instruction_seed stringlengths 5 2.9k | response_seed stringlengths 3 9.55k | input stringclasses 1
value | _source stringclasses 1
value |
|---|---|---|---|
Solve -5*t - 18 = -33 - 130 for t.\n | 29\n | ibivibiv/math_instruct | |
What is 929.512 years in centuries?\n | 9.29512\n | ibivibiv/math_instruct | |
Let b = -37 - -52. Calculate the greatest common divisor of b and 5.\n | 5\n | ibivibiv/math_instruct | |
Sort 2, -1.9, -0.05, -4, 9.5, 0.04 in descending order.\n | 9.5, 2, 0.04, -0.05, -1.9, -4\n | ibivibiv/math_instruct | |
Is -325/1441 greater than -0.4?\n | True\n | ibivibiv/math_instruct | |
Calculate (833/1904)/((-63)/(-180))*264/15.\n | 22\n | ibivibiv/math_instruct | |
Simplify (z/((z**(-4/5)*z)/z))/(z*z**(-11/4)*z)*z**(2/33)/(z*z*((z**16*z)/z*z)/z) assuming z is positive.\n | z**(-10157/660)\n | ibivibiv/math_instruct | |
Let l = 4042 + -3776. Is l a multiple of 14?\n | True\n | ibivibiv/math_instruct | |
Which is smaller: 2 or -120?\n | -120\n | ibivibiv/math_instruct | |
Calculate the common denominator of -43/106 and -39.\n | 106\n | ibivibiv/math_instruct | |
Solve 12553 = 16*f + 12681 for f.\n | -8\n | ibivibiv/math_instruct | |
Is -2/68307 greater than 1?\n | False\n | ibivibiv/math_instruct | |
Let o = -163 + 212. Suppose 26 = -5*d - 4. Let b = d - -16. What is the remainder when o is divided by b?\n | 9\n | ibivibiv/math_instruct | |
Work out -1141 * 0.\n | 0\n | ibivibiv/math_instruct | |
Is 5807 equal to 5809?\n | False\n | ibivibiv/math_instruct | |
Solve -k + 1 = -z, 5*k = 2*z - 12 - 1 for k.\n | -5\n | ibivibiv/math_instruct | |
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"Browse Questions
# If the sum $\; \large\frac{3}{1^{2}} + \large\frac{5}{1^{2} + 2^{2}} + \large\frac{7}{1^{2} + 2^{2} +3^{2}}+----+\;$ upto 20 terms is equal to $\;\large\frac{k}{21}\;$, then k is equal to :
$(a)\;120\qqua... | The given problem involves the summation of a series and finding the value of the constant k. To solve this problem, let's first understand the general term of the series and how it was derived.
The general term of a series is represented by Tn, where n denotes the position of the term in the sequence. For this parti... | ibivibiv/math_instruct | |
What is -28.4007661 rounded to zero decimal places?\n | -28\n | ibivibiv/math_instruct | |
Beckett is 12 and is x years younger than Olaf, while Shannen is two years younger than Olaf. If Jack is five more than twice as old as Shannen, what is the sum of the ages of all 4 people?
If we know the answer to the above question is 71, what is the value of unknown variable x? | We know that Beckett is 12 and is x years younger than Olaf, so Olaf's age is 12 + x.
We also know that Shannen is two years younger than Olaf, so Shannen's age is (12 + x) - 2 = 10 + x.
We are given that Jack is five more than twice as old as Shannen, so Jacks age is 2(10 + x) + 5 = 20 + 2x + 5 = 25 + 2x.
