instruction_seed stringlengths 5 2.9k | response_seed stringlengths 3 9.55k | input stringclasses 1
value | _source stringclasses 1
value |
|---|---|---|---|
Divide -424 by 212.\n | -2\n | ibivibiv/math_instruct | |
Let o = 44 - 43.4. Let y = 759.1 - 711. Let c = -48 + y. What is the second smallest value in o, -1, c?\n | c\n | ibivibiv/math_instruct | |
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"# Why do books titled “Abstract Algebra” mostly deal with groups/rings/fields?
As a computer science graduate who had only a basic course in abstract algebra, I want to study some abstract algebra in my free time. I've been ... | Abstract algebra is a branch of mathematics that studies algebraic structures such as groups, rings, and fields. While it may seem that semigroups, which are a type of algebraic structure similar to groups, should also be covered in texts focused on abstract algebra, they often are not. This can lead to confusion amon... | ibivibiv/math_instruct | |
Calculate (0 - 0) + (-5)/((-220)/8).\n | 2/11\n | ibivibiv/math_instruct | |
Calculate the remainder when 2234 is divided by 187.\n | 177\n | ibivibiv/math_instruct | |
Let h = 4724 - 2878. What are the prime factors of h?\n | 2, 13, 71\n | ibivibiv/math_instruct | |
Let i = -11 + 14. What is the second derivative of -5*z - i*z**3 - 5*z + 14*z wrt z?\n | -18*z\n | ibivibiv/math_instruct | |
Let z = 465 - 464.688. Let g = 53.688 + z. Which is the closest to g? (a) 4 (b) 0.4 (c) -2\n | a\n | ibivibiv/math_instruct | |
What is the highest common divisor of 5 and 557?\n | 1\n | ibivibiv/math_instruct | |
Let n = -18 - -25. Suppose 12 = n*w - 4*w. What is the units digit of w?\n | 4\n | ibivibiv/math_instruct | |
Let t = 11 + 43. Suppose -88 = -3*o - o - z, -2*o + 2*z = -t. What is the tens digit of o?\n | 2\n | ibivibiv/math_instruct | |
Which is the smallest value? (a) 3 (b) 13 (c) 71 (d) 6\n | a\n | ibivibiv/math_instruct | |
Determine t, given that t**5/9 + 1916*t**4/9 - 370933*t**3/9 + 18045808*t**2/9 - 9021760*t = 0.\n | -2097, 0, 5, 88\n | ibivibiv/math_instruct | |
Let q(d) = -2*d**3 - 5*d**2 - 9*d + 4. Let a(y) = -y + 21. Let w be a(16). Let c(u) = 3*u**3 + 7*u**2 + 13*u - 6. What is w*c(r) + 7*q(r)?\n | r**3 + 2*r - 2\n | ibivibiv/math_instruct | |
Does 27 divide 13573197?\n | True\n | ibivibiv/math_instruct | |
Which is the nearest to 4/7? (a) -1.2 (b) 0.115 (c) 2/13\n | c\n | ibivibiv/math_instruct | |
What is the ten millions digit of 728747269?\n | 2\n | ibivibiv/math_instruct | |
What are the prime factors of 389298318?\n | 2, 3, 64883053\n | ibivibiv/math_instruct | |
Calculate (-80)/136*49/245.\n | -2/17\n | ibivibiv/math_instruct | |
Suppose -5*v + 23 = -27. Let u be (-2)/(-6) + v/6. Solve -2*f - 20 = u*f for f.\n | -5\n | ibivibiv/math_instruct | |
Calculate prob of picking 2 s and 1 x when three letters picked without replacement from {w: 5, x: 4, s: 2, g: 2}.\n | 2/143\n | ibivibiv/math_instruct | |
How many minutes are there between 7:39 PM and 3:02 AM?\n | 443\n | ibivibiv/math_instruct | |
Simplify (g**(-5/2)/g**10)/(g/(g/g**(3/2)*g))**(-9/11) assuming g is positive.\n | g**(-133/11)\n | ibivibiv/math_instruct | |
20% of the vets in a state recommend Puppy Kibble. 30% recommend Yummy Dog Kibble. If there are 1000 vets in the state, how many more recommend Yummy Dog Kibble than Puppy Kibble? | If 20% of the vets recommend Puppy Kibble, then 20% of 1000 vets = 0.20 * 1000 = 200 vets recommend Puppy Kibble.
If 30% of the vets recommend Yummy Dog Kibble, then 30% of 1000 vets = 0.30 * 1000 = 300 vets recommend Yummy Dog Kibble.
