instruction_seed stringlengths 5 2.9k | response_seed stringlengths 3 9.55k | input stringclasses 1
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|---|---|---|---|
Let b = -1 - 3. Let o = b + 9. Let w(a) = a - 2. Calculate the smallest common multiple of w(6) and o.\n | 20\n | ibivibiv/math_instruct | |
Calculate the smallest common multiple of 50 and 470.\n | 2350\n | ibivibiv/math_instruct | |
Suppose 0 = 2*y - 3*z + z + 2, 0 = y + 4*z - 14. Calculate the common denominator of (-175)/30 + (1 - y - -2) and -20/9.\n | 18\n | ibivibiv/math_instruct | |
Let d(b) = b**2 - 9*b - 12. Calculate the lowest common multiple of 11 and d(11).\n | 110\n | ibivibiv/math_instruct | |
(-897)/6*(-2970)/6831\n | 65\n | ibivibiv/math_instruct | |
Expand (i**2 + 3 - 3 + (3*i - 3*i + 2*i)*(-3*i + 3*i - 2*i) + 3*i**2 - 6*i**2 + 2*i**2 + 7*i**2 + 9 - 9 - 1 + 2*i**2 + 1)*(0 + 4 - 5)*(5*i + 0*i + 0*i).\n | -25*i**3\n | ibivibiv/math_instruct | |
Let h be 1 + (-1 - -2) + -2. Let y be ((-3 - h) + 5)/(-1). What is the units digit of 1/y + 21/6?\n | 3\n | ibivibiv/math_instruct | |
Calculate the lowest common multiple of 10 and 10.\n | 10\n | ibivibiv/math_instruct | |
Solve -z - 14 = r - 12 + 1, -21 = -11*r + z - 66 for r.\n | -4\n | ibivibiv/math_instruct | |
Let d(q) = 180*q**2 + 3790*q + 15. Give d(-21).\n | -195\n | ibivibiv/math_instruct | |
What is 15/((-300)/(-152)) - 8?\n | -2/5\n | ibivibiv/math_instruct | |
Factor t**4 - 19722277*t**3 - 59166837*t**2 - 59166839*t - 19722280.\n | (t - 19722280)*(t + 1)**3\n | ibivibiv/math_instruct | |
Four letters picked without replacement from {u: 7, f: 5, o: 1}. Give prob of sequence ufuf.\n | 7/143\n | ibivibiv/math_instruct | |
Which is smaller: 10690 or 10513?\n | 10513\n | ibivibiv/math_instruct | |
Suppose 0 = -3*q + 5*k - 46, -5*q + 521 = 4*k + 536. Which is the nearest to 0.1? (a) q (b) 0.06 (c) 7/3\n | b\n | ibivibiv/math_instruct | |
Let l(z) = 2*z. Let f(r) = -260*r**2 - 299*r**2 + 175*r**2. What is f(l(w))?\n | -1536*w**2\n | ibivibiv/math_instruct | |
Let w = 209 - 135. Suppose 0 = -4*z + w - 6. What is the remainder when z is divided by 9?\n | 8\n | ibivibiv/math_instruct | |
How many minutes are there between 4:43 PM and 3:43 AM?\n | 660\n | ibivibiv/math_instruct | |
Calculate the greatest common factor of 272 and 1462.\n | 34\n | ibivibiv/math_instruct | |
Suppose v + 4 = 4*f - 22, -2*v - 2*f - 12 = 0. Let c = -5 + 26. Let a = c + v. Is a a composite number?\n | False\n | ibivibiv/math_instruct | |
How many kilograms are there in three tenths of a tonne?\n | 300\n | ibivibiv/math_instruct | |
Suppose -10 = -2*l - 0*l. Let t = 5 + -8. Let i = 3.1 + t. Is l equal to i?\n | False\n | ibivibiv/math_instruct | |
Suppose 41*a = -35 - 1605. Suppose -3*y - 604 = y. Let j = a - y. What is the tens digit of j?\n | 1\n | ibivibiv/math_instruct | |
Convert 95218.13um to centimeters.\n | 9.521813\n | ibivibiv/math_instruct | |
Three letters picked without replacement from okckhocockkcokckck. Give prob of picking 3 o.\n | 1/204\n | ibivibiv/math_instruct | |
Let o be (0 + -4)*(1 + 10/(-4)). Suppose -o*j + 8488 = 2*j. Is j prime?\n | True\n | ibivibiv/math_instruct | |
Is 1897 a factor of 8623762?\n | True\n | ibivibiv/math_instruct | |
Evaluate 3*(10/40)/((-15)/(-160)).\n | 8\n | ibivibiv/math_instruct | |
Is 2828797 a composite number?\n | False\n | ibivibiv/math_instruct | |
Find the number of moles of NaNO3 formed on combining 3 moles of NaCl and 3 moles of KNO3 | The reaction between NaCl and KNO3 does not directly produce NaNO3. These two compounds are salts and do not react with each other under normal conditions. They would simply form a mixture of salts.
