instruction_seed stringlengths 5 2.9k | response_seed stringlengths 3 9.55k | input stringclasses 1
value | _source stringclasses 1
value |
|---|---|---|---|
Let o(t) = -63*t - 190. What is o(-3)?\n | -1\n | ibivibiv/math_instruct | |
Is 1902059 composite?\n | True\n | ibivibiv/math_instruct | |
Are 2/9941 and 0 non-equal?\n | True\n | ibivibiv/math_instruct | |
What is prob of picking 3 x when three letters picked without replacement from yyyxyxxyyyy?\n | 1/165\n | ibivibiv/math_instruct | |
How many minutes are there between 12:07 AM and 4:11 AM?\n | 244\n | ibivibiv/math_instruct | |
Solve 2*w**5/3 - 4286*w**4 + 9189180*w**3 - 6579427176*w**2 + 19655694576*w = 0.\n | 0, 3, 2142\n | ibivibiv/math_instruct | |
Calculate (5 - (6 - 3)) + 266 + -249 + -9.\n | 10\n | ibivibiv/math_instruct | |
Solve 0 = 3*z + r - 43, 381*z - 15*r + 53 = 385*z - 18 for z.\n | 14\n | ibivibiv/math_instruct | |
Suppose -4*l + 5*u = -20, 12 = 3*l - 15*u + 12*u. What are the prime factors of (l - 3)/(-3) - (-528 + -2)?\n | 3, 59\n | ibivibiv/math_instruct | |
Simplify ((s*s**0)/((s/(s/s**(2/23)))/s))/((s**2/s)/s)**(6/35) assuming s is positive.\n | s**(44/23)\n | ibivibiv/math_instruct | |
Let d(p) = -8*p**2 + 15*p - 7. Let l = -5 + 1. Let u(o) = -8*o**2 + 14*o - 6. Let m(n) = l*d(n) + 5*u(n). Factor m(a).\n | -2*(a - 1)*(4*a - 1)\n | ibivibiv/math_instruct | |
Sort 9, 3, 5.\n | 3, 5, 9\n | ibivibiv/math_instruct | |
-10211 (base 4) to base 8\n | -445\n | ibivibiv/math_instruct | |
Calculate the remainder when 20522 is divided by 112.\n | 26\n | ibivibiv/math_instruct | |
What is -6 - -5*((-1728)/176 - -11)?\n | -1/11\n | ibivibiv/math_instruct | |
Three letters picked without replacement from iiii. What is prob of picking 3 i?\n | 1\n | ibivibiv/math_instruct | |
What is 81/4 of a meter in centimeters?\n | 2025\n | ibivibiv/math_instruct | |
What is prob of picking 2 t and 2 e when four letters picked without replacement from {t: 3, e: 3, w: 1}?\n | 9/35\n | ibivibiv/math_instruct | |
Calculate -75 divided by -15.\n | 5\n | ibivibiv/math_instruct | |
Suppose -3*p + 6 = 3*p. Put 4, -3, -7, p in decreasing order.\n | 4, p, -3, -7\n | ibivibiv/math_instruct | |
What is (785/(-157))/(25/(-155))?\n | 31\n | ibivibiv/math_instruct | |
Suppose 5*v + 3*h = 30, 13*v = 16*v + 4*h - 29. Suppose -n + 560 = v*j, j + 4*j - 10 = 0. What is the tens digit of n?\n | 5\n | ibivibiv/math_instruct | |
b"What is the xth term of 4176, 4173, 4168, 4161, 4152, 4141?\n" | -x**2 + 4177\n | ibivibiv/math_instruct | |
Simplify (0 + (-5 + (sqrt(1573) - (sqrt(1573) + sqrt(1573) + -1*sqrt(1573))) - sqrt(1573)))*6 + -4 + (-3*(sqrt(1573)*2 + 4))**2 + 5.\n | 1518*sqrt(13) + 56743\n | ibivibiv/math_instruct | |
What is next in 1000, 1998, 2994, 3988, 4980, 5970, 6958?\n | 7944\n | ibivibiv/math_instruct | |
In base 3, what is -220012221022212022 + -11?\n | -220012221022212110\n | ibivibiv/math_instruct | |
What is prob of picking 3 n and 1 j when four letters picked without replacement from {w: 3, i: 2, j: 3, n: 3, y: 3}?\n | 3/1001\n | ibivibiv/math_instruct | |
What is 2366 to the power of 1/3, to the nearest integer?\n | 13\n | ibivibiv/math_instruct | |
Collect the terms in -32*n**2 + 201550145*n - 201550145*n + 39*n**2.\n | 7*n**2\n | ibivibiv/math_instruct | |
