instruction_seed stringlengths 5 2.9k | response_seed stringlengths 3 9.55k | input stringclasses 1
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Suppose 0 = 2*t - 5*i - 5, 13 = 2*t - 0*t + 3*i. Let j(l) = l + t - l**2 + 16 + 7 - 40. Suppose 3*x + 3 = 2*b - 1, 0 = 4*x + 3*b - 6. Give j(x).\n | -12\n | ibivibiv/math_instruct | |
Round 4473070 to the nearest 1000000.\n | 4000000\n | ibivibiv/math_instruct | |
Suppose -2*g + 15341 = 4291. Calculate the highest common divisor of g and 884.\n | 221\n | ibivibiv/math_instruct | |
Solve 9*p + 28 = 2*p for p.\n | -4\n | ibivibiv/math_instruct | |
Is 16 a factor of 1225184730?\n | False\n | ibivibiv/math_instruct | |
Let w = 20 + -10. Let k be 8/(-2 - 1 - -4). Let z = k - w. Let d(u) = u**2 + 4*u + 3. What is d(z)?\n | -1\n | ibivibiv/math_instruct | |
Factor -36*o**4 - 46*o**3 + 22*o**3 + 16*o**3.\n | -4*o**3*(9*o + 2)\n | ibivibiv/math_instruct | |
Let s(j) = 3*j**3 + j**2 - 1. Suppose 78 = 63*w + 33 - 81. Let z(m) = m**2. Give w*z(x) + s(x).\n | 3*x**3 + 3*x**2 - 1\n | ibivibiv/math_instruct | |
Let s(f) = f**3 + 43*f**2 + 2*f + 91. Give s(-43).\n | 5\n | ibivibiv/math_instruct | |
Let p(m) = -224*m + 6. Let n be p(-3). Let a = n + -202. Let k = a + -293. List the prime factors of k.\n | 3, 61\n | ibivibiv/math_instruct | |
What is the hundreds digit of 12996?\n | 9\n | ibivibiv/math_instruct | |
Three letters picked without replacement from iliiilii. Give prob of picking 3 i.\n | 5/14\n | ibivibiv/math_instruct | |
What is the hundred thousands digit of 54945077?\n | 9\n | ibivibiv/math_instruct | |
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"# Lota Trigonometry Solving Equations Using Identities Example
## Trigonometric Identities and Equations
### Solving Trigonometric Equations with Identities – Precalculus
Solving equations using identities ExamSolutions.... | Trigonometry is a branch of mathematics that deals with the relationships between angles and the lengths of the corresponding sides of triangles. It has numerous applications in fields such as physics, engineering, computer science, and many others. One fundamental aspect of trigonometry involves solving equations and... | ibivibiv/math_instruct | |
Chip takes 2 pages of notes every day, x days a week, for each of his 5 classes. His notebook paper comes in packs of 100 sheets of paper per pack. After 6 weeks, how many packs of notebook paper will Chip use?
If we know the answer to the above question is 3, what is the value of unknown variable x? | Chip takes 2 pages of notes every day, x days a week, for each of his 5 classes. So he takes a total of 2 * x * 5 = 10x pages of notes per week.
After 6 weeks, he will take a total of 10x * 6 = 60x pages of notes.
If each pack of notebook paper has 100 sheets of paper, then Chip will need 60x / 100 = 0.6x packs of note... | ibivibiv/math_instruct | |
Round 575427.4 to the nearest 10000.\n | 580000\n | ibivibiv/math_instruct | |
Calculate the common denominator of -109/380 and -101/380.\n | 380\n | ibivibiv/math_instruct | |
What is 552989 to the power of 1/8, to the nearest integer?\n | 5\n | ibivibiv/math_instruct | |
What is -44780.4 rounded to the nearest one hundred thousand?\n | 0\n | ibivibiv/math_instruct | |
Expand (161*u**3 - 92*u**3 - 100*u**3)*(0 - 5 + 3 + (4 + 1 - 2)*(4 + 0 - 2)).\n | -124*u**3\n | ibivibiv/math_instruct | |
What is the result of the following expression?