However, if you are referring to a double displacement reaction where NaCl and KNO3 are dissolved in water and react to ... | ibivibiv/math_instruct | |
Three letters picked without replacement from gggjjbv. Give prob of sequence bgj.\n | 1/35\n | ibivibiv/math_instruct | |
What is the highest common factor of 3030 and 120?\n | 30\n | ibivibiv/math_instruct | |
Find the common denominator of 17/400 and -67/76.\n | 7600\n | ibivibiv/math_instruct | |
What comes next: -251367, -251282, -251141, -250944?\n | -250691\n | ibivibiv/math_instruct | |
Suppose 2*z - 10 = 3*v + 25, z = -5*v - 41. Calculate the lowest common multiple of 36 and 62914/747 + (0 - (-2)/v).\n | 252\n | ibivibiv/math_instruct | |
Express (1 + 0 - 24*w + 0)*(15*w - 40*w + 14*w) - w**2 - 2*w**2 + w**2 - 5*w**2 + 4*w**2 - w**2 in the form b*w + l + h*w**2 and give h.\n | 260\n | ibivibiv/math_instruct | |
Calculate the highest common divisor of 56 and 812.\n | 28\n | ibivibiv/math_instruct | |
What is 688 minutes before 2:13 AM?\n | 2:45 PM\n | ibivibiv/math_instruct | |
Suppose 8*l - 376 = -296. Let v be 123/12 - 2/8. Differentiate 6*h - v*h - l*h - 11 wrt h.\n | -14\n | ibivibiv/math_instruct | |
Suppose -63*m + 160 = -98*m + 67*m. Solve 8*f - 7*f = -2*x + 3, -m*x + 10 = 5*f for x.\n | 1\n | ibivibiv/math_instruct | |
Suppose h + n = 59, -102 = -2*h - 388*n + 390*n. Let s(w) = w**3 - 6*w**2 + w + 6. What is the remainder when h is divided by s(6)?\n | 7\n | ibivibiv/math_instruct | |
Let k = -1.9732 - 0.0268. Suppose 2*f + 0*o + 36 = -5*o, 4*o = -3*f - 40. Which is the fourth smallest value? (a) f (b) 0.4 (c) 5 (d) k\n | c\n | ibivibiv/math_instruct | |
What is 419 minutes after 5:03 AM?\n | 12:02 PM\n | ibivibiv/math_instruct | |
Is 174851 a composite number?\n | False\n | ibivibiv/math_instruct | |
Which is the biggest value? (a) 0.2 (b) 1.1405 (c) -7/3 (d) 3 (e) -5\n | d\n | ibivibiv/math_instruct | |
Let m = -1700.65 - -1616. Let j = m + -1.35. Let x = j + 88. Which is the third smallest value? (a) x (b) -1/16 (c) 0\n | a\n | ibivibiv/math_instruct | |
What is the smallest common multiple of 8640 and 2?\n | 8640\n | ibivibiv/math_instruct | |
Suppose 5*n - 432 = n - x, 2*n = -3*x + 226. What is the remainder when 429 is divided by n?\n | 1\n | ibivibiv/math_instruct | |
Suppose -9*n = -7*n - 352. Let l be n/80 - (-2)/(-10). Solve l*w = 5*b + w - 15, 9 = 3*b - 2*w for b.\n | 3\n | ibivibiv/math_instruct | |
Let o = -87 - -353/4. What is the closest to 0.1 in 0.3, 1, o?\n | 0.3\n | ibivibiv/math_instruct | |
Convert 121111010 (base 3) to base 8.\n | 27362\n | ibivibiv/math_instruct | |
Evaluate 10 + -22 + 2 + 3.\n | -7\n | ibivibiv/math_instruct | |
Let j = 0.14 - 0.34. What is the nearest to 0 in -0.5, 2, j?\n | j\n | ibivibiv/math_instruct | |
What is the difference between -0.14 and -14013.006756?\n | 14012.866756\n | ibivibiv/math_instruct | |
Let f = 67203/14 - 9505/2. Let x = f + -48. What is the second biggest value in -0.3, -2/5, x?\n | -0.3\n | ibivibiv/math_instruct | |
Product of -2 and 0.912.\n | -1.824\n | ibivibiv/math_instruct | |
