instruction_seed stringlengths 5 2.9k | response_seed stringlengths 3 9.55k | input stringclasses 1
value | _source stringclasses 1
value |
|---|---|---|---|
What is the lowest common multiple of 1430 and 47363420?\n | 520997620\n | ibivibiv/math_instruct | |
What is the value of 1/(-18)*53262/2959?\n | -1\n | ibivibiv/math_instruct | |
Calculate the highest common divisor of 175 and 10.\n | 5\n | ibivibiv/math_instruct | |
Calculate the common denominator of 99/4 and 10/(-15)*(-6)/(-264)*3.\n | 44\n | ibivibiv/math_instruct | |
How many centimeters are there in 487829.5 millimeters?\n | 48782.95\n | ibivibiv/math_instruct | |
Suppose -2*q**2 - 330*q + 332 = 0. What is q?\n | -166, 1\n | ibivibiv/math_instruct | |
Let k be (-6)/21*(-6 - 1). Suppose -k*u = -5*u + 210. Is u a multiple of 10?\n | True\n | ibivibiv/math_instruct | |
Let x = 10942 + -10900. Which is the closest to x? (a) -0.4 (b) -6/13 (c) 3/4 (d) -2/9\n | c\n | ibivibiv/math_instruct | |
Solve 30*f - 22*f - 24 = 0 for f.\n | 3\n | ibivibiv/math_instruct | |
Let m be (7*55/14)/((2/(-2))/(-2)). Solve 16 = -4*a + r, -2*a + m = -3*r + 53 for a.\n | -5\n | ibivibiv/math_instruct | |
Let s(g) = 4*g**3 - g**2 - g. Let b = -3 - -5. Suppose -t + b*t + 1 = 0. Let m be s(t). Put m, 4, 2 in ascending order.\n | m, 2, 4\n | ibivibiv/math_instruct | |
What are the prime factors of 36461275?\n | 5, 877, 1663\n | ibivibiv/math_instruct | |
Differentiate -1354*g**3*z + 82595*g**3 + 80*g**2 - 4025*z with respect to z.\n | -1354*g**3 - 4025\n | ibivibiv/math_instruct | |
What is 473 minutes after 5:05 AM?\n | 12:58 PM\n | ibivibiv/math_instruct | |
Let h = -23 + 41. What is the greatest common factor of h and 2?\n | 2\n | ibivibiv/math_instruct | |
Let p = -17.2 - -16. Let l = p - -0.2. Let h = -205262 - -205261.6. Which is the closest to 1/4? (a) 2/11 (b) l (c) h\n | a\n | ibivibiv/math_instruct | |
Convert 1783.767 millimeters to meters.\n | 1.783767\n | ibivibiv/math_instruct | |
Which is the second biggest value? (a) 2/13 (b) -0.4 (c) 2/3 (d) -31\n | a\n | ibivibiv/math_instruct | |
Let s(y) = -30*y**3 - 5*y**2 - 7*y + 1. Let a(m) = 5029*m**2 - 1 + 10*m + 45*m**3 - 10026*m**2 + 5004*m**2. Calculate -5*a(u) - 7*s(u).\n | -15*u**3 - u - 2\n | ibivibiv/math_instruct | |
Two letters picked without replacement from kkkjkpkejjpjakj. What is prob of sequence pk?\n | 2/35\n | ibivibiv/math_instruct | |
Rearrange (-2*i - 1 + 1)*(-3 - 5 + 4) + 2*i - i + 1 + 2 to t*i + k and give t.\n | 9\n | ibivibiv/math_instruct | |
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"# complex number to polar form calculator with steps
There is another way by which we can represent the complex numbers. Products and Quotients of Complex Numbers; Graphical explanation of multiplying and dividing complex nu... | When dealing with complex numbers, there are two main ways to represent them: rectangular form and polar form. Rectangular form, also known as standard form, represents a complex number as a + bi where a and b are real numbers and i is the imaginary unit, defined as i²=-1. On the other hand, polar form represents a co... | ibivibiv/math_instruct | |