-30.371 / -13.252 | 2.2918 | ibivibiv/math_instruct | |
Let j = 49 + -23. What are the prime factors of j?\n | 2, 13\n | ibivibiv/math_instruct | |
Let k(y) = y**2 + 60*y + 596. What is k(-10)?\n | 96\n | ibivibiv/math_instruct | |
Simplify ((-4*sqrt(396)*-3 - sqrt(396) - sqrt(396))*-5)**2.\n | 990000\n | ibivibiv/math_instruct | |
Three letters picked without replacement from {q: 6, b: 1, z: 2, y: 2}. Give prob of picking 2 q and 1 y.\n | 2/11\n | ibivibiv/math_instruct | |
Sort -3, 999, 1, 4, 8, 5, -1.\n | -3, -1, 1, 4, 5, 8, 999\n | ibivibiv/math_instruct | |
Simplify ((k*k**(5/3))/(k*k**(1/5)*k)*(k*(k*k/(k**(-1/4)/k))/k)**(-1/40))**(-6/5) assuming k is positive.\n | k**(-37/80)\n | ibivibiv/math_instruct | |
What is the common denominator of 123/392224 and 37/1030?\n | 1961120\n | ibivibiv/math_instruct | |
Three letters picked without replacement from pmppmphkaakapp. Give prob of sequence haa.\n | 1/364\n | ibivibiv/math_instruct | |
What is the millions digit of 5472363?\n | 5\n | ibivibiv/math_instruct | |
What is 319846 to the power of 1/3, to the nearest integer?\n | 68\n | ibivibiv/math_instruct | |
What is the hundred thousands digit of 13063104?\n | 0\n | ibivibiv/math_instruct | |
Let u = 15 - 8. Solve -3*j + 2 = -u for j.\n | 3\n | ibivibiv/math_instruct | |
b"What is the oth term of -21964, -43421, -64878, -86335, -107792, -129249?\n" | -21457*o - 507\n | ibivibiv/math_instruct | |
Let i(t) = 4*t**3 - 3*t**2 - 8*t - 8. Let k(n) = 3*n**3 - 3*n**2 - 7*n - 7. What is -5*i(v) + 6*k(v)?\n | -2*v**3 - 3*v**2 - 2*v - 2\n | ibivibiv/math_instruct | |
What is the value of -3480 + 3451 + 472/14 + -1?\n | 26/7\n | ibivibiv/math_instruct | |
Convert -2b (base 12) to base 6.\n | -55\n | ibivibiv/math_instruct | |
Solve -6*g + 9*x - 7*x = -4*x - 66, 2*x + 8 = 4*x + 2*x for g.\n | 13\n | ibivibiv/math_instruct | |
Let p(g) = 11*g**4 + 11*g**3 - 18*g**2 - 6. Let x(b) = -23*b**4 - 24*b**3 + 37*b**2 + 13. Let o(v) = 13*p(v) + 6*x(v). Find the third derivative of o(m) wrt m.\n | 120*m - 6\n | ibivibiv/math_instruct | |
What is the third biggest value in -1/14885, 24, -2/11?\n | -2/11\n | ibivibiv/math_instruct | |
Let k be 10/(-2) + (-9 - -10). Let g be 1/k - (-188)/(-16). Let c = 659 + -672. Which is greater: c or g?\n | g\n | ibivibiv/math_instruct | |
Solve 696846*q + 303 = 696904*q - 2056 - 135 for q.\n | 43\n | ibivibiv/math_instruct | |
Evaluate (-40)/2*(-9)/((-90)/(-4)).\n | 8\n | ibivibiv/math_instruct | |
Suppose -4*a + 438 = -5*h + 7*h, -4*a + 459 = -5*h. Let v = -105 + a. Solve 0*s - j = -s + v, -5*s = -3*j - 28 for s.\n | 5\n | ibivibiv/math_instruct | |
Let h(t) be the first derivative of t**6/14 + 3*t**5/35 - 15*t**4/28 - t**3/7 + 12*t**2/7 - 12*t/7 - 19. What is u in h(u) = 0?\n | -2, 1\n | ibivibiv/math_instruct | |
Solve 0 = -11*y + 21 - 10 for y.\n | 1\n | ibivibiv/math_instruct | |
Let a = 6 - -12. Calculate the remainder when 53 is divided by a.\n | 17\n | ibivibiv/math_instruct | |
Round 36.2158 to 0 dps.\n | 36\n | ibivibiv/math_instruct | |
Calculate the common denominator of 17/4205 and 20/261.\n | 37845\n | ibivibiv/math_instruct | |
In base 5, what is 342 + -11411110?\n | -11410213\n | ibivibiv/math_instruct | |