Let t(g) = 19*g**2. Let u(f) = 93*f - 6 + 9 - 1 - f. Determine t(u(m)).\n | 160816*m**2 + 6992*m + 76\n | ibivibiv/math_instruct | |
How many minutes are there between 6:15 PM and 7:04 PM?\n | 49\n | ibivibiv/math_instruct | |
Calculate the lowest common multiple of 112 and 308.\n | 1232\n | ibivibiv/math_instruct | |
Calculate ((-2030)/(-60) - 34)*-150.\n | 25\n | ibivibiv/math_instruct | |
Let r(b) = 192*b - 2 + 2 - 191*b. Let f(u) = 3*u**2 - 1. Give r(f(k)).\n | 3*k**2 - 1\n | ibivibiv/math_instruct | |
What is the closest to 0 in 4, -5, 1238.76?\n | 4\n | ibivibiv/math_instruct | |
What is -11472 divided by 847?\n | -11472/847\n | ibivibiv/math_instruct | |
Collect the terms in -1901880*d**3 - 1901749*d**3 + 3803635*d**3.\n | 6*d**3\n | ibivibiv/math_instruct | |
Evaluate (3/6*6)/((-1)/35*-15).\n | 7\n | ibivibiv/math_instruct | |
Solve 300*z = 2586 + 14214 for z.\n | 56\n | ibivibiv/math_instruct | |
Let p(r) = -66*r + 3209. Determine p(48).\n | 41\n | ibivibiv/math_instruct | |
Collect the terms in -5301*l + 10375*l - 5294*l.\n | -220*l\n | ibivibiv/math_instruct | |
Suppose 3*s + 234 = -105. Let l = s + 46. Let k = -43 - l. What is the remainder when k is divided by 13?\n | 11\n | ibivibiv/math_instruct | |
Express -18*x**2 - 17 + 38*x**2 - 18*x**2 as t + c*x + z*x**2 and give z.\n | 2\n | ibivibiv/math_instruct | |
Let n(j) = -15*j**3 - 2*j**2 - 2*j + 1. Let a be n(1). Let o = 5 - a. What is the tens digit of o?\n | 2\n | ibivibiv/math_instruct | |
Divide -73 by -50731.\n | 73/50731\n | ibivibiv/math_instruct | |
What is the highest common divisor of 23769 and 340272?\n | 1251\n | ibivibiv/math_instruct | |
Two letters picked without replacement from {h: 2, x: 1, b: 1, e: 1, n: 1, m: 1}. What is prob of sequence ex?\n | 1/42\n | ibivibiv/math_instruct | |
Let j be -1*(1/1 + -6). Suppose 5*t + j*a + 40 = 0, -2*t + 5*a - 10 = 3*t. Let i = -93.5 + 93. Sort 5, t, i in increasing order.\n | t, i, 5\n | ibivibiv/math_instruct | |
Convert -102 (base 14) to base 10.\n | -198\n | ibivibiv/math_instruct | |
Suppose 0 = 2*b + 3*g - 22, 2*b + 14 - 4 = 5*g. Suppose -104 = -3*s - b*s. Suppose -1680 = p - s*p. Is 35 a factor of p?\n | True\n | ibivibiv/math_instruct | |
Let v = -12514176071079/23026795340 + 30007471/54797. Let u = 2/21011 - v. What is the common denominator of 2 + (2 - 156/16) and u?\n | 20\n | ibivibiv/math_instruct | |
Simplify ((q/q**(-2))**43)**48*((q*q/(q/(((q*q**1*q)/q)/q))*q)**43)**(1/23) assuming q is positive.\n | q**(142545/23)\n | ibivibiv/math_instruct | |
What is the units digit of 959?\n | 9\n | ibivibiv/math_instruct | |
Suppose -5*c + 42 = -3*i, -c + 6*i + 4 = i. Let m be 3/2*24/c. Let v(w) = m*w - 4*w + 27 - 6*w - 7. Let h(f) = 2*f - 7. What is -17*h(p) - 6*v(p)?\n | 2*p - 1\n | ibivibiv/math_instruct | |
Bill gets paid differently depending on the hours and days of the week. On weekdays, he earns $20 for every hour up to a total of 40 hours. After 40 hours, his weekday pay structure is as follows: for odd-numbered hours, he gets double pay, and for even-numbered hours, he gets $5 less than the previous odd hour. On wee... | Let's break down Bill's earnings for the week:
**Weekday Earnings:**
Bill works 8 hours per weekday. Since there are 5 weekdays, he works a total of 40 hours on weekdays. He earns $20 per hour for these hours.
