instruction_seed stringlengths 5 2.9k | response_seed stringlengths 3 9.55k | input stringclasses 1
value | _source stringclasses 1
value |
|---|---|---|---|
Solve 4*m + v = -11, 0 = 15*m - 13*m - 2*v - 2 for m.\n | -2\n | ibivibiv/math_instruct | |
What is the highest common divisor of 44444 and 271?\n | 271\n | ibivibiv/math_instruct | |
What is (1 - (2 - 0)) + (-85 - -86)?\n | 0\n | ibivibiv/math_instruct | |
Solve -20141*y = -20248*y + 535 for y.\n | 5\n | ibivibiv/math_instruct | |
Let m(l) = l**3 - l**2 - l + 2. Let b be m(2). Suppose i + 2*g - 18 = 6*g, -5*g = -b*i + 28. Solve u = -c - 0*c - i, 4*u - 5*c + 26 = 0 for u.\n | -4\n | ibivibiv/math_instruct | |
Simplify (t**(-2/9))**(-25) assuming t is positive.\n | t**(50/9)\n | ibivibiv/math_instruct | |
Let u(n) be the third derivative of 0*n**3 + 0 - 13/24*n**4 - 64*n**2 + 0*n. Let o(l) = -8*l. Give u(o(j)).\n | 104*j\n | ibivibiv/math_instruct | |
Let q = -1/380 - 11/380. Is 1 != q?\n | True\n | ibivibiv/math_instruct | |
Simplify ((((a**10/a*a)/a)/a*a**(1/6))**15)**12 assuming a is positive.\n | a**1470\n | ibivibiv/math_instruct | |
Total of -461.106 and -0.08277.\n | -461.18877\n | ibivibiv/math_instruct | |
Three letters picked without replacement from {t: 6, o: 12}. Give prob of picking 1 o and 2 t.\n | 15/68\n | ibivibiv/math_instruct | |
Let l(x) = 4*x**2. Let n be (250 - 0) + 0/2. Let s(b) = -2*b + n - b - 250. Calculate s(l(v)).\n | -12*v**2\n | ibivibiv/math_instruct | |
Is -3 + 9/(45/5720) prime?\n | False\n | ibivibiv/math_instruct | |
Simplify 1*(2*sqrt(56)/sqrt(2) + 1).\n | 1 + 4*sqrt(7)\n | ibivibiv/math_instruct | |
Simplify -2 + (-2*(5*((-2*sqrt(720) - sqrt(720)) + sqrt(720)) - sqrt(720) - sqrt(720)))/(4*((sqrt(60)/sqrt(3) - sqrt(20))/sqrt(2) - 4*sqrt(10)*-1)).\n | -2 + 9*sqrt(2)\n | ibivibiv/math_instruct | |
Let v = 15 + 24. Suppose -5*k = -5*u - 85, -k - 2*k + v = -2*u. Let h be (-2)/3*u/2. Let j(a) = -a**3 + 4*a**2 - 4*a + 4. Determine j(h).\n | -12\n | ibivibiv/math_instruct | |
In base 11, what is -364 - -3?\n | -361\n | ibivibiv/math_instruct | |
What is the result of the following expression?