Let j(z) = -14*z**2 - 40*z + 1. Let r(c) = -5*c**2 - 14*c. Let f(t) = -4*j(t) + 11*r(t). Give f(-6).\n | -4\n | ibivibiv/math_instruct | |
Calculate the remainder when 7268 is divided by 1418.\n | 178\n | ibivibiv/math_instruct | |
Let f(u) be the second derivative of 1/6*u**4 + 0*u**2 + 0*u**3 + 0 - 9*u. Let g(r) be the first derivative of 2*r**3/3 - 2. Determine f(g(k)).\n | 8*k**4\n | ibivibiv/math_instruct | |
Collect the terms in 1383*u + 846*u + 1509*u - 4825*u.\n | -1087*u\n | ibivibiv/math_instruct | |
-4036493 divided by 2\n | -4036493/2\n | ibivibiv/math_instruct | |
What is the value of (17 - (5 - -9)) + -7 + 27?\n | 23\n | ibivibiv/math_instruct | |
Evaluate ((-13)/(-130))/((-1)/170).\n | -17\n | ibivibiv/math_instruct | |
74168850 times 0.3\n | 22250655\n | ibivibiv/math_instruct | |
What is the greatest common factor of 605 and 34430?\n | 55\n | ibivibiv/math_instruct | |
Differentiate 43*b**3*d**2 - 9861*b**3 - 5*b**2*d**3 wrt d.\n | 86*b**3*d - 15*b**2*d**2\n | ibivibiv/math_instruct | |
Let k = 13 + -2. Let f(n) = -6*n**3 + 6*n**2 + 5*n + 25. Let z(i) = -i**3 + i**2 + i + 5. Let b(l) = k*z(l) - 2*f(l). What is the units digit of b(0)?\n | 5\n | ibivibiv/math_instruct | |
Three letters picked without replacement from {u: 1, c: 3, q: 1, l: 3, t: 6}. What is prob of picking 3 t?\n | 5/91\n | ibivibiv/math_instruct | |
Let y(d) = -19*d + 2. Let n be y(-3). Suppose -n*o + 61*o - 78 = 0. Suppose -37*a - 70 = -o*a. What is the greatest common divisor of a and 7?\n | 7\n | ibivibiv/math_instruct | |
Let g = -58.49 + 62.49. Let u = -2.9 + -0.1. Which is the fourth biggest value? (a) u (b) -4 (c) g (d) -5\n | d\n | ibivibiv/math_instruct | |
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"# Is $\lfloor \zeta(-n) \rfloor$ only prime for $n=23$?
I searched for primes of the form of $$\lfloor \zeta(-n) \rfloor$$, where $$n \in \Bbb{N}$$, for a range of $$n \le 10^4$$ on PARI/GP and found $$\lfloor \zeta(-n) \rfl... | The topic at hand revolves around investigating certain forms of numbers derived from the Riemann zeta function, specifically those of the type ⌊ζ(-n)⌋ and ⌈ζ(-n)⌉, where n belongs to the set of natural numbers N. Before delving into the questions posed, let's first establish some essential background knowledge on the... | ibivibiv/math_instruct | |
Find the common denominator of 117/301460 and -61/602920.\n | 602920\n | ibivibiv/math_instruct | |
Let x(g) = 26*g**3 - g + 1. Let s(d) = 5*d**3. Suppose -5*a = 4*v - 0*v - 71, 2*a = -v + 26. What is a*s(l) - 2*x(l)?\n | 3*l**3 + 2*l - 2\n | ibivibiv/math_instruct | |
Let q(k) be the third derivative of 29*k**5/30 + k**2 - 46*k. Let b(c) = 21*c**2. Calculate q(b(a)).\n | 25578*a**4\n | ibivibiv/math_instruct | |
Is -170/29 less than -7?\n | False\n | ibivibiv/math_instruct | |
Suppose 5*p + 30 = -0*p. Let q be (26 + 2)*22/8. What is the tens digit of p/15 + q/5?\n | 1\n | ibivibiv/math_instruct | |
Let c = -5632 + 5631.8. What is the smallest value in -29, 78, c?\n | -29\n | ibivibiv/math_instruct | |
Let g be (17298/496)/((-6)/(-32)). Calculate the greatest common factor of 21 and g.\n | 3\n | ibivibiv/math_instruct | |