Suppose 0 = 2*q - u, 0 = -0*q - q - 4*u + 9. What is the units digit of -7*((-3)/q + 0)?\n | 1\n | ibivibiv/math_instruct | |
What is the nearest to 0.1 in -0.14, 0.5, 1.61, -0.1, -28, 0.4?\n | -0.1\n | ibivibiv/math_instruct | |
What is the cube root of 43814 to the nearest integer?\n | 35\n | ibivibiv/math_instruct | |
Solve -734*x - 86565 = 6653 for x.\n | -127\n | ibivibiv/math_instruct | |
-1489 divided by -11\n | 1489/11\n | ibivibiv/math_instruct | |
In base 10, what is -39 - -5?\n | -34\n | ibivibiv/math_instruct | |
Let r(k) = -k**2 + 8*k + 7. What is the tens digit of r(6)?\n | 1\n | ibivibiv/math_instruct | |
Suppose -4*c = 4*i - 20, 0 = -24*c + 29*c - 5*i - 15. Let h(t) = t**3 - 7*t**2 - 9*t + 12. Let z be h(8). Solve -3*p + z*p = c for p.\n | 4\n | ibivibiv/math_instruct | |
Work out -2.17 * -98.\n | 212.66\n | ibivibiv/math_instruct | |
Collect the terms in 4*p + p - 4 + 9.\n | 5*p + 5\n | ibivibiv/math_instruct | |
What is the units digit of 1302522547?\n | 7\n | ibivibiv/math_instruct | |
Suppose -v - 7*v = 19*v. Solve 7*q + 0*q - 7 = v for q.\n | 1\n | ibivibiv/math_instruct | |
What is the value of (-10 + -7 - -165) + -75?\n | 73\n | ibivibiv/math_instruct | |
Let u(q) = -2*q**2 + 7*q + 20. Let a be u(10). What is the tens digit of -12 - a - (1 + 1)?\n | 9\n | ibivibiv/math_instruct | |
Let m = 109 - 106. Suppose -3*z = -t - z - 5, -m*z = 5*t - 27. Solve -t = 36*l - 33*l for l.\n | -1\n | ibivibiv/math_instruct | |
Solve 0 = -187*u - 10631977 + 10609350 for u.\n | -121\n | ibivibiv/math_instruct | |
Suppose -5*d = -4*w + 496, -3*w - 96 = 2*d + 107. Let h = 103 + d. Find the third derivative of 4*z**3 + 10*z**4 - 32*z**2 - 2*z**4 - z**3 - z**h wrt z.\n | 192*z + 12\n | ibivibiv/math_instruct | |
Let t(o) = o**2. Let r be 6/12 + 10/4. Let c = 3 - 0. Let h(l) = r*l - 3*l + c*l**2. Give t(h(n)).\n | 9*n**4\n | ibivibiv/math_instruct | |
What is 53 minutes after 9:02 AM?\n | 9:55 AM\n | ibivibiv/math_instruct | |
Suppose -3*b - 1 = -t + 8, -5*t - 5*b + 5 = 0. Let s be 8*-1*(t - 4). Suppose -j + 9 + s = 0. What are the prime factors of j?\n | 17\n | ibivibiv/math_instruct | |
Let k = 11 - 17. Suppose 20 = -4*v, -6*v = -3*q - v + 22. Let j = q - k. What is the units digit of j?\n | 5\n | ibivibiv/math_instruct | |
Let m(n) = -1907*n - 350948. Determine m(-184).\n | -60\n | ibivibiv/math_instruct | |
Sort -3, -5, -9157.\n | -9157, -5, -3\n | ibivibiv/math_instruct | |
Is 44130631 prime?\n | True\n | ibivibiv/math_instruct | |
Write an educational piece suited for college students related to the following text snippet:
"# How many 3 digit numbers can be formed using digits 1,2,3,4 and 5 such that the number is divisible by 6
How many $3$ digit numbers can be formed using digits $1,2,3,4$ and $5$ without repetition such that the number is di... | To solve the problem of forming 3-digit numbers using the digits 1, 2, 3, 4, and 5 without repetition such that the number is divisible by 6, let's first review some relevant mathematical concepts.