The sum of t... | ibivibiv/math_instruct | |
Solve 2*j - 34 + 58 = -4*g, 0 = 4*j for g.\n | -6\n | ibivibiv/math_instruct | |
List the prime factors of 641748.\n | 2, 3, 53479\n | ibivibiv/math_instruct | |
Let s = 5 + 3. Suppose -3*u - 4*d = 0, 0*u = -4*u + 2*d - 22. Let a be (270/(-65) - u) + (-1566)/(-39). What is the highest common divisor of s and a?\n | 8\n | ibivibiv/math_instruct | |
What is prob of picking 1 y and 1 w when two letters picked without replacement from twyyttyttytwtywyyt?\n | 7/51\n | ibivibiv/math_instruct | |
Calculate the common denominator of 109/484 and -85/8832056.\n | 1068678776\n | ibivibiv/math_instruct | |
Suppose 0 = -2*x - 10, -4*a + 115 = 4*x - 7*x. Let r be a + 3/(3/(-2)). Suppose -3*j + 10 + r = 0. What is the highest common factor of 77 and j?\n | 11\n | ibivibiv/math_instruct | |
Find s such that -456*s**2 - 284/3*s**3 - 4*s**4 - 882*s + 2/3*s**5 - 612 = 0.\n | -3, -2, 17\n | ibivibiv/math_instruct | |
Let h be (-3022)/(-7) - (-68)/238. Suppose -12*c + 0*c = -h. Let u(j) = j**2 - 5*j + 10. What is the smallest common multiple of u(6) and c?\n | 144\n | ibivibiv/math_instruct | |
Let c(d) = -d**2 - 12*d - 1. Suppose -4*h + 0*h + 108 = 0. Let k = -39 + h. Let q be c(k). Which is smaller: 1/31 or q?\n | q\n | ibivibiv/math_instruct | |
What is the second derivative of d**2*z**5 - 1143*d**2*z + 2*d*z - 311*z**2 wrt z?\n | 20*d**2*z**3 - 622\n | ibivibiv/math_instruct | |
Let u be 0*(7 - 40/5). Suppose -2*z + 0 = -4*a + 2, u = -5*a + 5*z - 5. Sort 0.4, 2/23, a, 1/3 in increasing order.\n | 2/23, 1/3, 0.4, a\n | ibivibiv/math_instruct | |
What is the nearest to 0.1 in 0.4, -0.019, -0.8?\n | -0.019\n | ibivibiv/math_instruct | |
Suppose 3*n + 3*i - 9 = 0, n - 4*i = -0*i + 8. Let w(b) = -b**2 - 8*b - 1. Calculate the remainder when w(-6) is divided by n.\n | 3\n | ibivibiv/math_instruct | |
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"# Transformation of a vector operator
1. Sep 25, 2013
### andre220
1. The problem statement, all variables and given/known data
Calculate the result of the transformation of the vector operator $$\hat{V_{y}}$$ by rotation... | Vector operators, also known as differential operators, are mathematical constructs used in physics and engineering to describe operations involving vectors. They can be transformed through rotations, which results in changes to their coordinate representation while preserving their inherent properties. This concept i... | ibivibiv/math_instruct | |
Suppose 5*q + 2*b - 27 = -0*b, -2*b - 22 = -2*q. What is the remainder when 69 is divided by q?\n | 6\n | ibivibiv/math_instruct | |
Is 195 a factor of 1042393748?\n | False\n | ibivibiv/math_instruct | |
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"# Calculate $\frac13+\frac29+\frac{1}{27}+\frac{2}{81}+\frac{1}{243}+\frac{2}{729}+\ldots$
How can we calculate the formula for the following series?