Let v = 1.489 + -1.689. Sort -51/16, v, -0.3.\n | -51/16, -0.3, v\n | ibivibiv/math_instruct | |
What is the nearest to 0 in 1, 3, 0.05, 6.09?\n | 0.05\n | ibivibiv/math_instruct | |
Let i(z) = -z**3 - 10*z**2 + 12*z + 13. Let o be i(-11). Which is the third biggest value? (a) o (b) -6/7 (c) -3/2\n | c\n | ibivibiv/math_instruct | |
Let c = -8 + 36. Suppose 4*q + 2*w - 33 = -q, 2*w - c = -4*q. Let v(n) = 2*n**3 - 7*n**2 + n - 2. List the prime factors of v(q).\n | 2, 3, 13\n | ibivibiv/math_instruct | |
Let m(a) = 15*a + 10. Let f be m(5). Let y = -42 - -18. Let n be (-402)/y - (-3)/12. Calculate the greatest common factor of n and f.\n | 17\n | ibivibiv/math_instruct | |
Let b be (-8)/5 - (-8 - -7). Let q = -15.73 + -0.27. Let l = q + 16. What is the nearest to 2 in l, b, -0.3?\n | l\n | ibivibiv/math_instruct | |
Factor 5*x**3 + 7155*x**2 + 7150*x.\n | 5*x*(x + 1)*(x + 1430)\n | ibivibiv/math_instruct | |
Calculate -449 divided by -2.\n | 449/2\n | ibivibiv/math_instruct | |
Product of 11.7 and 529768.\n | 6198285.6\n | ibivibiv/math_instruct | |
Add 1758.91 and 0.0095.\n | 1758.9195\n | ibivibiv/math_instruct | |
Let f(u) = -u**2 - 9*u - 7. Suppose 40 = -4*o + 9*o. Suppose 6 = -2*y - o. What is the units digit of f(y)?\n | 7\n | ibivibiv/math_instruct | |
Let o(a) = 7*a + 235. Let l be o(-33). Solve -3*r = l*r + 21 for r.\n | -3\n | ibivibiv/math_instruct | |
Is 15413383 prime?\n | True\n | ibivibiv/math_instruct | |
What is 79/3 of a week in hours?\n | 4424\n | ibivibiv/math_instruct | |
Is 12007027 a prime number?\n | True\n | ibivibiv/math_instruct | |
How many milligrams are there in 1/20 of a gram?\n | 50\n | ibivibiv/math_instruct | |
Let g = -1.0273 - -113.0073. What is g rounded to the nearest integer?\n | 112\n | ibivibiv/math_instruct | |
Let a = -619/3 + 9691/48. Calculate the common denominator of a and 49/(-9 + 16)*13/16.\n | 16\n | ibivibiv/math_instruct | |
Suppose -52*i - 31*i + 3060 = -32*i. Solve o = -4*g - 3, -i*g = -56*g for o.\n | -3\n | ibivibiv/math_instruct | |
Let c = 68 - 70. Let r(t) be the first derivative of t**4/4 - t**3/3 + t**2/2 - 2. Determine r(c).\n | -14\n | ibivibiv/math_instruct | |
What is 3/25 of a milligram in micrograms?\n | 120\n | ibivibiv/math_instruct | |
Find the common denominator of -55/1668 and 115/12594.\n | 3501132\n | ibivibiv/math_instruct | |
Let b(x) = -35*x**4 - 205*x**3 + 575*x**2 - 25*x. Let i(t) = 3*t**4 + 17*t**3 - 48*t**2 + 2*t. Let c(f) = -2*b(f) - 25*i(f). Factor c(u).\n | -5*u**2*(u - 2)*(u + 5)\n | ibivibiv/math_instruct | |
What is the next term in 289, 2178, 7293, 17248, 33657, 58134, 92293?\n | 137748\n | ibivibiv/math_instruct | |
Let p = -123079 + 123083.9. Let x be (-12)/56 - (-1)/2. Which is the second smallest value? (a) 2 (b) p (c) x\n | a\n | ibivibiv/math_instruct | |
What is the ten millions digit of 574851534?\n | 7\n | ibivibiv/math_instruct | |
Let b = -53 - -55. Suppose -b*j - 5*o = -55, -3*j + 5*o + 50 = 2*j. Calculate the remainder when 71 is divided by j.\n | 11\n | ibivibiv/math_instruct | |
What is the first derivative of -33*y**3*z + 13645437*y**3 + 3342*z - 47083 wrt y?\n | -99*y**2*z + 40936311*y**2\n | ibivibiv/math_instruct |
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