Total weekday earnings = 40 hours * $20/hour = $800
**Weekend Earnings:**
Bill works 10 hours per day on th... | ibivibiv/math_instruct | |
Two letters picked without replacement from {w: 4, e: 4, l: 3}. What is prob of sequence le?\n | 6/55\n | ibivibiv/math_instruct | |
Which is the closest to -7? (a) -4 (b) -0.03 (c) -0.2\n | a\n | ibivibiv/math_instruct | |
Let c be (-99)/(-11)*(-40)/(-15). Suppose 105 = c*z - 87. Which is smaller: 9 or z?\n | z\n | ibivibiv/math_instruct | |
Factor -14472*q**2 - 225156*q - 560.\n | -4*(9*q + 140)*(402*q + 1)\n | ibivibiv/math_instruct | |
Let a(u) = -u + 41. Calculate the smallest common multiple of a(8) and 6.\n | 66\n | ibivibiv/math_instruct | |
List the prime factors of 7565.\n | 5, 17, 89\n | ibivibiv/math_instruct | |
Expand (-2 + 3 + 1)*(-3 - x + 3) + (-2 + 146 - 16 + (0 + 5 - 4)*(-1 + 1 - 2) + (1 - 3 + 1)*(6 - 4 + 0) - 4 + 2 + 1)*(0*x + 2*x - 5*x).\n | -371*x\n | ibivibiv/math_instruct | |
Find the common denominator of -109/10110 and 2/11121.\n | 111210\n | ibivibiv/math_instruct | |
What is the closest to -1 in 0.3, -0.93, 5, -3/5?\n | -0.93\n | ibivibiv/math_instruct | |
What is the third derivative of -12*c**3 - 340*c**2?\n | -72\n | ibivibiv/math_instruct | |
(-52 - (2 + (-4 - -7))) + 163 + -153\n | -47\n | ibivibiv/math_instruct | |
What is -120.71 rounded to the nearest 10?\n | -120\n | ibivibiv/math_instruct | |
Which is the third smallest value? (a) 2/5 (b) 166 (c) -0.03 (d) -0.5\n | a\n | ibivibiv/math_instruct | |
Suppose -4*l**5 - 48*l**4 - 24*l**3 + 208*l**2 - 132*l = 0. What is l?\n | -11, -3, 0, 1\n | ibivibiv/math_instruct | |
Suppose 3*d - 79 = -4*r, 4*r = 3*d + 12 + 61. Suppose 5*c - 64 = 3*c. Suppose -4*u + 4*f + c = 0, 3*f = 7 - 1. Calculate the remainder when r is divided by u.\n | 9\n | ibivibiv/math_instruct | |
Collect the terms in u - 13*u + 0*u + 11*u.\n | -u\n | ibivibiv/math_instruct | |
Find the first derivative of q**4 - q**3 + 71908*q**2 - q*u + 2*u + 330407 wrt q.\n | 4*q**3 - 3*q**2 + 143816*q - u\n | ibivibiv/math_instruct | |
What is 197 minutes before 7:07 PM?\n | 3:50 PM\n | ibivibiv/math_instruct | |
What are the prime factors of 1570427?\n | 1570427\n | ibivibiv/math_instruct | |
Three letters picked without replacement from ivywzdz. What is prob of sequence wyz?\n | 1/105\n | ibivibiv/math_instruct | |
Expand -15 + 15 + 3*x**2 - 4*x + (2*x - 4*x + 3*x + (4 - 2 + 0)*(6*x - 4*x - x) + 4*x - 5*x + 14*x)*(-x + 2 - 2).\n | -13*x**2 - 4*x\n | ibivibiv/math_instruct | |
b"What is the ith term of -30743, -29790, -28837?\n" | 953*i - 31696\n | ibivibiv/math_instruct | |
Divide 144574602 by -1980474.\n | -73\n | ibivibiv/math_instruct | |
Solve -413*t - 2*h + 41 = -210*t - 208*t, -3*t + 43 = 4*h for t.\n | -3\n | ibivibiv/math_instruct | |
