instruction_seed stringlengths 5 2.9k | response_seed stringlengths 3 9.55k | input stringclasses 1
value | _source stringclasses 1
value |
|---|---|---|---|
What is -0.00910417 rounded to 3 dps?\n | -0.009\n | ibivibiv/math_instruct | |
Factor w**2 - 15272*w + 56085415.\n | (w - 9127)*(w - 6145)\n | ibivibiv/math_instruct | |
Rearrange (1 - 1 + 1)*(u**4 - u**2 + u**2) + (-u**2 + u**2 - u**2)*(28*u + 2*u + 5*u)*(-3 - u + 3) to the form v*u**3 + l*u + f + c*u**2 + g*u**4 and give v.\n | 0\n | ibivibiv/math_instruct | |
Let z = -3 + 6. Suppose 4*h = 3*i - 11 + 44, -z = i. Suppose 0 = 17*f - 16*f + h. Let n(c) = -c**2 - 4*c + 7. Determine n(f).\n | -5\n | ibivibiv/math_instruct | |
b"What is the nth term of -24315834, -48631668, -72947502?\n" | -24315834*n\n | ibivibiv/math_instruct | |
Let v be (-56)/(-21) - 4/6. Suppose -d = -4*l + 8 + v, -4*d - 2*l + 50 = 0. What is the highest common divisor of 30 and d?\n | 10\n | ibivibiv/math_instruct | |
Solve -b = b, -10 = 2*w + b for w.\n | -5\n | ibivibiv/math_instruct | |
b"What is the zth term of -632187, -1264376, -1896563, -2528748?\n" | z**2 - 632192*z + 4\n | ibivibiv/math_instruct | |
Let f be 209/(-22)*(-1 - -2 - 3). Solve 25*j = -6 - f for j.\n | -1\n | ibivibiv/math_instruct | |
Rearrange -4*n**4 + 0*n**4 + 4*n**4 - n**4 + n**2 + n to d + h*n**4 + y*n**2 + f*n**3 + j*n and give h.\n | -1\n | ibivibiv/math_instruct | |
Let j(b) = 2*b**3 + 3*b**2 - 6*b + 8. Let i(f) be the third derivative of f**6/60 + f**5/30 - 5*f**4/24 + 7*f**3/6 - 82*f**2. Give 6*i(a) - 5*j(a).\n | 2*a**3 - 3*a**2 + 2\n | ibivibiv/math_instruct | |
List the prime factors of 9803.\n | 9803\n | ibivibiv/math_instruct | |
Which is smaller: -738726 or -738323?\n | -738726\n | ibivibiv/math_instruct | |
Let s = 962/595 - 2/119. What is the nearest to s in 1/3, -1/6, -1?\n | 1/3\n | ibivibiv/math_instruct | |
What is the tens digit of (0 - 1808725/(-85)) + 0 + 10/(-85)?\n | 7\n | ibivibiv/math_instruct | |
Let t(a) = 6*a + 8. Let z(c) = 5*c**3 - 2*c**2 + 1. Let n be z(1). Suppose -j = n*i + j - 46, 5*i - 50 = -j. Does 7 divide t(i)?\n | False\n | ibivibiv/math_instruct | |
Let t(b) = b**2 - b. Let k be t(-1). Let l(r) = r**2 - 8*r - 5. Let m be l(9). Suppose 0*w + m*w + 5*p = 14, 5*w - k*p = 1. What is the units digit of w?\n | 1\n | ibivibiv/math_instruct | |
Write an educational piece suited for college students related to the following text snippet:
"# Homework Help: Linear Algebra - Showing a Matrix is not Diagonalizable
1. Dec 11, 2011
### Rockoz
1. The problem statement, all variables and given/known data
Show that the matrix A is not diagonalizable. Explain your re... | To show that a matrix is not diagonalizable, we must prove that it does not have enough linearly independent eigenvectors for diagonalization. This can be done by using the following important theorem:
*An *nxn* matrix **A** is diagonalizable if and only if it has *n* linearly independent eigenvectors.*
Let's analyz... | ibivibiv/math_instruct | |
Which is the closest to -0.1? (a) -3 (b) -12/269 (c) 37 (d) 28/13 (e) 5\n | b\n | ibivibiv/math_instruct | |
