instruction_seed stringlengths 5 2.9k | response_seed stringlengths 3 9.55k | input stringclasses 1
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Let u = 229681/180 + -1276. Let g(a) be the third derivative of -u*a**5 + 1/18*a**3 + 0*a + 0*a**4 - a**2 + 0. Let g(w) = 0. Calculate w.\n | -1, 1\n | ibivibiv/math_instruct | |
Let z = -0.61 + 0.01. Let p = z + 0.1. Suppose 3*t - 3 + 10 = 2*i, t = -3. Which is the second smallest value? (a) -2/7 (b) p (c) i\n | b\n | ibivibiv/math_instruct | |
Let f = 1029069.098104958 - 7663.088104578. Let x = 1021406 - f. Let q = x - -0.01. What is q rounded to 7 dps?\n | -0.0000004\n | ibivibiv/math_instruct | |
In base 14, what is -12b + -1?\n | -12c\n | ibivibiv/math_instruct | |
Suppose w - 3 - 1 = 0. Let t be (w/12)/(-1)*6. Let i = 1 + 0. Put 5, i, t in decreasing order.\n | 5, i, t\n | ibivibiv/math_instruct | |
Let -o**2/7 + 20*o/7 + 3 = 0. Calculate o.\n | -1, 21\n | ibivibiv/math_instruct | |
Let n(s) be the third derivative of -s**5/30 + 4*s**2. Let d(r) be the first derivative of r**3/3 + 2*r**2 - 100. Give n(d(z)).\n | -2*z**4 - 16*z**3 - 32*z**2\n | ibivibiv/math_instruct | |
What is the smallest common multiple of 4 and 1284963?\n | 5139852\n | ibivibiv/math_instruct | |
Write an educational piece suited for college students related to the following text snippet:
"What is the answer of this equation?
What is the answer(s) of this equation? ($w$ is a complex number.)
$$\frac{w + \bar{w}}{w - \bar{w}} = -w^2$$
-
...and $\omega$ is supposed to be what? – Ｊ. Ｍ. Jul 23 '11 at 17:30
Are ... | Let us begin by clarifying the given equation and addressing some of the comments from the original post. We are asked to solve the following equation for the complex variable $w$:
$$\frac{w + \bar{w}}{w - \bar{w}} = -w^2\qquad(\star)$$
where $\bar{w}$ denotes the conjugate of $w$. It seems there was some confusion ... | ibivibiv/math_instruct | |
What is 3 (base 16) in base 13?\n | 3\n | ibivibiv/math_instruct | |
What is the thousands digit of 9605020?\n | 5\n | ibivibiv/math_instruct | |
What is the closest to 2 in 181, 17, -2/19?\n | -2/19\n | ibivibiv/math_instruct | |
Simplify (sqrt(108)/(sqrt(36)/sqrt(3))*-2*-2)/((sqrt(24) - sqrt(72)/sqrt(3)*2)/(4*sqrt(8)*2)).\n | -32*sqrt(3)\n | ibivibiv/math_instruct | |
Collect the terms in 4466*u**2 - 4466*u**2 + 41 + 64*u - 4*u**3 - 64*u.\n | -4*u**3 + 41\n | ibivibiv/math_instruct | |
Collect the terms in j - 10*j + j - 14*j.\n | -22*j\n | ibivibiv/math_instruct | |
Let s(b) be the second derivative of 2*b + 1/10*b**5 + 0*b**3 + 0*b**4 + 5*b**2 + 0. Find the first derivative of s(z) wrt z.\n | 6*z**2\n | ibivibiv/math_instruct | |
What is the value of $z^2$ if $z = 3 + 4i$ (where $i^2 = -1$)? | We can substitute $z = 3 + 4i$ into the expression $z^2$ to find:
$z^2 = (3 + 4i)^2$
Expanding, we get:
$z^2 = 3^2 + 2(3)(4i) + (4i)^2$
Simplifying, we have:
$z^2 = 9 + 24i - 16$
Combining like terms, we get:
$z^2 = -7 + 24i$
Therefore, $z^2 = \boxed{-7 + 24i}$.
The answer is: -7+24i | ibivibiv/math_instruct | |
What is 474 minutes after 7:47 PM?\n | 3:41 AM\n | ibivibiv/math_instruct | |
What is the result of the following expression?