Let j(i) = -635*i - 3 - 3 + 633*i. Suppose 3*x - 5 = 4*x. Let h be j(x). Calculate the greatest common divisor of 20 and h.\n | 4\n | ibivibiv/math_instruct | |
Let g(v) be the third derivative of -v**4/3 - 15*v**3/2 - 1571*v**2. Calculate g(-4).\n | -13\n | ibivibiv/math_instruct | |
What is the lowest common multiple of 951885 and 605745?\n | 6663195\n | ibivibiv/math_instruct | |
What is the greatest common factor of 6858 and 47411894?\n | 254\n | ibivibiv/math_instruct | |
Rearrange 2 + 2*x**4 - 14*x**2 + 12*x**2 - 4 - 2*x**3 to h*x**4 + s*x**3 + w*x + o + f*x**2 and give s.\n | -2\n | ibivibiv/math_instruct | |
Two letters picked without replacement from kgwsndd. Give prob of sequence gw.\n | 1/42\n | ibivibiv/math_instruct | |
What is 1/4 of a tonne in kilograms?\n | 250\n | ibivibiv/math_instruct | |
Let k(s) = 3*s**2 - 104*s + 132. Let v be k(34). Calculate the greatest common factor of 52 and v.\n | 4\n | ibivibiv/math_instruct | |
2057085 divided by -1\n | -2057085\n | ibivibiv/math_instruct | |
What is the biggest value in -3/11, -21, 2/17?\n | 2/17\n | ibivibiv/math_instruct | |
List the prime factors of 1194819.\n | 3, 398273\n | ibivibiv/math_instruct | |
Let i be 3 + -7*22/77. Suppose 2*h + 1 = -3*t, t = -4*h - 2*t + 1. Let y be 1/(h + 2/i - 2). Solve -x - 3 = -y for x.\n | -2\n | ibivibiv/math_instruct | |
Let i(o) = -22*o**4 + 4*o**3 + 26*o**2 + 4*o - 2. Let l(c) = c**4 + c**3 + c. Let m(p) = -i(p) + 4*l(p). Find the third derivative of m(v) wrt v.\n | 624*v\n | ibivibiv/math_instruct | |
Which is the closest to -0.3? (a) 5 (b) 5/16 (c) -0.4 (d) -0.5\n | c\n | ibivibiv/math_instruct | |
What is -0.00002759910485 rounded to six decimal places?\n | -0.000028\n | ibivibiv/math_instruct | |
What is 37 (base 10) in base 16?\n | 25\n | ibivibiv/math_instruct | |
Solve -2*x + 7*x - w = 21, 2*x = -w + 7 for x.\n | 4\n | ibivibiv/math_instruct | |
Write an educational piece suited for college students related to the following text snippet:
"# Two different answers when computing dimension of Zariski cotangent space?
Let $V = V(X^2-Y^3,Y^2 - Z^3)$. Let $P= (0,0,0)$ that is a point in $V$. I want to compute $\dim_k \mathfrak{m}_P/\mathfrak{m}_P^2$ where $\mathfra... | The topic at hand concerns the computation of the dimension of the Zariski cotangent space of a variety at a given point. This is an important concept in algebraic geometry, which involves studying the geometric properties of solutions to polynomial equations. To understand this problem, let us first define some key t... | ibivibiv/math_instruct | |
What is the second derivative of 17*k**5 + 12 - 3*k - 10 + 63*k**5 + 55*k wrt k?\n | 1600*k**3\n | ibivibiv/math_instruct | |
In base 2, what is 10100010 - 11?\n | 10011111\n | ibivibiv/math_instruct | |
Which is smaller: -9011 or -9009?\n | -9011\n | ibivibiv/math_instruct |
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