To find the difference, we subtract the number of vets who recommend Puppy Kibble fr... | ibivibiv/math_instruct | |
Let j(t) = -3*t**2 + 1. Let x(u) = -217*u**2 + 12. What is 22*j(s) - 2*x(s)?\n | 368*s**2 - 2\n | ibivibiv/math_instruct | |
Does 3 divide 1989?\n | True\n | ibivibiv/math_instruct | |
What comes next: -4452, -17812, -40082, -71262, -111352, -160352, -218262?\n | -285082\n | ibivibiv/math_instruct | |
Add 116 and -3.788.\n | 112.212\n | ibivibiv/math_instruct | |
Mary had 7 nickels in her bank. Her dad gave her 5 nickels and 3 dimes. The next day, Mary bought a toy with 2 dimes, and then her mom gave her twice as many nickels as she had remaining. How many nickels does Mary have now? | Mary originally had 7 nickels.
Her dad gave her 5 more nickels, so now she has:
7 nickels + 5 nickels = 12 nickels
Her dad also gave her 3 dimes, but we're focusing on the nickels for now.
Mary bought a toy with 2 dimes, which doesnt affect the number of nickels she has.
After buying the toy, her mom gave her twice... | ibivibiv/math_instruct | |
Let o(u) = -u**3 + 3*u**2 - 2*u - 2. Let a be o(2). Sort 0, a, 1, -1 in decreasing order.\n | 1, 0, -1, a\n | ibivibiv/math_instruct | |
In base 9, what is -4 - -48746?\n | 48742\n | ibivibiv/math_instruct | |
What comes next: 18459, 36914, 55369, 73824?\n | 92279\n | ibivibiv/math_instruct | |
Sort -0.1, 2, -0.11, 1 in increasing order.\n | -0.11, -0.1, 1, 2\n | ibivibiv/math_instruct | |
Evaluate (22 - 11 - 41) + 39 + -5.\n | 4\n | ibivibiv/math_instruct | |
Divide 2348 by 71.\n | 2348/71\n | ibivibiv/math_instruct | |
What is the closest to 11 in -0.72, 2/9, -2/31, -3?\n | 2/9\n | ibivibiv/math_instruct | |
In base 14, what is -22 + 818c9?\n | 818a7\n | ibivibiv/math_instruct | |
Solve -2*s**3/9 + 374602*s**2/9 + 41624*s - 249736 = 0 for s.\n | -3, 2, 187302\n | ibivibiv/math_instruct | |
Let c(t) = -13*t**2 + 17*t + 4. Let a be (3 - 2)*(-72)/8. Suppose -s - 3*s = -8. Let r(v) = -3*v**2 + 4*v + 1. Calculate a*r(b) + s*c(b).\n | b**2 - 2*b - 1\n | ibivibiv/math_instruct | |
Let m(t) be the third derivative of 7*t**5/120 - t**4/12 + 5*t**3/6 - t**2. Let u(i) be the first derivative of m(i). Determine u(-2).\n | -16\n | ibivibiv/math_instruct | |
What is 416643437 to the power of 1/7, to the nearest integer?\n | 17\n | ibivibiv/math_instruct | |
Convert -2002111220022 (base 3) to base 13.\n | -2cc41a\n | ibivibiv/math_instruct | |
Four letters picked without replacement from {s: 1, i: 1, a: 2, d: 1, n: 2, t: 1}. Give prob of sequence tddn.\n | 0\n | ibivibiv/math_instruct | |
Suppose 10 = 4*q + 5*l, 3*q + 4*l + 0*l - 7 = 0. Let k = -3.4 - -3. Sort k, 2/13, q.\n | k, 2/13, q\n | ibivibiv/math_instruct | |
Let x(y) = y**2. Let n(z) = -z**2 + z + 1. Let j(h) = 7*h**2 - 8*h - 8. Suppose -5*u = -10, 48 = -3*d - 3*u - 18. Let l(r) = d*n(r) - 3*j(r). What is x(l(c))?\n | 9*c**4\n | ibivibiv/math_instruct | |
Solve 45*z + 60 = 100*z - 45*z for z.\n | 6\n | ibivibiv/math_instruct | |
What is the third derivative of 3*x**6 + 4*x**5 - 2326*x**3 - 146*x**2 - 38655*x - 2 wrt x?\n | 360*x**3 + 240*x**2 - 13956\n | ibivibiv/math_instruct | |
Factor 45369*r**4 - 2664204*r**3 + 149988*r**2 - 2112*r.\n | 3*r*(3*r - 176)*(71*r - 2)**2\n | ibivibiv/math_instruct | |
Evaluate ((-2)/(2*(-21)/2))/(12/42).\n | 1/3\n | ibivibiv/math_instruct | |
Calculate (-54)/(-216) - ((-78)/8 - -1).\n | 9\n | ibivibiv/math_instruct | |
Round -2.186 to the nearest integer.\n | -2\n | ibivibiv/math_instruct | |
Suppose -55 = h - 6*h. Let v(s) = 5*s**2 - s - 2. Let i be v(2). Suppose g - i = -3*g. Calculate the remainder when h is divided by g.\n | 3\n | ibivibiv/math_instruct | |
Solve -66*t + 259 + 71 = 0 for t.\n | 5\n | ibivibiv/math_instruct | |
What is the result of the following expression?