Divisibility Rules: A number is divisible by 6 if it is divisible by both 2 and 3. For a number to be divisible by 2, it... | ibivibiv/math_instruct | |
Let v(z) = -1475*z - 42782. Determine v(-29).\n | -7\n | ibivibiv/math_instruct | |
Calculate prob of picking 1 c and 1 k when two letters picked without replacement from {k: 2, c: 1, e: 1, w: 1, v: 2, h: 1}.\n | 1/14\n | ibivibiv/math_instruct | |
Suppose 2*c = -c + 5*d - 11, -5 = 2*c - d. Let k be (-273274)/2*c/44. Let a = 6212 - k. Calculate the common denominator of 47/6 and a.\n | 66\n | ibivibiv/math_instruct | |
What is the eighth root of 5080123496 to the nearest integer?\n | 16\n | ibivibiv/math_instruct | |
Suppose -5*a = 4*i + 8437 - 4646, -a - 2*i - 769 = 0. Which is greater: a or -1503/2?\n | a\n | ibivibiv/math_instruct | |
Calculate the highest common divisor of 21 and 616.\n | 7\n | ibivibiv/math_instruct | |
Write an educational piece suited for college students related to the following text snippet:
"# Implicit Differentiation
## Graphs of equations
An equation in $y$ and $x$ is an algebraic expression involving an equality with two (or more) variables. An example might be $x^2 + y^2 = 1$.
The solutions to an equation ... | Equations in several variables, such as x and y, represent relationships between those variables. These equations consist of an algebraic expression linked by an equals sign, expressing that both sides of the equation hold equal value. A familiar illustration would be the circle equation: x^2 + y^2 = 1. The pairings o... | ibivibiv/math_instruct | |
Let b = 154 + -149. Suppose 4*q - q + b*s = 110, 5*q - 204 = 2*s. Calculate the highest common factor of 64 and q.\n | 8\n | ibivibiv/math_instruct | |
Solve 0 = 1064*y - 484*y + 4060 for y.\n | -7\n | ibivibiv/math_instruct | |
What is prob of picking 1 n and 2 i when three letters picked without replacement from ttinktntgqkgnkt?\n | 0\n | ibivibiv/math_instruct | |
Solve -4*b + 96 - 58 = 3*z, 10 = z + b for z.\n | 2\n | ibivibiv/math_instruct | |
Solve 1360*l - 51757 - 25763 = 0 for l.\n | 57\n | ibivibiv/math_instruct | |
Let g = -0.4 + -2.6. Let v = -1.362 - -1.562. Put -0.4, v, g, 0.5 in decreasing order.\n | 0.5, v, -0.4, g\n | ibivibiv/math_instruct | |
Expand (u**3 + 855 - 867 - 7*u**2 - u + u**2)*(7 - 7 - 9).\n | -9*u**3 + 54*u**2 + 9*u + 108\n | ibivibiv/math_instruct | |
Let t(w) = w**2. Let v(s) = 7*s**2 + 5*s + 7. Let j(o) = -6*t(o) + v(o). Calculate j(-5).\n | 7\n | ibivibiv/math_instruct | |
Let h(t) = 14*t**2 - 4*t + 9. Give h(2).\n | 57\n | ibivibiv/math_instruct | |
Let d = -34 - -38. Let n(w) = 77*w - 7. Is n(d) a composite number?\n | True\n | ibivibiv/math_instruct | |
Product of 357123 and 0.019.\n | 6785.337\n | ibivibiv/math_instruct | |
Let x(s) = -s + 2. Let v = -82 + 79. Let k be x(v). Find the second derivative of -30*u - u - 3*u**5 + 15*u**4 - 17*u - k*u wrt u.\n | -60*u**3 + 180*u**2\n | ibivibiv/math_instruct |
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