instruction_seed stringlengths 5 2.9k | response_seed stringlengths 3 9.55k | input stringclasses 1
value | _source stringclasses 1
value |
|---|---|---|---|
Suppose -45 = 5*g - 60. Solve 0*q = 5*b - 2*q - 13, 2*b + g*q = -10 for b.\n | 1\n | ibivibiv/math_instruct | |
Let v(q) = 3 + 6884*q - 162*q**3 - 7*q**2 + 163*q**3 - 6890*q. Determine v(8).\n | 19\n | ibivibiv/math_instruct | |
Let i = -111 - -143. Suppose i*a - 42*a + 10 = 0. Sort -2, -27, -4, a.\n | -27, -4, -2, a\n | ibivibiv/math_instruct | |
Round -0.000002778 to 6 dps.\n | -0.000003\n | ibivibiv/math_instruct | |
Let b(r) = 5*r**3 + 273*r**2 - 431*r - 2187. Calculate b(-56).\n | -3\n | ibivibiv/math_instruct | |
What is the hundreds digit of 21151951?\n | 9\n | ibivibiv/math_instruct | |
Let n be 4/(-6)*(-12)/(-8). Let r be 2*n - (-3 - -1). Let t = -8 + 5. Which is the nearest to -1? (a) 5 (b) t (c) r\n | c\n | ibivibiv/math_instruct | |
What comes next: 808578, 807932, 807286?\n | 806640\n | ibivibiv/math_instruct | |
What is 216385 to the power of 1/5, to the nearest integer?\n | 12\n | ibivibiv/math_instruct | |
Is 2505/11 < 227?\n | False\n | ibivibiv/math_instruct | |
Find the common denominator of 31/170316 and 11/31374.\n | 1192212\n | ibivibiv/math_instruct | |
Let z(f) = -f + 13. Let m be z(8). Let j(d) be the third derivative of -d**6/120 + 7*d**5/60 - d**4/3 + d**3/2 + 4*d**2 + 542. Give j(m).\n | 13\n | ibivibiv/math_instruct | |
Let q(v) = 2*v - 1. Let d be q(1). Let m be -3*(d/3 - -1). Let u be (0 - -5)/(((-16)/(-12))/(24/(-18))). Sort u, 1, m in descending order.\n | 1, m, u\n | ibivibiv/math_instruct | |
Let v(m) = 1970*m**3 + m**2 + m - 1. Is 9 a factor of v(1)?\n | True\n | ibivibiv/math_instruct | |
-1 divided by -1423\n | 1/1423\n | ibivibiv/math_instruct | |
Simplify sqrt(17) - (-1 + sqrt(17))**2*-2 - (sqrt(2448) - (2*sqrt(2448) + sqrt(2448)) - sqrt(2448))**2.\n | -21996 - 3*sqrt(17)\n | ibivibiv/math_instruct | |
What is the eighth root of 43692747 to the nearest integer?\n | 9\n | ibivibiv/math_instruct | |
Convert 22 (base 12) to base 16.\n | 1a\n | ibivibiv/math_instruct | |
Calculate prob of picking 1 g and 2 j when three letters picked without replacement from jjgjjjjgjjgjjjgjjj.\n | 91/204\n | ibivibiv/math_instruct | |
Let r(y) = -y**3 + 24*y**2 - 3*y - 469. Give r(23).\n | -9\n | ibivibiv/math_instruct | |
Sum -4 and -34.11897.\n | -38.11897\n | ibivibiv/math_instruct | |
Three letters picked without replacement from {y: 2, x: 5, d: 8}. Give prob of picking 1 y and 2 x.\n | 4/91\n | ibivibiv/math_instruct | |
A system is described by the differential equation y' + 9y = 0.
Using the Fourier transform, calculate the frequency response of the system and determine if it is stable or unstable. | To find the frequency response of the system, we first need to take the Fourier transform of the given differential equation. The Fourier transform of y''(t) is (-jω)^2Y(ω) and the Fourier transform of y(t) is Y(ω), where Y(ω) is the Fourier transform of y(t) and ω is the angular frequency.