-11.3697 / (-54.8079 + -97.274) | 0.0748 | ibivibiv/math_instruct | |
Let b(r) be the second derivative of -r**8/14 + r**5/5 - 7*r**4/6 + r**3/3 - 4*r + 3. Find the third derivative of b(v) wrt v.\n | -480*v**3 + 24\n | ibivibiv/math_instruct | |
Is 28329173 prime?\n | False\n | ibivibiv/math_instruct | |
Suppose 4*u = -3*d + 6*d - 497, 0 = -d + 2*u + 163. Let w be -5*3/(-45)*d. Suppose -132 = -7*l + w. Calculate the lowest common multiple of l and 6.\n | 54\n | ibivibiv/math_instruct | |
Is 98 a factor of 588?\n | True\n | ibivibiv/math_instruct | |
Calculate -19364 divided by 3831.\n | -19364/3831\n | ibivibiv/math_instruct | |
Which is the fourth biggest value? (a) -0.4 (b) 0.09 (c) -0.41 (d) 1/11 (e) 2/7\n | a\n | ibivibiv/math_instruct | |
What is 649 to the power of 1/2, to the nearest integer?\n | 25\n | ibivibiv/math_instruct | |
Do 46069 and 47503 have different values?\n | True\n | ibivibiv/math_instruct | |
In base 3, what is -100221200 - 21110?\n | -101020010\n | ibivibiv/math_instruct | |
Suppose 3*q = -q + 16. Let v(h) = 2*h**2 - 6*h. Let u be v(q). Solve 0 = 4*n + 5*r - u, 4*r - 2*r = -2*n + 2 for n.\n | -3\n | ibivibiv/math_instruct | |
Let z = 9.2 + -2.2. Let y = -7.29 + z. Let c = -2.71 + y. What is the nearest to -1 in c, 0.2, 1/4?\n | 0.2\n | ibivibiv/math_instruct | |
Let m(v) = v**3 + 94*v**2 - 334*v + 5937. Give m(-98).\n | 253\n | ibivibiv/math_instruct | |
Determine r, given that 3*r**3 - 21858*r**2 - 350451*r - 328590 = 0.\n | -15, -1, 7302\n | ibivibiv/math_instruct | |
What is the highest common divisor of 219050 and 39000?\n | 650\n | ibivibiv/math_instruct | |
A certain university will select 1 of 5 candidates eligible to fill a position in the mathematics department and 4 of 7 candidates eligible to fill 2 identical positions in the computer science department. If none of the candidates is eligible for a position in both departments, how many different sets of 3 candidates ... | math_candidates = 5
cs_candidates = 7
# calculate the number of ways to select 1 candidate for the mathematics department
math_selection = math_candidates
# calculate the number of ways to select 4 candidates for the computer science department
cs_selection = cs_candidates * (cs_candidates - 1) * (cs_candidates - 2) ... | ibivibiv/math_instruct | |
Suppose -4*n + 45 = 5. Let q(b) = -b + 3. Let h be q(-2). Let z be (h/2)/((-6)/(-192)). What is the highest common divisor of n and z?\n | 10\n | ibivibiv/math_instruct | |
Suppose -3*i + 61 = -2. Suppose -y + 4*g = -61, y - 3*g - 35 = i. Is y a multiple of 12?\n | False\n | ibivibiv/math_instruct | |
Is 2285849 a multiple of 55?\n | False\n | ibivibiv/math_instruct | |
Let q = 8.8 - 8. Let l = q + -0.8. Which is the third biggest value? (a) -0.1 (b) l (c) -5\n | c\n | ibivibiv/math_instruct | |
Calculate the remainder when 2397174 is divided by 158.\n | 156\n | ibivibiv/math_instruct | |
Three letters picked without replacement from {v: 1, h: 2, g: 1, z: 1, u: 1, o: 1}. What is prob of sequence guv?\n | 1/210\n | ibivibiv/math_instruct | |
Let d(v) = -10*v + 13. Let y(r) = -7*r + 9. Let k = 9 + -16. Let i(t) = k*y(t) + 5*d(t). Determine i(0).\n | 2\n | ibivibiv/math_instruct | |
What is the tens digit of 35102768?\n | 6\n | ibivibiv/math_instruct | |
Solve 78*f - 7*f - 1116 = -22*f for f.\n | 12\n | ibivibiv/math_instruct | |
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"# Diffeomorphic connected hypersurfaces
Given a four dimensional Lorentzian manifold $\mathcal{M}$ (a manifold with a metric $g_{\mu\nu}$ in the tangent bundle with signature (-1, 1, 1, 1)), we define a global spatial foliat... | We begin by defining several key terms and concepts necessary for understanding the statement in question. This will provide us with a solid foundation upon which to build our analysis.
