_instruct | |
Suppose -4*n + 6751 = -13*d + 8*d, 0 = -2*n + 4*d + 3380. Suppose 7*q - 598 = n. What is the hundreds digit of q?\n | 3\n | ibivibiv/math_instruct | |
What is the common denominator of -37/1737 and 3/4?\n | 6948\n | ibivibiv/math_instruct | |
Suppose -426*h + 453*h = 8154. Solve 0 = -v + h - 295 for v.\n | 7\n | ibivibiv/math_instruct | |
How many minutes are there between 2:46 PM and 10:56 PM?\n | 490\n | ibivibiv/math_instruct | |
Calculate 10/(-8)*-1*28/7.\n | 5\n | ibivibiv/math_instruct | |
Which is greater: 0 or 69/146?\n | 69/146\n | ibivibiv/math_instruct | |
Express (-3*i**3 - 3*i**3 + 7*i**3)*(-2 - 1 + 4 + 5*i) + 3*i**4 + 2 - 2 as t + b*i**3 + l*i + g*i**4 + x*i**2 and give b.\n | 1\n | ibivibiv/math_instruct | |
Is 7393411 a composite number?\n | False\n | ibivibiv/math_instruct | |
Collect the terms in 163629 - 163629 - 3811*j.\n | -3811*j\n | ibivibiv/math_instruct | |
What is next in 20887, 9715, -1457, -12629, -23801, -34973?\n | -46145\n | ibivibiv/math_instruct | |
What is the second derivative of -2237601*l**2*v**2 + 6*l**2*v - 25*l**2*w**2 + l*w**2 - 18*l - 2*v**2*w**2 - 3*v*w + 2*w**2 wrt v?\n | -4475202*l**2 - 4*w**2\n | ibivibiv/math_instruct | |
Two letters picked without replacement from gsggsssgin. Give prob of picking 2 g.\n | 2/15\n | ibivibiv/math_instruct | |
What is the thousands digit of 5254389?\n | 4\n | ibivibiv/math_instruct | |
Expand -4 + 1 - 2*w + 4 + 1 - 1 - 2*w + (w - 2*w - w)*(1 - 5 + 5) + 3*w - 2*w + 0*w.\n | -5*w + 1\n | ibivibiv/math_instruct | |
Solve -58 = 2*c + 33*c + 23*c for c.\n | -1\n | ibivibiv/math_instruct | |
Let i(d) = -53*d + 4304. What is i(82)?\n | -42\n | ibivibiv/math_instruct | |
What is next in -3118, -3402, -3686, -3970, -4254, -4538?\n | -4822\n | ibivibiv/math_instruct | |
Suppose -3*k + 182 = y, 3*k + 125 = 5*k - 3*y. Suppose 5*s - s + 228 = 0. Let v = k + s. Solve -v*q - 29 = 5*w, 3*w = 2*q - 7*q - 20 for q.\n | -1\n | ibivibiv/math_instruct | |
Calculate -47 + -8 + 1 + 0 + (-74 - -172) + -91.\n | -47\n | ibivibiv/math_instruct | |
Suppose 4*k = -4 - 12. Let u be 1266*k/(-28) - (-1)/7. Suppose 173 = 3*x - u. List the prime factors of x.\n | 2, 59\n | ibivibiv/math_instruct | |
What is the ninth root of 68062712 to the nearest integer?\n | 7\n | ibivibiv/math_instruct | |
What is the third derivative of 21408*i**5 + 1322*i**2 + 4*i?\n | 1284480*i**2\n | ibivibiv/math_instruct | |
Let h(a) = -9*a + 8*a + 74*a - 146 + 16*a. Is h(11) a multiple of 49?\n | True\n | ibivibiv/math_instruct | |
Simplify ((sqrt(78) - (sqrt(78) + (sqrt(78) - -1*sqrt(78)*-6)))/(sqrt(24)/(sqrt(12)/sqrt(3))))**2.\n | 325\n | ibivibiv/math_instruct | |
Calculate prob of picking 2 u when two letters picked without replacement from {u: 4, p: 15}.\n | 2/57\n | ibivibiv/math_instruct | |
b"What is the ith term of -39, 153, 679, 1707, 3405, 5941, 9483?\n" | 28*i**3 - i**2 - i - 65\n | ibivibiv/math_instruct | |
1423095234 divided by -6\n | -237182539\n | ibivibiv/math_instruct | |
What is -538693 times -1?\n | 538693\n | ibivibiv/math_instruct | |
Let q be (-110)/44*(-11)/((-275)/(-20)). Let x = -162 + 1780/11. Which is the closest to q? (a) x (b) 3 (c) 0.4\n | b\n | ibivibiv/math_instruct | |
Evaluate (-1350)/405 - (-16)/(-6).\n | -6\n | ibivibiv/math_instruct | |
Write an educational piece suited for college students related to the following text snippet:
"# Is a probability of 0 or 1 given information up to time t unchanged by information thereafter?
Given a filtered probability space $(\Omega, \mathscr{F}, \{\mathscr{F}_n\}_{n \in \mathbb{N}}, \mathbb{P})$, let $A \in \maths... | In the study of probability theory, particularly within the context of stochastic processes, filtrations are used to model the flow of information over time. A filtration is an increasing sequence of sigma-algebras, denoted by ${\mathcal{F}_t : t \in T}$, where $T$ is usually taken to be either ${\mathbb{N}}$ or ${[0,... | ibivibiv/math_instruct | |
Suppose r = -86*b + 91*b + 5, 3*r + 5*b = 15. Sort r, 7/4, 2/7, -0.4 in increasing order.\n | -0.4, 2/7, 7/4, r\n | ibivibiv/math_instruct | |
Let x = -308 - -305. Sort x, 13, -5 in decreasing order.\n | 13, x, -5\n | ibivibiv/math_instruct | |
What is (10 - -3) + 48 + -111 + 42?\n | -8\n | ibivibiv/math_instruct | |
Suppose -a + 13 = -21. What is the derivative of 12*l - 12*l - 5 - 26 - a*l**3 wrt l?\n | -102*l**2\n | ibivibiv/math_instruct | |
How many minutes are there between 2:22 PM and 2:01 AM?\n | 699\n | ibivibiv/math_instruct | |
What is the tenth root of 3835 to the nearest integer?\n | 2\n | ibivibiv/math_instruct | |
Simplify ((((b/(b/b**(-1)))**(5/8))**47)**48)**(-1/4) assuming b is positive.\n | b**(705/2)\n | ibivibiv/math_instruct | |
Find q, given that 7*q**5/5 - 852*q**4/5 + 4348*q**3/5 + 33792*q**2/5 + 1856*q = 0.\n | -4, -2/7, 0, 10, 116\n | ibivibiv/math_instruct | |
Simplify p/p**(4/9)*p*p**(-3)*(p**(-1/3)/p*p)**(-38) assuming p is positive.\n | p**(101/9)\n | ibivibiv/math_instruct | |
b"What is the ith term of -2121, -5266, -8747, -12732, -17389, -22886?\n" | -28*i**3 - 2949*i + 856\n | ibivibiv/math_instruct | |
Let l(a) = 2*a - a + 0 + 7 + 5. What is l(-6)?\n | 6\n | ibivibiv/math_instruct |
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