$\frac13+\frac29+\frac{1}{27}+\frac{2}{81}+\frac{1}{243}+\frac{2}{729}+\l... | To analyze the given series, let us first understand what a series is. A series is the sum of the terms of a sequence, often denoted by the Greek letter sigma (Σ). The series presented to us is:
$$\frac13 + \frac29 + \frac{1}{27} + \frac{2}{81} + \frac{1}{243} + \frac{2}{729} + \dots$$
As mentioned in the text snipp... | ibivibiv/math_instruct | |
Collect the terms in 60*t**3 - 82*t**3 + 3*t + 19*t**3 - 3*t.\n | -3*t**3\n | ibivibiv/math_instruct | |
Let a = -1691.9 + 1692. What is the closest to a in 1, 1/10, 0.2, -3?\n | 1/10\n | ibivibiv/math_instruct | |
Let r(p) be the second derivative of p**5/20 - p**4 + 4*p**3 + 11*p**2 + 33*p. Let q be r(9). Let z = 0 + -4. Which is the nearest to 0? (a) 0.07 (b) q (c) z\n | a\n | ibivibiv/math_instruct | |
656 (base 13) to base 11\n | 8a7\n | ibivibiv/math_instruct | |
Is 28075991 composite?\n | False\n | ibivibiv/math_instruct | |
Let v = -473 - -494. Suppose -5*w + 28 = 2*g - 0*g, -3*w - v = -3*g. Calculate the highest common factor of g and 48.\n | 3\n | ibivibiv/math_instruct | |
Calculate -385764 divided by -1.\n | 385764\n | ibivibiv/math_instruct | |
Expand (20 - 2*i - 20)*(2 - 2 - 2*i**2).\n | 4*i**3\n | ibivibiv/math_instruct | |
Factor 4*w**2 - 848*w - 1712.\n | 4*(w - 214)*(w + 2)\n | ibivibiv/math_instruct | |
Let m = -0.02 + -0.04. Let x = 1.06 + m. Let v = x + -1.4. Which is the closest to 2/3? (a) v (b) -2 (c) -0.3\n | c\n | ibivibiv/math_instruct | |
Is 65 a factor of 20222995?\n | True\n | ibivibiv/math_instruct | |
Let h = 7091 - 7087. Let n = 5 - 3. Suppose r - n*a - 20 = 0, a = -r + h*a + 23. Is r a multiple of 3?\n | False\n | ibivibiv/math_instruct | |
Suppose 130 - 109 = 2*v - 3*q, 0 = 2*q + 14. Suppose -3/8*a**2 - 1/8*a**4 + 0*a - 1/2*a**3 + v = 0. Calculate a.\n | -3, -1, 0\n | ibivibiv/math_instruct | |
Calculate -3492.762*5.\n | -17463.81\n | ibivibiv/math_instruct | |
Calculate 0 divided by -1461.\n | 0\n | ibivibiv/math_instruct | |
Let l = -5906 + 442949/75. Which is smaller: 1 or l?\n | l\n | ibivibiv/math_instruct | |
Is 626741 a prime number?\n | True\n | ibivibiv/math_instruct | |
Three letters picked without replacement from nljjlnlnnnjnlnnjnnll. Give prob of sequence jll.\n | 1/57\n | ibivibiv/math_instruct | |
Convert 55.75411ng to micrograms.\n | 0.05575411\n | ibivibiv/math_instruct | |
Let u be 2/1*(-5 + (-471)/(-2)). Let x = u - 457. Let z be -1*1/(-9)*2. What is the nearest to -0.2 in x, 1/5, z?\n | 1/5\n | ibivibiv/math_instruct | |
Sorry, but its not possible to provide a precise numerical problem for the subtopic of Non-monotonic logic as it is a type of logic that deals with systems where the addition of new premises may invalidate previously drawn conclusions. It would require a statement or a scenario to apply non-monotonic logic, rather than... | That's correct. Non-monotonic logic is not a numerical problem but rather a type of logic used in artificial intelligence, reasoning, and knowledge representation. If you have a statement or scenario related to non-monotonic logic, Id be happy to help you analyze it. | ibivibiv/math_instruct | |