What comes next: -122, -134, -160, -206, -278, -382?\n | -524\n | ibivibiv/math_instruct | |
In base 7, what is 2 - -6106?\n | 6111\n | ibivibiv/math_instruct | |
What is the value of (-9)/((-27)/21) + ((-2)/5)/((-14)/(-560))?\n | -9\n | ibivibiv/math_instruct | |
Suppose 4*k = 4*t + 12, -2*t + 3*k - 9 = -6*t. Which is smaller: t or 3/49?\n | t\n | ibivibiv/math_instruct | |
Calculate (-3)/21 - (2 - (-1057)/(-539)).\n | -2/11\n | ibivibiv/math_instruct | |
Is 23/263047 less than or equal to 1?\n | True\n | ibivibiv/math_instruct | |
-3.26*1\n | -3.26\n | ibivibiv/math_instruct | |
Let g = -4 - -1. Let l = g + 8. Calculate the least common multiple of l and 10.\n | 10\n | ibivibiv/math_instruct | |
Are -139/6 and -23 equal?\n | False\n | ibivibiv/math_instruct | |
Let u(y) = -4*y - 9. Let c be u(-2). Let j(g) = -g. Calculate j(c).\n | 1\n | ibivibiv/math_instruct | |
Collect the terms in 4517*a**2 + 4534*a**2 - 9045*a**2 - 89 + 89.\n | 6*a**2\n | ibivibiv/math_instruct | |
Let r(w) = -3 + 427*w**2 - 50*w - 853*w**2 + 425*w**2. What is the units digit of r(-25)?\n | 2\n | ibivibiv/math_instruct | |
Collect the terms in -72*c - 8 + 17 - 9.\n | -72*c\n | ibivibiv/math_instruct | |
Let m be (2 - -34)*(-2)/4. Suppose 6*r = 4*r - 28. Let z = r - m. Solve -6 = -z*n + n for n.\n | 2\n | ibivibiv/math_instruct | |
Evaluate (-33)/(-99)*(10 + 5 + -10).\n | 5/3\n | ibivibiv/math_instruct | |
What is the greatest common factor of 8720946 and 12?\n | 6\n | ibivibiv/math_instruct | |
Let m(n) be the third derivative of n**4/8 - n**3/2 + 9*n**2. Let b(w) = -7*w. Let c be b(0). Let j be 3 + 2/6*c. What is m(j)?\n | 6\n | ibivibiv/math_instruct | |
Collect the terms in -36*m + 15*m**2 + 103*m - 67*m.\n | 15*m**2\n | ibivibiv/math_instruct | |
Does 427 divide 911864?\n | False\n | ibivibiv/math_instruct | |
Let i(b) = b**3 + 7*b**2 - 3*b + 16. Is 37 a factor of i(-7)?\n | True\n | ibivibiv/math_instruct | |
Let k = 1.099 + -1.699. What is the biggest value in 2/15, -4/9, k?\n | 2/15\n | ibivibiv/math_instruct | |
Sort 3/11, -0.25, 4 in descending order.\n | 4, 3/11, -0.25\n | ibivibiv/math_instruct | |
Let c = 3331 + -3330.987625. What is c rounded to 4 dps?\n | 0.0124\n | ibivibiv/math_instruct | |
Simplify (2*(-1*sqrt(432) + sqrt(432))*-5 + (2*sqrt(300) - (sqrt(36)/sqrt(3))/sqrt(4)) + 0)**2.\n | 1083\n | ibivibiv/math_instruct | |
Let j(h) = 40*h**4 - 39*h**2 + 7*h + 7. Let m(c) = 20*c**4 - 20*c**2 + 3*c + 3. Let n(o) = 3*j(o) - 7*m(o). Find the third derivative of n(k) wrt k.\n | -480*k\n | ibivibiv/math_instruct | |
Expand (-64 + 43*l - 57 + 123)*(-1892*l + 60*l**4 + 1892*l).\n | 2580*l**5 + 120*l**4\n | ibivibiv/math_instruct | |
What are the prime factors of 5133325?\n | 5, 19, 101, 107\n | ibivibiv/math_instruct | |
What are the prime factors of 1533?\n | 3, 7, 73\n | ibivibiv/math_instruct | |
Let d(y) be the third derivative of -y**4/24 + y**3/3 + 7*y**2. Let i be d(2). Let r be (5 - i)*(-16)/(-20). Solve r*c = 3 - 19 for c.\n | -4\n | ibivibiv/math_instruct | |
Expand (3 + 6*q - 3)*(-740707*q + 740707*q - 1629*q**2).\n | -9774*q**3\n | ibivibiv/math_instruct | |