(58.2712 % -93.6478) % 83.7598 | 48.3832 | ibivibiv/math_instruct | |
Let z(s) = -23*s**2 - 9661*s - 411. Calculate z(-420).\n | 9\n | ibivibiv/math_instruct | |
Let i = 2929479 - 2929496.205145. Let q = -12.60505 - i. Let y = q + -4.6. What is y rounded to 5 decimal places?\n | 0.0001\n | ibivibiv/math_instruct | |
Let y(z) = 6*z**2. Let c(f) = -6766*f + 1. Calculate c(y(b)).\n | -40596*b**2 + 1\n | ibivibiv/math_instruct | |
Rearrange (f + 0*f - 2*f)*(61 - 61 + 139*f**2) + f**3 - f**3 + 2*f**3 to g*f + s + c*f**2 + b*f**3 and give b.\n | -137\n | ibivibiv/math_instruct | |
Let f = 14472 + -14357. What is the remainder when 1064 is divided by f?\n | 29\n | ibivibiv/math_instruct | |
Work out 0.7285 * 5.\n | 3.6425\n | ibivibiv/math_instruct | |
Two letters picked without replacement from {o: 4, y: 3}. What is prob of sequence oy?\n | 2/7\n | ibivibiv/math_instruct | |
How many litres are there in 0.9560924 millilitres?\n | 0.0009560924\n | ibivibiv/math_instruct | |
What is 130 minutes after 8:45 AM?\n | 10:55 AM\n | ibivibiv/math_instruct | |
Let x(s) = -1373*s - 160634. Calculate x(-117).\n | 7\n | ibivibiv/math_instruct | |
Divide 171216 by 246.\n | 696\n | ibivibiv/math_instruct | |
Evaluate 35*(-12)/(-504)*12/(-4).\n | -5/2\n | ibivibiv/math_instruct | |
Let x = -352 - -1569. Is x a prime number?\n | True\n | ibivibiv/math_instruct | |
Calculate the common denominator of 52/9 and 13/29130.\n | 87390\n | ibivibiv/math_instruct | |
0.2 times 27824\n | 5564.8\n | ibivibiv/math_instruct | |
Rearrange 0*u + 829 - 727 - 2*u to m + v*u and give v.\n | -2\n | ibivibiv/math_instruct | |
What is the ten millions digit of 369762872?\n | 6\n | ibivibiv/math_instruct | |
Calculate the common denominator of -18/217 and -37/9548.\n | 9548\n | ibivibiv/math_instruct | |
What is the result of the following expression?
-97.5518 - (88.2637 % -22.3481) | -96.4231 | ibivibiv/math_instruct | |
How many minutes are there between 8:24 PM and 11:29 PM?\n | 185\n | ibivibiv/math_instruct | |
Let d(r) = -95*r**3 + 6*r**2 - 17*r - 5. Is d(-6) prime?\n | False\n | ibivibiv/math_instruct | |
Suppose 21 = -2*i + n - 4*n, -3*i + 3*n + 6 = 0. Let y = -4 + 6. What is the closest to y in -1, i, -0.1?\n | -0.1\n | ibivibiv/math_instruct | |
Let w = 12 + -6. Let o be 7 - 1 - 95*4/60. What is the smallest value in o, 3/2, w?\n | o\n | ibivibiv/math_instruct | |
Simplify (sqrt(63) + 3*4*sqrt(63))/sqrt(9).\n | 13*sqrt(7)\n | ibivibiv/math_instruct | |
Is 1003 a multiple of 29?\n | False\n | ibivibiv/math_instruct | |
Calculate the remainder when 42012988 is divided by 6540.\n | 28\n | ibivibiv/math_instruct | |
What comes next: 72, 74, 62, 30, -28, -118?\n | -246\n | ibivibiv/math_instruct | |
b"What is the zth term of 49479, 100904, 152329, 203754, 255179?\n" | 51425*z - 1946\n | ibivibiv/math_instruct | |
Suppose 0 = 3*g - 9, f - 3*g - 910 = -5*g. Let u = -888 + f. Calculate the remainder when (-678)/(-22) - 2/(-11) is divided by u.\n | 15\n | ibivibiv/math_instruct | |
Collect the terms in 8139 + 43*d**3 - 8139 + 0*d**2 + 0*d**2.\n | 43*d**3\n | ibivibiv/math_instruct | |
Write an educational piece suited for college students related to the following text snippet:
"# Thread: Help finding critical points?
1. ## Help finding critical points?