Four letters picked without replacement from iuuewweeewewiuele. What is prob of picking 1 i and 3 u?\n | 1/1190\n | ibivibiv/math_instruct | |
Suppose -3*q = -9, -2*g - 4*q + 48 = -2*q. Find the common denominator of 6/g*(-3 + -9) and (-40)/(-5) - (-73)/2.\n | 14\n | ibivibiv/math_instruct | |
Let i = 10 + -6. Let w(y) be the third derivative of 10*y**2 + 0 - 1/8*y**4 + 2/3*y**3 + 0*y. Determine w(i).\n | -8\n | ibivibiv/math_instruct | |
Let d be (52117/422)/(1/6). Which is smaller: d or 757?\n | d\n | ibivibiv/math_instruct | |
What is prob of sequence yqfi when four letters picked without replacement from {i: 3, f: 1, y: 3, q: 1, j: 2}?\n | 1/560\n | ibivibiv/math_instruct | |
Let j = 241 - 79. What is the remainder when j is divided by 61?\n | 40\n | ibivibiv/math_instruct | |
2 (base 15) to base 12\n | 2\n | ibivibiv/math_instruct | |
What is the third root of 4502 to the nearest integer?\n | 17\n | ibivibiv/math_instruct | |
What is the greatest common divisor of 230529970 and 22?\n | 22\n | ibivibiv/math_instruct | |
Suppose 3*f - 155 = 5*r, 4*r = 8*f - 3*f - 254. Suppose -3*m + 157 = -2*g, -5*m + g + f = -200. Round m to the nearest ten.\n | 50\n | ibivibiv/math_instruct | |
Which is greater: 3/13204 or -4?\n | 3/13204\n | ibivibiv/math_instruct | |
Let w(q) = -248*q**3 + 12*q**2 + 13*q + 1. Determine w(-1).\n | 248\n | ibivibiv/math_instruct | |
Suppose 15 = 23*a - 54. Suppose -4*r = -3*c - 25160, 5*r + a*c = 8*c + 31455. Is r a composite number?\n | False\n | ibivibiv/math_instruct | |
Let c(i) = 59 + 50 - 109 + i + i. Let b(u) = 8*u**2 + 2*u**2 - 4*u**2. Calculate b(c(p)).\n | 24*p**2\n | ibivibiv/math_instruct | |
How many minutes are there between 11:00 AM and 5:50 PM?\n | 410\n | ibivibiv/math_instruct | |
Simplify (sqrt(80) + 2 + sqrt(80))**2 - (sqrt(5) - (sqrt(55)/(sqrt(11) - -4*sqrt(11)) + sqrt(5))).\n | 161*sqrt(5)/5 + 324\n | ibivibiv/math_instruct | |
Let m be 2/3 - 7/(-3). Let s(n) = 13*n**3 - 17*n**2 + 8. Suppose -5*f - 4 = 26. Let l(w) = 7*w**3 - 9*w**2 + 4. Let r(i) = f*s(i) + 11*l(i). Calculate r(m).\n | -4\n | ibivibiv/math_instruct | |
Calculate the common denominator of 79/1872 and -74/10515.\n | 6561360\n | ibivibiv/math_instruct | |
84785150.5 - 114577\n | 84670573.5\n | ibivibiv/math_instruct | |
What is the least common multiple of 3216 and 201?\n | 3216\n | ibivibiv/math_instruct | |
Let 2*a**3/9 - 352052*a**2 - 3168470*a/9 = 0. What is a?\n | -1, 0, 1584235\n | ibivibiv/math_instruct | |
Let f(q) = -3*q**2 + 8*q + 6. Let v(j) = -5*j**2 + 16*j + 12. Let k(z) = z - 2. Let i be k(-5). Let y(o) = i*f(o) + 4*v(o). What is the units digit of y(-8)?\n | 6\n | ibivibiv/math_instruct | |