77.725 + 97.534 | 175.2590 | ibivibiv/math_instruct | |
Is 14224328717 prime?\n | False\n | ibivibiv/math_instruct | |
2*1/(-2) - (-17)/(85/40)\n | 7\n | ibivibiv/math_instruct | |
Which is the nearest to -1/4? (a) -4 (b) 3/7 (c) 4 (d) 5\n | b\n | ibivibiv/math_instruct | |
Which is the closest to -1/2? (a) -2 (b) 28 (c) 2\n | a\n | ibivibiv/math_instruct | |
Express 7 - 8*h - 6 - 1 in the form o*h + t and give o.\n | -8\n | ibivibiv/math_instruct | |
Which is the fourth smallest value? (a) -54 (b) 4 (c) -67.3 (d) 3\n | b\n | ibivibiv/math_instruct | |
What comes next: 130, 254, 376, 496, 614?\n | 730\n | ibivibiv/math_instruct | |
Let l be 6*-1*4/6. List the prime factors of l/(-6) + (-427)/(-21).\n | 3, 7\n | ibivibiv/math_instruct | |
What is (-82)/(-6)*(-2574)/572*10/15?\n | -41\n | ibivibiv/math_instruct | |
What are the prime factors of 2101?\n | 11, 191\n | ibivibiv/math_instruct | |
Solve 19*l = -24*l + 172 for l.\n | 4\n | ibivibiv/math_instruct | |
What is 354 minutes after 8:16 AM?\n | 2:10 PM\n | ibivibiv/math_instruct | |
What is -1125446 (base 7) in base 3?\n | -21011200202\n | ibivibiv/math_instruct | |
Collect the terms in 8 - u + 3 + 3 + 3.\n | -u + 17\n | ibivibiv/math_instruct | |
-5*-0.025\n | 0.125\n | ibivibiv/math_instruct | |
Calculate -2408 + 2422 + (-45 - 2).\n | -33\n | ibivibiv/math_instruct | |
Sort -1, 33, -3, 11, 3, -14 in increasing order.\n | -14, -3, -1, 3, 11, 33\n | ibivibiv/math_instruct | |
What is the second derivative of 7*d + 13*d**2 - 4*d**2 - 3*d - 26 - 6*d**2 + 29*d**2 + 3*d**4 wrt d?\n | 36*d**2 + 64\n | ibivibiv/math_instruct | |
When listing the integers from 1 to a certain number, the digit 3 appears 300 times. What is that number? | To solve this problem, we need to count how many times the digit 3 appears in each position (ones, tens, hundreds, etc.) as we list the integers from 1 up to a certain number.
Let's start by considering the ones place. The digit 3 will appear once every 10 numbers (3, 13, 23, 33, 43, 53, 63, 73, 83, 93). So for every ... | ibivibiv/math_instruct | |
-70 divided by 2576\n | -5/184\n | ibivibiv/math_instruct | |
Martha starts with 76.0 cards. She gives 3.0 more to Emily. How many cards does Martha end with? | Martha starts with 76.0 cards and gives away 3.0 cards to Emily. To find out how many cards Martha ends with, we subtract the number of cards she gives away from the number of cards she starts with:
76.0 cards - 3.0 cards = 73.0 cards
Martha ends with 73.0 cards. | ibivibiv/math_instruct | |
Solve -1884 = -220709*h + 219767*h for h.\n | 2\n | ibivibiv/math_instruct | |
Let q = -476 - -822. Let z = -347 + q. What is the smallest value in 7, 5, 4, z?\n | z\n | ibivibiv/math_instruct | |
Solve 6482*u + 285 = 6463*u for u.\n | -15\n | ibivibiv/math_instruct | |
What is the value of (-72)/126*7/10?\n | -2/5\n | ibivibiv/math_instruct | |
Let d = 0.3 - 0.2. Suppose -2*r + 2 = -2. What is the closest to d in -2, 0.2, r?\n | 0.2\n | ibivibiv/math_instruct | |
Let n(f) = 4*f**2 - 4*f + 8. Let a = -7 - -14. Let w be n(a). Suppose -2 = -3*z - 5, -w = -3*y - z. Is y prime?\n | True\n | ibivibiv/math_instruct | |
Let v(s) = s**2 + 55*s + 206. List the prime factors of v(-4).\n | 2\n | ibivibiv/math_instruct | |
Let x(o) = 2*o**2. Let a(k) = 116*k. What is x(a(s))?\n | 26912*s**2\n | ibivibiv/math_instruct | |
Solve 0 = 4*r + 4, 5*x - 10*x + 38 = 4*r + 2 for x.\n | 8\n | ibivibiv/math_instruct | |
Collect the terms in -15698*m - 14783*m + 1821*m.\n | -28660*m\n | ibivibiv/math_instruct | |