I get the derivative f'(x)= 3x^2+14x-3 now I am stuck. I used the quadratic equation and set answer = 0 but dont get the right answer. Could someon... | Critical points of a function occur at values of x where the function's rate of change (the derivative) is either zero or undefined. To find these critical points, we first need to find the derivative of the function and then solve for x when the derivative equals zero or is undefined. Let's break down this process us... | ibivibiv/math_instruct | |
ade0e7 (base 16) to base 11\n | 6483507\n | ibivibiv/math_instruct | |
Put -5, 3, 31, 4, -4, 778 in decreasing order.\n | 778, 31, 4, 3, -4, -5\n | ibivibiv/math_instruct | |
Let b(l) be the first derivative of l**4/4 + 4*l**3/3 - l**2 - 5*l + 2. Let u = -2 + -2. Let i be b(u). Solve -5*f = -i + 8 for f.\n | -1\n | ibivibiv/math_instruct | |
Write an educational piece suited for college students related to the following text snippet:
"Prove that $xy+yz+zx \leq x^2+y^2+z^2$ [duplicate]
This question already has an answer here:
Prove that $xy+yz+zx \leq x^2+y^2+z^2$ . Hint: Use $\frac{a+b}{2}\geq\sqrt{ab}$
First I tried using the hint by setting $a=x$ and... | The problem you're facing involves proving that $xy + yz + zx \leq x^2 + y^2 + z^2$. This type of inequality falls under the category of symmetric inequalities since the variables $x, y,$ and $z$ appear in a symmetric manner. To tackle this problem, let's consider some strategies and relevant background information.
... | ibivibiv/math_instruct | |
Let h = 2523 - 2526. Sort 3, 16, h, -2 in increasing order.\n | h, -2, 3, 16\n | ibivibiv/math_instruct | |
Is 38443 prime?\n | False\n | ibivibiv/math_instruct | |
What is next in 18114, 18158, 18268, 18474, 18806?\n | 19294\n | ibivibiv/math_instruct | |
In base 12, what is -2 - 9762?\n | -9764\n | ibivibiv/math_instruct | |
Let h(a) = a**3 - 15*a**2 - 8*a. Let w be h(9). Let g = w + 352. Find the common denominator of (2 + g/100)*2 and -81/2.\n | 50\n | ibivibiv/math_instruct | |
Let r(o) = 325*o + 1147. Calculate r(0).\n | 1147\n | ibivibiv/math_instruct | |
Add -1656 and -497671389086.\n | -497671390742\n | ibivibiv/math_instruct | |
Let 1212/5 - 27/5*h**2 + 5448/5*h = 0. What is h?\n | -2/9, 202\n | ibivibiv/math_instruct | |
Calculate (51/(306/(-16)))/((-7)/39*38/(-133)).\n | -52\n | ibivibiv/math_instruct | |
Solve 0 = 16156*g - 16195*g - 936 for g.\n | -24\n | ibivibiv/math_instruct | |
What is the closest to -0.1 in 9, 4/13, 0.2?\n | 0.2\n | ibivibiv/math_instruct | |
Let l(n) = -2*n + 3. Let f be l(5). Let p(g) = -g**3 - 7*g**2 - g - 7. Let b be p(f). Suppose 3*y + 10753 = 5*q, 4*q + b*y = -5*y + 8632. Is q composite?\n | False\n | ibivibiv/math_instruct | |
Let b(g) = 2*g**2 - 5*g + 17. Let n(i) = 24*i - 152 + 15 - 52*i. Let k be n(-5). Let m(d) = -d**2 + 2*d - 8. Calculate k*b(r) + 7*m(r).\n | -r**2 - r - 5\n | ibivibiv/math_instruct | |
Let g(y) = -11*y - 72. Let t be g(4). Which is bigger: t or -115?\n | -115\n | ibivibiv/math_instruct | |
Which is greater: -7/117779 or 0?\n | 0\n | ibivibiv/math_instruct | |
Let o(y) = 3*y - 1. Let b be o(1). Suppose 0 = -b*j - 3*j + m + 153, -4*j + 3*m + 129 = 0. Is j a multiple of 15?\n | True\n | ibivibiv/math_instruct | |
Let y be -5 - (-1 - 1 - 0). Let f(r) = -r - 3. Let o be f(y). Solve 4*a = -o*a + 12 for a.\n | 3\n | ibivibiv/math_instruct | |