**Manifold:** A topological space that locally resembles Euclidean space near each point. More precisely, each point has a neighborh... | ibivibiv/math_instruct | |
Which is smaller: 0.4 or -121?\n | -121\n | ibivibiv/math_instruct | |
7*(-30)/(-66150)*-21\n | -1/15\n | ibivibiv/math_instruct | |
Let 2*r**2/3 - 671904*r + 2015706 = 0. Calculate r.\n | 3, 1007853\n | ibivibiv/math_instruct | |
Let u = -56 - -56.4. Let z = 1 + -0.7. Put z, u, 5 in increasing order.\n | z, u, 5\n | ibivibiv/math_instruct | |
Simplify -5 + (-3*sqrt(44) + 2 + sqrt(11) + -1 - (4 + sqrt(176)*1))**2*-2.\n | -1805 - 108*sqrt(11)\n | ibivibiv/math_instruct | |
What is the area of the largest circular component of the Mandelbrot set with center at -0.75 + 0i and radius 1? | The largest circular component of the Mandelbrot set with center at -0.75 + 0i and radius 1 is known as the main cardioid. The equation for the main cardioid is given by:
r(θ) = 1/2 - 1/2 * cos(θ)
To find the area of the main cardioid, we can integrate the square of the radius function with respect to the angle θ fro... | ibivibiv/math_instruct | |
What is the hundred thousands digit of 6169007?\n | 1\n | ibivibiv/math_instruct | |
Calculate prob of picking 1 u and 1 n when two letters picked without replacement from {y: 1, q: 1, j: 4, n: 1, u: 1}.\n | 1/28\n | ibivibiv/math_instruct | |
Solve -4*l - 35 = 5*m, 134*l = 129*l + 3*m - 16 for l.\n | -5\n | ibivibiv/math_instruct | |
Let u = -20 - -22. Suppose 0 = -3*m + u*m. What is the second smallest value in 5, -0.5, m?\n | m\n | ibivibiv/math_instruct | |
Let n(m) = -m - 1. Suppose 4*l + 8 = 3*v, l + 4 = 4*v - 3*l. Let t be n(v). Solve 3*d = 9 - t for d.\n | 2\n | ibivibiv/math_instruct | |
Evaluate -9 - (-5 - 155/(-30))*-114.\n | 10\n | ibivibiv/math_instruct | |
Convert -1 (base 14) to base 16.\n | -1\n | ibivibiv/math_instruct | |
Let b(o) = 111*o. Let s(x) be the third derivative of -x**5/60 + 51*x**2 - 2*x. What is b(s(w))?\n | -111*w**2\n | ibivibiv/math_instruct | |
Solve 151*w - 835 = -1137 for w.\n | -2\n | ibivibiv/math_instruct | |
Calculate prob of sequence yycy when four letters picked without replacement from ycycyyycyc.\n | 2/21\n | ibivibiv/math_instruct | |
Simplify ((sqrt(627) + 2*sqrt(627)*-6 + sqrt(627))/(sqrt(11) + sqrt(198)/sqrt(2)))/(-4*(sqrt(147) - sqrt(147)*2*3)).\n | -sqrt(19)/56\n | ibivibiv/math_instruct | |
Let k(h) = -4*h + 3. Let d(c) = -c**3 + 7*c**2 - 6*c + 2. Let a be d(6). Let v(y) = 2 - 4 + a + y. Let l = -156 - -150. Calculate l*v(p) - k(p).\n | -2*p - 3\n | ibivibiv/math_instruct | |
Let u = -75 - -75. Let t be (u + -1 - 0)/(-4). Let v = -37 + 8. Which is the second smallest value? (a) -5 (b) t (c) v\n | a\n | ibivibiv/math_instruct | |
What is the third derivative of -240538739*s**5 - 703655166*s**2?\n | -14432324340*s**2\n | ibivibiv/math_instruct | |
Evaluate 105/5 + 26 + ((-60)/(-75))/(2/15).\n | 53\n | ibivibiv/math_instruct |
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