So, the Fourier transform o... | ibivibiv/math_instruct | |
Solve 0 = -97*b + 2*b + 10*b for b.\n | 0\n | ibivibiv/math_instruct | |
Simplify ((i**4/i)/(i/i**(-1/2)))/(i**(-2/19)/(i**(-6)/i)) assuming i is positive.\n | i**(-205/38)\n | ibivibiv/math_instruct | |
Let d(t) = 4*t**3 + t**2 - t + 1. Let z be d(1). Suppose 18 = z*l - 2. Solve 4*w + l*p + 14 = -w, 2*w = -5*p - 9 for w.\n | -2\n | ibivibiv/math_instruct | |
What is the hundred millions digit of 188565741?\n | 1\n | ibivibiv/math_instruct | |
Calculate prob of picking 1 g and 1 t when two letters picked without replacement from {k: 2, t: 2, l: 1, f: 2, g: 2, e: 3}.\n | 2/33\n | ibivibiv/math_instruct | |
Product of -2 and 2674.\n | -5348\n | ibivibiv/math_instruct | |
Let p(q) = 2*q**2. Let d(i) = -i**2 - 1. Let r(c) = -10*c**2 - 9. Let j(g) = -18*d(g) + 2*r(g). Calculate j(p(a)).\n | -8*a**4\n | ibivibiv/math_instruct | |
Let x(s) = -2*s**2 + 2*s - 2. Let l be x(-4). Let q be l/4*10*-1. What is the greatest common divisor of 21 and q?\n | 21\n | ibivibiv/math_instruct | |
Suppose 3*h**4/4 - 35505*h**3/2 + 418063275*h**2/4 + 6335020125*h = 0. What is h?\n | -60, 0, 11865\n | ibivibiv/math_instruct | |
Let s(z) = 1584*z**3 + 24*z**2 + 2051. Let l(t) = -1583*t**3 - 20*t**2 - 2051. Let g(x) = 6*l(x) + 5*s(x). Find the first derivative of g(f) wrt f.\n | -4734*f**2\n | ibivibiv/math_instruct | |
Calculate the greatest common divisor of 110 and 2166406.\n | 22\n | ibivibiv/math_instruct | |
Expand -2*f**5 + f**4 - f**4 - 1478*f**5 - 2299*f**5 - 1680*f**5 - f**5 + 1 - 1 + (3 - 1 - 3)*(-f**2 + f**2 - 2*f**5).\n | -5458*f**5\n | ibivibiv/math_instruct | |
What is the result of the following expression?
(95.6521 + -10.372) * -6.2469 | -532.7363 | ibivibiv/math_instruct | |
What is 171 minutes after 10:54 AM?\n | 1:45 PM\n | ibivibiv/math_instruct | |
What is the biggest value in -792, 4, 2.2?\n | 4\n | ibivibiv/math_instruct | |
What is the greatest common factor of 16 and 14512?\n | 16\n | ibivibiv/math_instruct | |
Does 8 divide 275952?\n | True\n | ibivibiv/math_instruct | |
Evaluate the expression 3(2x + 5) - 4(3x - 2) when x = 4. | First, we will substitute the value of x into the expression:
3(2(4) + 5) - 4(3(4) - 2)
Now, we will perform the operations inside the parentheses:
3(8 + 5) - 4(12 - 2)
Next, we will perform the addition and subtraction inside the parentheses:
3(13) - 4(10)
Now, we will perform the multiplication:
39 - 40
Final... | ibivibiv/math_instruct | |
In base 4, what is -110210 - 10313213?\n | -11030023\n | ibivibiv/math_instruct | |
What is 678 minutes before 12:45 AM?\n | 1:27 PM\n | ibivibiv/math_instruct | |
Product of -0.1228 and -53.\n | 6.5084\n | ibivibiv/math_instruct | |
If Javier spends 30 minutes outlining his speech and 28 more minutes writing than outlining, and also dedicates half as much time practicing as writing, what is the total amount of time he spends on his speech? | Javier spends 30 minutes outlining his speech.
He spends 28 more minutes writing than outlining, so he spends 30 + 28 = 58 minutes writing.
He dedicates half as much time practicing as writing, so he spends 58 / 2 = 29 minutes practicing.
The total amount of time he spends on his speech is 30 + 58 + 29 = 117 minutes.