What is the least common multiple of 140 and 112?\n | 560\n | ibivibiv/math_instruct | |
What are the prime factors of 1953?\n | 3, 7, 31\n | ibivibiv/math_instruct | |
How many minutes are there between 2:46 PM and 5:39 PM?\n | 173\n | ibivibiv/math_instruct | |
What is the nearest to -1/3 in -1, 0.4, -1/3, 18?\n | -1/3\n | ibivibiv/math_instruct | |
What is 0.0000865 rounded to five decimal places?\n | 0.00009\n | ibivibiv/math_instruct | |
Let i(r) = -r - 2. Suppose 0 = -5*a - 3*v - 19, 1 = 5*a + 4*v + 18. Let m be i(a). Solve 0 = -5*n + 2*n + m for n.\n | 1\n | ibivibiv/math_instruct | |
Three letters picked without replacement from uruuruuukkkkuuuruuur. What is prob of picking 2 k and 1 u?\n | 6/95\n | ibivibiv/math_instruct | |
Is 239234 a composite number?\n | True\n | ibivibiv/math_instruct | |
b"What is the vth term of -874698, -3498841, -7872424, -13995447, -21867910, -31489813?\n" | -874720*v**2 + 17*v + 5\n | ibivibiv/math_instruct | |
Does 44 divide 41182758?\n | False\n | ibivibiv/math_instruct | |
Let s = 1.1 - 1.05. Let o = -0.25 + s. What is the closest to 2 in -0.4, o, 0.3?\n | 0.3\n | ibivibiv/math_instruct | |
How many grams are there in 12/25 of a kilogram?\n | 480\n | ibivibiv/math_instruct | |
Let b(c) = c**3 - 1321*c**2 - 1773*c + 2342128. Give b(1321).\n | -5\n | ibivibiv/math_instruct | |
Let p(b) = -b**3 + 4*b**2 + 3*b - 5. Let s = -37 + 41. Calculate p(s).\n | 7\n | ibivibiv/math_instruct | |
Simplify (((b/(b/(b/(b*(b/(b/(b*b**(-3)))*b)/b*b))))/b**3)/(b**0/b)**(-42))/(b**8/b*b*b*b**(4/9))**(-8/11) assuming b is positive.\n | b**(-3676/99)\n | ibivibiv/math_instruct | |
Let k(x) = -x**3 + 152*x**2 - 2036*x - 2606. What is k(137)?\n | -3\n | ibivibiv/math_instruct | |
Add together 5.0662 and -5174716.\n | -5174710.9338\n | ibivibiv/math_instruct | |
What is the result of the following expression?
61.032 - 39.682 | 21.3500 | ibivibiv/math_instruct | |
What is the next term in -61, -360, -1147, -2662, -5145?\n | -8836\n | ibivibiv/math_instruct | |
What is the result of the following expression?
(7.599 + 19.465) / 9.664 | 2.800 | ibivibiv/math_instruct | |
Collect the terms in 6*o**3 + 13*o**3 + 16*o**3 + o**3.\n | 36*o**3\n | ibivibiv/math_instruct | |
-82293*2.442\n | -200959.506\n | ibivibiv/math_instruct | |
Let w(b) be the first derivative of 11*b - 11 - 1/3*b**3 + 3/2*b**2. What is the tens digit of w(0)?\n | 1\n | ibivibiv/math_instruct | |
What is 36532191 to the power of 1/5, to the nearest integer?\n | 33\n | ibivibiv/math_instruct | |
Let q = -39 + 27. Let f = q + 17. Which is the smallest value? (a) 6 (b) f (c) 3/8\n | c\n | ibivibiv/math_instruct | |
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"# Why doesn't universality imply existence?