Rearrange 0*f - 2*f**3 - 2*f - 61 + f**3 - 14*f**4 + 4*f + 13*f**4 to t*f**4 + a*f**3 + c*f**2 + p + g*f and give t.\n | -1\n | ibivibiv/math_instruct | |
Simplify -5*((2 + sqrt(48))*-5 + sqrt(48) + ((1*sqrt(48))**2 + sqrt(48) - sqrt(48))*-1).\n | 80*sqrt(3) + 290\n | ibivibiv/math_instruct | |
Evaluate (-2*(-3)/(-18))/(1/9).\n | -3\n | ibivibiv/math_instruct | |
What is three tenths of a hour in minutes?\n | 18\n | ibivibiv/math_instruct | |
8 (base 11) to base 12\n | 8\n | ibivibiv/math_instruct | |
Let r(y) be the second derivative of -2*y**2 + 1/15*y**6 - y**3 + 3/10*y**5 + 0 + 15*y + 1/6*y**4. Factor r(k).\n | 2*(k - 1)*(k + 1)**2*(k + 2)\n | ibivibiv/math_instruct | |
Let l = -7 - -4. Let f be -3*(35/12 + l). Let d = -0.02 + -3.98. What is the closest to f in d, 1/2, 5?\n | 1/2\n | ibivibiv/math_instruct | |
Let l = -7 + 7. Suppose l = -3*b + 16 + 2. Let s = -3 + b. Calculate the remainder when s is divided by 3.\n | 0\n | ibivibiv/math_instruct | |
Product of -7.6802 and 0.00692.\n | -0.053146984\n | ibivibiv/math_instruct | |
Let x = -3330 - -3340. What is the highest common factor of x and 35?\n | 5\n | ibivibiv/math_instruct | |
Convert 8357.109um to millimeters.\n | 8.357109\n | ibivibiv/math_instruct | |
Let s(n) = -n + 8. Let y be s(6). Let g = 399 - 391. Solve 4 = y*m - 0*m, -m - g = -5*k for k.\n | 2\n | ibivibiv/math_instruct | |
What is the value of 0 + 3 - ((-74 - -199) + -72)?\n | -50\n | ibivibiv/math_instruct | |
Ginger owns a flower shop, where she sells roses, lilacs, and gardenias. On Tuesday, she sold three times more roses than lilacs, and x% as many gardenias as lilacs. If she sold 10 lilacs, The total number of flowers sold on Tuesday is 45. What is the value of unknown variable x? | To solve this problem, we need to determine the value of x, which represents the percentage of gardenias sold compared to the number of lilacs sold.
Let's break down the information given:
Number of lilacs sold: 10
Number of roses sold: 3 times more than lilacs
Number of gardenias sold: x% as many as lilacs
Total numbe... | ibivibiv/math_instruct | |
Expand ((-4 + 1 + 4)*(0 - 2*j + 0) + j - 3*j + 0*j)*(608 + 232 + 281 - 120).\n | -4004*j\n | ibivibiv/math_instruct | |
Let t(r) = r**3 - 8*r**2 - 10*r + 11. Let g be -2*(2 + (-14)/4). Suppose v + j = 2 + 12, -5*v - g*j = -60. Let i be t(v). Which is greater: 3 or i?\n | 3\n | ibivibiv/math_instruct | |
Suppose 107 = 5*g - 4*x, -3*x + 86 = g + 4*g. Determine l, given that 23*l**2 + 4 - 7*l - g*l**2 - l + 0*l = 0.\n | 1\n | ibivibiv/math_instruct | |
Expand (-a**2 + a**2 - 2*a**2)*(-a + a - 9*a) - 2*a**3 + 2*a**3 - a**3 + (4*a + 0*a - 5*a)*(4*a**2 - 5*a**2 - a**2).\n | 19*a**3\n | ibivibiv/math_instruct | |
Does 120 divide 2928360?\n | True\n | ibivibiv/math_instruct | |
What is 3097 (base 11) in base 3?\n | 12121211\n | ibivibiv/math_instruct | |
Let x(b) = 425*b - 198. Let n be x(7). Is 4/((-8)/(-2))*n a prime number?\n | True\n | ibivibiv/math_instruct |
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