#... | ibivibiv/math_instruct | |
Simplify ((c**(-2/7)/c)**4*((c*c/c**24)/c*c)/(c/(c/(c**(-18/11)/c)*c)))**(-26) assuming c is positive.\n | c**(47060/77)\n | ibivibiv/math_instruct | |
Let z be (4/5)/(312/60). Let n = -15 + 16. What is the nearest to n in 1, z, 2/21?\n | 1\n | ibivibiv/math_instruct | |
Solve -10*h = 14*h + 17*h + 2337 for h.\n | -57\n | ibivibiv/math_instruct | |
(6 - 0) + 14 + -13 - -6\n | 13\n | ibivibiv/math_instruct | |
Let l(i) = -412*i**3 + 2*i**2 + i. Let n be l(-1). Let b = -197 - n. Round b to the nearest one hundred.\n | -600\n | ibivibiv/math_instruct | |
Let k = 10 + 26. Suppose -40*h = -39*h - k. Let r(u) = 5*u**2 + 4*u + 5. Calculate the remainder when r(-4) is divided by h.\n | 33\n | ibivibiv/math_instruct | |
What is the highest common divisor of 8355 and 23310?\n | 15\n | ibivibiv/math_instruct | |
Let f(a) = -a**3 - 5*a**2 - 7*a - 5. Let c(i) = -3*i**3 - i**2 - 10*i + 10. Let l be c(1). What is f(l)?\n | 7\n | ibivibiv/math_instruct | |
Let l(b) = -b - 2. Let w be l(3). What is the nearest to -0.1 in w, 3, 0.1?\n | 0.1\n | ibivibiv/math_instruct | |
-220814.35 * -0.5\n | 110407.175\n | ibivibiv/math_instruct | |
Let j(y) = -4*y**2 - 16*y - 2. Let m(c) = -5*c**2 - 18*c - 3. Calculate -6*j(r) + 5*m(r).\n | -r**2 + 6*r - 3\n | ibivibiv/math_instruct | |
Let s = 433 + -432.9999995. What is s rounded to five dps?\n | 0\n | ibivibiv/math_instruct | |
Let a be (-33)/6 + 4 - 4/(-8). What are the prime factors of 7 - (a + 4) - -643?\n | 647\n | ibivibiv/math_instruct | |
What is the common denominator of -7/4571258 and -115/13713774?\n | 13713774\n | ibivibiv/math_instruct | |
Expand -3*u + 3*u + u + (-5 + 2 + 2)*(-2*u + 0*u + 4*u) + u - 5*u + 3*u + (1 + 0 + 0)*(-u + 2*u - 2*u).\n | -3*u\n | ibivibiv/math_instruct | |
What is the second derivative of -20*c**3*n**2 - 17*c**3*n + 8*c**2*n**2 - 5*c**2*n - c**2 + 9*c*n**2 - n**2 + 74*n wrt n?\n | -40*c**3 + 16*c**2 + 18*c - 2\n | ibivibiv/math_instruct | |
Let v be (-12 - -21 - 12) + 18944/2. Suppose -11*n = -v - 6987. List the prime factors of n.\n | 2, 11, 17\n | ibivibiv/math_instruct | |
What is the thousands digit of 6575?\n | 6\n | ibivibiv/math_instruct | |
Evaluate 402/268*16/84.\n | 2/7\n | ibivibiv/math_instruct | |
Work out -27076 - 222326.\n | -249402\n | ibivibiv/math_instruct | |
What is -5 - (1 + -1 + 5) - -8?\n | -2\n | ibivibiv/math_instruct | |
Simplify ((j*j/(j*j**(-2/21)*j))/j*j*j/(j*j*j*(j/j**8)/j*j*j*j*j))**(1/18)*((j**(-2))**16)**(-5/4) assuming j is positive.\n | j**(7582/189)\n | ibivibiv/math_instruct | |
Suppose -3*y - 31*p = -27*p - 1629339, -3*y + p + 1629324 = 0. Is y composite?\n | True\n | ibivibiv/math_instruct | |
Suppose 0 = -4*q + 73 + 207. Is q a multiple of 5?\n | True\n | ibivibiv/math_instruct | |
Sort 13, -0.2, 1.7 in descending order.\n | 13, 1.7, -0.2\n | ibivibiv/math_instruct | |
Let p(s) = -3*s - 5. Let t be p(-6). Let j = 10 - t. Let d = -5404/17 + 318. What is the closest to -2/5 in 4, d, j?\n | d\n | ibivibiv/math_instruct | |