I am currently learning the Lean proof assistant, and I had a hard time proving the following implication: $$\forall x, p (x) \implies \exists x,p(x)$$ I gave up after some time an... | The issue you encountered while working with the Lean proof assistant highlights a fundamental principle in mathematical logic known as the distinction between universally quantified statements and existentially quantified statements. Specifically, it challenges the intuition that the truth of a universal proposition ... | ibivibiv/math_instruct | |
List the prime factors of 342968075.\n | 5, 41, 334603\n | ibivibiv/math_instruct | |
Let f = -64.1 + 64. Sort -4, 0.1, 4, f.\n | -4, f, 0.1, 4\n | ibivibiv/math_instruct | |
In base 9, what is -7 + -1058?\n | -1066\n | ibivibiv/math_instruct | |
Expand (-646 + 996 + 1181)*(5*h**2 - 4*h**2 - 4*h**2) - 3*h**2 + 0 + 0.\n | -4596*h**2\n | ibivibiv/math_instruct | |
Determine a, given that -a**2/2 - 537*a/2 - 3150 = 0.\n | -525, -12\n | ibivibiv/math_instruct | |
Put -63, 0, -2, -68 in ascending order.\n | -68, -63, -2, 0\n | ibivibiv/math_instruct | |
Let u(o) = 4*o - 24. Let l be u(6). Solve j = -m + 4, 2*m = j + 2 - l for m.\n | 2\n | ibivibiv/math_instruct | |
Which is the nearest to -4336? (a) 0.2 (b) -0.5 (c) 5\n | b\n | ibivibiv/math_instruct | |
Let p = -0.125 + 0.425. Sort 2, p, 11/6 in decreasing order.\n | 2, 11/6, p\n | ibivibiv/math_instruct | |
Sort -3, -5, -3501903.\n | -3501903, -5, -3\n | ibivibiv/math_instruct | |
Sort -271, 1363, 1/4, -3/7, -0.5 in descending order.\n | 1363, 1/4, -3/7, -0.5, -271\n | ibivibiv/math_instruct | |
Collect the terms in 94 - 46*s + 36 - 16*s.\n | -62*s + 130\n | ibivibiv/math_instruct | |
What is the closest to -0.08 in 3/49, -2, 5, 0.5, -3/13?\n | 3/49\n | ibivibiv/math_instruct | |
Let y(r) = -17*r**2 + 60*r - 8. Let z(s) = 4*s**2 - 8*s + 2. Let o(k) = y(k) + 4*z(k). Let a = 33 + -19. List the prime factors of o(a).\n | 2, 7\n | ibivibiv/math_instruct | |
Let g(o) = -o**2 + 15454*o - 2356213. Give g(154).\n | -13\n | ibivibiv/math_instruct | |
Let m = 73873/16218 - -1/1802. Calculate the common denominator of m and 35/3.\n | 9\n | ibivibiv/math_instruct | |
Let l(u) = -338*u + 4029. Calculate l(11).\n | 311\n | ibivibiv/math_instruct | |
Express 37*f - 3*f**4 + 1 + 2*f**2 - 3*f**2 - 39*f as d*f**3 + k*f**4 + r*f**2 + j*f + z and give j.\n | -2\n | ibivibiv/math_instruct | |
Let i be (-2904)/10*150/12. Let j be i/(-4)*6400/48. What is j rounded to the nearest ten thousand?\n | 120000\n | ibivibiv/math_instruct | |
Let w(r) = 43*r - 24. Let j be w(5). Suppose -a + 65 = t, 3*a - 4*a - j = -3*t. List the prime factors of t.\n | 2\n | ibivibiv/math_instruct | |
What is next in -64765, -65126, -65487?\n | -65848\n | ibivibiv/math_instruct | |
Sort 1, 33, 65, 2, 8, -12, -2.\n | -12, -2, 1, 2, 8, 33, 65\n | ibivibiv/math_instruct | |
What is the common denominator of -59/148 and -101/70?\n | 5180\n | ibivibiv/math_instruct | |
What is prob of picking 4 w when four letters picked without replacement from {w: 6}?\n | 1\n | ibivibiv/math_instruct | |
(1 - 58) + 3168/(-67 + 163)\n | -24\n | ibivibiv/math_instruct | |
Put -149, 59, -606, 1, 3 in descending order.\n | 59, 3, 1, -149, -606\n | ibivibiv/math_instruct | |
What is -24423401 (base 5) in base 11?\n | -14a047\n | ibivibiv/math_instruct | |
Let s = 110.96 - 110.9. Put 1/2, 42, s in descending order.\n | 42, 1/2, s\n | ibivibiv/math_instruct | |
Solve 4*h + i = -20, -5*h - 10 = -i + 6 for h.\n | -4\n | ibivibiv/math_instruct | |
What is the next term in -3224, -3237, -3268, -3317, -3384?\n | -3469\n | ibivibiv/math_instruct | |
Let f = -33.99 + 34. Let o = f + -1.01. Let r be 4/14 - 52/(-14). What is the nearest to 0.1 in 5, o, r?\n | o\n | ibivibiv/math_instruct | |
What is prob of sequence bt when two letters picked without replacement from {b: 1, u: 4, d: 4, t: 1}?\n | 1/90\n | ibivibiv/math_instruct | |
Is 315 a factor of 407463?\n | False\n | ibivibiv/math_instruct | |
Which is the nearest to -1.4? (a) -4 (b) 5 (c) 1/2 (d) -2/7\n | d\n | ibivibiv/math_instruct | |
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"# Optimization - find two points on a curve with a common tangent line?