Simplify (((b*b**(1/5))/b)**(3/14))**(7/6)/(((b**6/b)/(b/(b*(b**6*b)/b)*b))/(b**(-1/3)*b)**(17/2)) assuming b is positive.\n | b**(-257/60)\n | ibivibiv/math_instruct | |
Evaluate 1 + (-18 - (-10 + 0 - -1)) + 16.\n | 8\n | ibivibiv/math_instruct | |
Suppose 6 = -2*o, -4*r - 24 = -0*r - 4*o. Let p = r + 11. What is the first derivative of -3*s - p*s + 2*s - 1 wrt s?\n | -3\n | ibivibiv/math_instruct | |
In base 5, what is -4201003 + -30212?\n | -4231220\n | ibivibiv/math_instruct | |
(646/57 - 12)/((-5)/30 + 2)\n | -4/11\n | ibivibiv/math_instruct | |
Simplify ((sqrt(33) - (sqrt(33) + (sqrt(33) - ((sqrt(33) + (sqrt(33) - sqrt(33)*-2) - sqrt(33)) + sqrt(33)))))/sqrt(3))**2 + sqrt(110)/(2*sqrt(10)) + 3.\n | sqrt(11)/2 + 102\n | ibivibiv/math_instruct | |
What is the ten thousands digit of 1865311085?\n | 1\n | ibivibiv/math_instruct | |
What is -3*1 + (-8)/42*-15?\n | -1/7\n | ibivibiv/math_instruct | |
If two positive numbers are in the ratio 1 / 6 : 1 / 5, by what percent is the second number more than the first? | Lets denote the first positive number as A and the second positive number as B. According to the given ratio, we have:
A / B = 1/6 / 1/5
To compare the two numbers, we need to find a common denominator for the fractions. The common denominator for 6 and 5 is 30. So we can rewrite the fractions with the common denomin... | ibivibiv/math_instruct | |
Four letters picked without replacement from {c: 4, m: 15}. What is prob of picking 1 c and 3 m?\n | 455/969\n | ibivibiv/math_instruct | |
What is 2310947645 to the power of 1/3, to the nearest integer?\n | 1322\n | ibivibiv/math_instruct | |
There are 6 people in the elevator with an average weight of some lbs. Another person enters the elevator, and increases the average weight to 151 lbs. The weight of the 7th person is 121 lbs. What was the initial average weight of the people in the elevator? | Lets denote the initial average weight of the 6 people in the elevator as \( A \) lbs.
The total weight of the 6 people before the 7th person enters is \( 6 \times A \).
When the 7th person, who weighs 121 lbs, enters the elevator, the total weight becomes \( 6A + 121 \).
Now there are 7 people in the elevator, and ... | ibivibiv/math_instruct | |
Let z be ((-2)/(-3))/((-4)/(-30)). Let l = -14 - -4. Let w = l - -14. Put -2, w, z in decreasing order.\n | z, w, -2\n | ibivibiv/math_instruct | |
Expand (-2*y + 2*y + y)*(-36 - 2 + 85)*(-2 + 3 - 3).\n | -94*y\n | ibivibiv/math_instruct | |
What is the next term in -62849, -62642, -62435, -62228, -62021?\n | -61814\n | ibivibiv/math_instruct | |
What is the third root of 3033185 to the nearest integer?\n | 145\n | ibivibiv/math_instruct | |
List the prime factors of 20883.\n | 3, 6961\n | ibivibiv/math_instruct | |
Let b(o) = o**3 - 18*o**2 - 17*o - 36. Calculate the smallest common multiple of b(19) and 37.\n | 74\n | ibivibiv/math_instruct | |
Let o(w) be the first derivative of -11*w**5/15 - 7*w**4/2 - 47*w**3/9 - 2*w**2 + 4*w/3 + 1185. Find u, given that o(u) = 0.\n | -2, -1, 2/11\n | ibivibiv/math_instruct | |
In base 4, what is 133 + 101200030?\n | 101200223\n | ibivibiv/math_instruct | |
Write an educational piece suited for college students related to the following text snippet:
"# Confidence interval for distance from center
We have a bivariate normal process where $X \sim N(\mu_x, \sigma), \, Y \sim N(\mu_y, \sigma)$, with no covariance.
$(\mu_x, \mu_y)$ are unknown.