Solve -6*m**4 - 98*m**2 + 78*m**2 + 11*m**3 + 484*m**3 - 5820*m - 95*m**2 - 1440 - 14*m**4 = 0 for m.\n | -3, -1/4, 4, 24\n | ibivibiv/math_instruct | |
Is 3163 a composite number?\n | False\n | ibivibiv/math_instruct | |
Let n = 10.46 + -11. Let k = -3.66 + n. Let b = k + 4.1996. Round b to three decimal places.\n | 0\n | ibivibiv/math_instruct | |
Calculate 0 divided by -2357096.\n | 0\n | ibivibiv/math_instruct | |
Evaluate 7 - (11 + -45 - -88).\n | -47\n | ibivibiv/math_instruct | |
What is the hundred thousands digit of 1084640?\n | 0\n | ibivibiv/math_instruct | |
Suppose 0 = 5*b + 2*z - 1, 0 = 3*b + z - 0 - 1. Is b less than -20/137?\n | False\n | ibivibiv/math_instruct | |
List the prime factors of 3958.\n | 2, 1979\n | ibivibiv/math_instruct | |
Suppose -5*q + 358 = -517. Let c(l) = l**2 + 176*l + 5357. What is the remainder when q is divided by c(-137)?\n | 7\n | ibivibiv/math_instruct | |
Let t be -1*(3/(-9))/(-1). Let y be (-170)/(-24) + (-7 - 996/(-144)). Which is smaller: y or t?\n | t\n | ibivibiv/math_instruct | |
Collect the terms in -77 + 313 - 40*d**2 - 77 - 81 - 73.\n | -40*d**2 + 5\n | ibivibiv/math_instruct | |
Solve 8*u = -u - 27 for u.\n | -3\n | ibivibiv/math_instruct | |
Suppose 52 = -6*z - 134. Let x be (0 - z/(-2))*2. What is the least common multiple of 16 and 1 + 74/4 - x/62?\n | 80\n | ibivibiv/math_instruct | |
Put 9, 6, -3175 in decreasing order.\n | 9, 6, -3175\n | ibivibiv/math_instruct | |
Sort -44, -6, 4, -2, -1 in increasing order.\n | -44, -6, -2, -1, 4\n | ibivibiv/math_instruct | |
Let m = -48.992232898 - 0.007810102. Let a = m - -49. Round a to 5 decimal places.\n | -0.00004\n | ibivibiv/math_instruct | |
Calculate -22 + -134 + 62 + -19.\n | -113\n | ibivibiv/math_instruct | |
Calculate -8220 divided by 822.\n | -10\n | ibivibiv/math_instruct | |
Let o = 22.77 + -23. Which is bigger: 3 or o?\n | 3\n | ibivibiv/math_instruct | |
What is (6 - 7) + ((-9)/7)/(-1)?\n | 2/7\n | ibivibiv/math_instruct | |
Simplify ((r**0*r)**(-20)*r**(-5)/(r**(2/3)/r*r))/((r/r**(-5/3)*r**(-2/25))/(r/(r*(r/(r/r**(-2))*r)/r)*r/r**2)) assuming r is positive.\n | r**(-2044/75)\n | ibivibiv/math_instruct | |
Suppose -5*m + 9 + 16 = 0. List the prime factors of m.\n | 5\n | ibivibiv/math_instruct | |
Suppose -392 - 268 = -2*z. What is the common denominator of 46/48 + (z/40 - 8) and -113/30?\n | 120\n | ibivibiv/math_instruct | |
What is -3 (base 6) in base 9?\n | -3\n | ibivibiv/math_instruct | |
Let s = 0.018 + -14.018. Let u = 1271969502.99999998 + -1271969517. Let i = s - u. What is i rounded to 7 dps?\n | 0\n | ibivibiv/math_instruct | |
Expand -5*i - 6*i + i + 3*i - 4*i + 0*i + (i + i - i)*(1 + 1 - 4) - 6*i + 2*i + 2*i - 2*i + 3*i - 3*i + 100*i - 235 + 2*i + 233.\n | 85*i - 2\n | ibivibiv/math_instruct | |
Calculate -2160891.97 - -130679.\n | -2030212.97\n | ibivibiv/math_instruct | |
Expand (0*r + 0*r + r)*(4*r**4 - 3*r**4 + r**4) + 9*r**5 + 0*r**5 - 2*r**5.\n | 9*r**5\n | ibivibiv/math_instruct | |
Let o(m) = 6*m**3 + 3*m**2 - 3*m. Let t be o(2). Let f = t - 24. Calculate the least common multiple of f and 24.\n | 120\n | ibivibiv/math_instruct | |
3086 (base 15) to base 16\n | 280b\n | ibivibiv/math_instruct |
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