1. Jan 9, 2010
### therest
1. The problem statement, all variables and given/known data
Find two points on curve y=x4-2x2-x that have a common tangent... | To solve the optimization problem presented, let us first understand the key concept involved – determining the equation of a tangent line to a curve at a particular point. This will provide us with the foundation necessary to tackle the main question of identifying two points on the given curve with a common tangent ... | ibivibiv/math_instruct | |
Calculate the highest common divisor of 8 and 17896.\n | 8\n | ibivibiv/math_instruct | |
Suppose 0 = 12*f - 7*f - 3065. Is f a composite number?\n | False\n | ibivibiv/math_instruct | |
Let f(n) = 3*n**3 + n**2 - 1. Suppose -2*m + 0 = 2. Let r be f(m). Is 2*(441/(-6))/r a composite number?\n | True\n | ibivibiv/math_instruct | |
Let r(s) be the third derivative of 251*s**4/24 + 63*s**2 - 2*s + 18. Let a(q) = 2*q**2. Determine a(r(v)).\n | 126002*v**2\n | ibivibiv/math_instruct | |
Solve -3*f = 4*x - 11, 5*f - x + 1 = 2*x for f.\n | 1\n | ibivibiv/math_instruct | |
Is 110 a factor of 330?\n | True\n | ibivibiv/math_instruct | |
Suppose -5*w + 125 + 210 = 0. Differentiate -9 - 53*h**3 + 0 + w*h**3 with respect to h.\n | 42*h**2\n | ibivibiv/math_instruct | |
What is the biggest value in -9, -178, -2/7, -5?\n | -2/7\n | ibivibiv/math_instruct | |
Let x = -141 + 157. Differentiate 27 + 5*y**2 + x*y - 5*y**2 - 4*y**2 + 6*y**2 with respect to y.\n | 4*y + 16\n | ibivibiv/math_instruct | |
Let b(c) = -c**3 + 4*c**2 + c - 4. Let d be b(4). Suppose d = -5*n + 2*n + 39. What are the prime factors of n?\n | 13\n | ibivibiv/math_instruct | |
Collect the terms in -12 - 9*n + 33 - 21.\n | -9*n\n | ibivibiv/math_instruct | |
What are the prime factors of 1998053215?\n | 5, 399610643\n | ibivibiv/math_instruct | |
How many minutes are there between 10:28 AM and 3:21 PM?\n | 293\n | ibivibiv/math_instruct | |
Collect the terms in 5*s + 3*s - 11*s + 6*s.\n | 3*s\n | ibivibiv/math_instruct | |
triathlete dan runs along a 3 - mile stretch of river and then swims back along the same route . if dan runs at a rate of 10 miles per hour and swims at a rate of 6 miles per hour , what is his average rate for the entire trip in miles per minute ? Lets program in Python in the response. | n0 = 3.0
n1 = 10.0
n2 = 6.0
t0 = n0 + n0
t1 = n0 / n2
t2 = n0 / n1
t3 = t1 * 60.0
t4 = t2 * 60.0
t5 = t3 + t4
answer = t0 / t5
print(answer) | ibivibiv/math_instruct | |
Suppose 5*n - 15 = 0, 11 = 2*v + 3*n - 0. Is 7/10 at least v?\n | False\n | ibivibiv/math_instruct | |
Calculate prob of sequence okkk when four letters picked without replacement from kkokokokkkkkkkkkkkko.\n | 112/969\n | ibivibiv/math_instruct |
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