(For convenience we can asser... | To address the problem of constructing a confidence interval for the random variable R(n), which represents the distance between the sample center and the true center in a bivariate normal distribution with zero covariance, we will first introduce some necessary statistical concepts and then apply them to this particu... | ibivibiv/math_instruct | |
Suppose -7*x**5 - 173*x**4 - 1301*x**3 - 2239*x**2 + 4908*x - 1188 = 0. What is x?\n | -11, -9, -6, 2/7, 1\n | ibivibiv/math_instruct | |
Suppose 82*q - 87*q - 34156 = -4*z, 0 = -2*q. What is the units digit of z?\n | 9\n | ibivibiv/math_instruct | |
Put 3, 2, -4, 5, -2, 1497 in ascending order.\n | -4, -2, 2, 3, 5, 1497\n | ibivibiv/math_instruct | |
Let o be (1/(-1) - -2)*0. Suppose o*n - 1 = 4*n - 3*p, 13 = 5*n + p. Calculate the least common multiple of 3 and n.\n | 6\n | ibivibiv/math_instruct | |
What are the prime factors of 628?\n | 2, 157\n | ibivibiv/math_instruct | |
What is prob of picking 2 p when two letters picked without replacement from ppppp?\n | 1\n | ibivibiv/math_instruct | |
Let v(x) be the second derivative of -11*x**3/6 - 2*x**2 - 15*x + 11. Let r(g) = 4*g. What is r(v(o))?\n | -44*o - 16\n | ibivibiv/math_instruct | |
What is the nearest to 0 in 0.16, -2/35, 0.5?\n | -2/35\n | ibivibiv/math_instruct | |
Let p(f) = 23*f + 649. Let g be p(-28). Solve -16*u = -g*u + 22 for u.\n | -2\n | ibivibiv/math_instruct | |
Round 2081.09488 to 1 dp.\n | 2081.1\n | ibivibiv/math_instruct | |
What is -10b00a3 (base 12) in base 9?\n | -6038046\n | ibivibiv/math_instruct | |
What is the units digit of 819?\n | 9\n | ibivibiv/math_instruct | |
Let s = 17 + -8. Suppose 0 = s*i - 124 - 65. Find the second derivative of -7*o**2 + i*o**2 - 13*o**2 - 13*o wrt o.\n | 2\n | ibivibiv/math_instruct | |
Rearrange 30*i**2 + 35 - 80*i**2 + 57*i**2 + 2*i + i - 2*i to g + c*i + p*i**2 and give g.\n | 35\n | ibivibiv/math_instruct | |
b"What is the uth term of -37208, -37247, -37284, -37319, -37352, -37383, -37412?\n" | u**2 - 42*u - 37167\n | ibivibiv/math_instruct | |
Calculate (975/(-52) - -4)*26/(-117)*18.\n | 59\n | ibivibiv/math_instruct | |
Let c(t) = 129*t**5 + 10*t**4 + 109*t**2 - 5*t. Let x(m) = -2*m**4 - m**2 + m. Let n(k) = -c(k) - 5*x(k). Find the third derivative of n(p) wrt p.\n | -7740*p**2\n | ibivibiv/math_instruct | |
What is the derivative of 156031*p*q - 16*p - 150 wrt q?\n | 156031*p\n | ibivibiv/math_instruct | |
Which is greater: -902 or -10?\n | -10\n | ibivibiv/math_instruct | |
Let l = -2.963 - 0.037. Let u be (12/(-20))/((-3)/15). Let v be 14*u/(-12) + 4. Which is the closest to 2? (a) l (b) v (c) 0.2\n | b\n | ibivibiv/math_instruct | |
Let i = -1 - -20. Suppose -10*g - i = -11*g. Is 8 a factor of g?\n | False\n | ibivibiv/math_instruct | |
What is the hundred thousands digit of 2023774?\n | 0\n | ibivibiv/math_instruct | |
Let h(v) = 25*v**3 - v. Let z be h(1). Suppose -4*m + z = -2*t, 2*m + 4*t + 3 = -5. What is the smallest common multiple of m and 4?\n | 4\n | ibivibiv/math_instruct | |
Suppose -2 = y, 4*h - 26 = -0*h - 3*y. Let p(a) = a + 9. Let u be p(-5). Calculate the highest common divisor of h and u.\n | 4\n | ibivibiv/math_instruct | |
Evaluate (-2)/(-2)*4408/1102.\n | 4\n | ibivibiv/math_instruct | |
What is the next term in -854, -855, -856?\n | -857\n | ibivibiv/math_instruct | |
What is the hundreds digit of 66783083?\n | 0\n | ibivibiv/math_instruct | |
Let b(w) = 1 - 16*w - 2 - 3 + 1. Let q(h) = h**2 - 4. Let x be q(0). Is 21 a factor of b(x)?\n | False\n | ibivibiv/math_instruct | |
Calculate the least common multiple of 10 and 92.\n | 460\n | ibivibiv/math_instruct |
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