Suppose 4*w**4 - 56*w**3/3 + 92*w**2/3 - 64*w/3 + 16/3 = 0. Calculate w.\n | 2/3, 1, 2\n | ibivibiv/math_instruct | |
What is the common denominator of -75/17066 and (-11)/20 - (378/(-567))/((-5)/3)?\n | 170660\n | ibivibiv/math_instruct | |
Solve 0 = u + 250 - 253 for u.\n | 3\n | ibivibiv/math_instruct | |
What is 3485.55 rounded to the nearest 1000?\n | 3000\n | ibivibiv/math_instruct | |
What is 5/4 of a litre in millilitres?\n | 1250\n | ibivibiv/math_instruct | |
Let h(b) = -40*b**3 - b**2 + 2*b - 2. Let f(u) = u**3 - u**2 + u - 1. Determine -2*f(w) + h(w).\n | -42*w**3 + w**2\n | ibivibiv/math_instruct | |
Is 147413 a prime number?\n | False\n | ibivibiv/math_instruct | |
Calculate the least common multiple of 664770 and 1462494.\n | 7312470\n | ibivibiv/math_instruct | |
Let z(p) = -7*p + 19*p - 11*p. Let r(j) = -2*j. Determine r(z(c)).\n | -2*c\n | ibivibiv/math_instruct | |
What is ((-6)/(-285))/(572/(-2717))?\n | -1/10\n | ibivibiv/math_instruct | |
b"What is the tth term of -497, -2031, -4589, -8171, -12777, -18407, -25061?\n" | -512*t**2 + 2*t + 13\n | ibivibiv/math_instruct | |
What is (8 - 4) + -21 - (9 + (25 - 23))?\n | -28\n | ibivibiv/math_instruct | |
Calculate the highest common divisor of 145486 and 66.\n | 22\n | ibivibiv/math_instruct | |
What is the next term in 46594, 46539, 46454, 46339, 46194, 46019?\n | 45814\n | ibivibiv/math_instruct | |
Express (-1 + 1 + 5*f**2)*((4*f + 4*f - 6*f)*(-2 + 0 + 0) + 3 - 3 - f + 22*f + 1502 - 1502) as s*f**2 + a*f + t*f**3 + o and give t.\n | 85\n | ibivibiv/math_instruct | |
Solve -5*f + 6*b - 65 = 0, -2*f + 181*b = 177*b + 50 for f.\n | 5\n | ibivibiv/math_instruct | |
What is the fifth biggest value in 0.1, 0.4, -1/7, 6/2525, -2/11?\n | -2/11\n | ibivibiv/math_instruct | |
What is the tens digit of 64874?\n | 7\n | ibivibiv/math_instruct | |
b"What is the yth term of 1543, 6415, 14611, 26131, 40975, 59143, 80635?\n" | 1662*y**2 - 114*y - 5\n | ibivibiv/math_instruct | |
Let u(h) = -h**3 + 50*h**2 - 72*h - 44. Is u(43) composite?\n | False\n | ibivibiv/math_instruct | |
What is the greatest common factor of 575 and 50?\n | 25\n | ibivibiv/math_instruct | |
Is 2113 a multiple of 18?\n | False\n | ibivibiv/math_instruct | |
Calculate 2/10 - 19/(-5).\n | 4\n | ibivibiv/math_instruct | |
Let h = -258 - 38. Let c = -205 - h. List the prime factors of c.\n | 7, 13\n | ibivibiv/math_instruct | |
In base 4, what is -1202001 - 10?\n | -1202011\n | ibivibiv/math_instruct | |
What is 2390 to the power of 1/2, to the nearest integer?\n | 49\n | ibivibiv/math_instruct | |
Let m = 4 + -8. Let h = -382.72 + 385.72. Which is the nearest to 3/7? (a) 1 (b) m (c) h\n | a\n | ibivibiv/math_instruct | |
Is (23 - 11) + 0 + -1 a multiple of 10?\n | False\n | ibivibiv/math_instruct | |
What is the value of 29 - 21 - 1475/175?\n | -3/7\n | ibivibiv/math_instruct |
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