Let r = -220 - -1321/6. Suppose -u = 5*o - 0*u + 99, 82 = -4*o + 2*u. What is the second smallest value in r, o, 2?\n | r\n | ibivibiv/math_instruct | |
In base 12, what is -3 - 224?\n | -227\n | ibivibiv/math_instruct | |
What is the nearest to -0.03 in 9, 8, 2/1689, 1, -4/3, -0.5?\n | 2/1689\n | ibivibiv/math_instruct | |
What is the nearest to 12 in -3, 0.2, -468776?\n | 0.2\n | ibivibiv/math_instruct | |
Calculate the highest common factor of 101 and 1313.\n | 101\n | ibivibiv/math_instruct | |
Suppose 43*w**3 - 123*w + 39*w**3 + 26 - 125*w**3 + 42*w**3 + 35 + 63*w**2 = 0. Calculate w.\n | 1, 61\n | ibivibiv/math_instruct | |
Let n(l) = -11*l**3 + 7*l**2 + 7*l - 17. Let u(y) = -6*y**3 + 4*y**2 + 4*y - 8. Calculate 4*n(m) - 7*u(m).\n | -2*m**3 - 12\n | ibivibiv/math_instruct | |
Which is smaller: -1 or 2/1103747?\n | -1\n | ibivibiv/math_instruct | |
If $\sqrt{2\sqrt{t-2}} = \sqrt[4]{7 - t}$, then find $t$. | We can start by squaring both sides of the equation to eliminate the square roots. This gives us
$2\sqrt{t-2} = \sqrt[4]{(7-t)^2}$.
Next, we can raise both sides to the fourth power to eliminate the fourth root. This gives us
$(2\sqrt{t-2})^4 = (7-t)^2$.
Simplifying both sides, we have
$16(t-2)^2 = (7-t)^2$.
Expanding ... | ibivibiv/math_instruct | |
Let r(b) = 2*b**3 - 5*b - 5. Let x(o) = -2*o**3 + 4*o + 4. Give 4*r(a) + 5*x(a).\n | -2*a**3\n | ibivibiv/math_instruct | |
((-6)/(-2))/((-2)/(-4*7/(-42)))\n | -1\n | ibivibiv/math_instruct | |
Suppose 0 = 3*g + 39 + 3. Let s = g + 26. Is 7 a factor of s?\n | False\n | ibivibiv/math_instruct | |
What is prob of picking 3 k when three letters picked without replacement from kkkkkhkkkhkkhhhkkkkk?\n | 91/228\n | ibivibiv/math_instruct | |
Is 1019175593 prime?\n | False\n | ibivibiv/math_instruct | |
Collect the terms in 28*l - 14*l - 14*l - 394*l**2.\n | -394*l**2\n | ibivibiv/math_instruct | |
What is the third derivative of 2*o*p**4 - 36*o*p**3 - 10*o*p**2 - 141*o - p**4 wrt p?\n | 48*o*p - 216*o - 24*p\n | ibivibiv/math_instruct | |
Three letters picked without replacement from vhwhghghwvhhvhhwhhh. What is prob of picking 3 v?\n | 1/969\n | ibivibiv/math_instruct | |
What is prob of picking 1 d and 1 u when two letters picked without replacement from {d: 5, u: 8}?\n | 20/39\n | ibivibiv/math_instruct | |
Calculate 115308 divided by 4.\n | 28827\n | ibivibiv/math_instruct | |
Let v(i) = 41*i + 3. Let q(h) = -163*h - 13. Calculate -2*q(d) - 9*v(d).\n | -43*d - 1\n | ibivibiv/math_instruct | |
Collect the terms in -2177*p + p**2 + 2177*p.\n | p**2\n | ibivibiv/math_instruct | |
Calculate the remainder when 120 is divided by 56.\n | 8\n | ibivibiv/math_instruct | |
Let c = 37 - 36. Suppose 4*r - 117 = -c. List the prime factors of r.\n | 29\n | ibivibiv/math_instruct | |
Simplify ((1*(sqrt(847) + -1 + sqrt(847)))**2 - (sqrt(847) + sqrt(847) + 1 + 2)) + 3*6*(-1 + sqrt(567)).\n | 96*sqrt(7) + 3368\n | ibivibiv/math_instruct | |
How many micrograms are there in nine tenths of a milligram?\n | 900\n | ibivibiv/math_instruct | |
What is (-2)/5*(3 - (-3 + 1))?\n | -2\n | ibivibiv/math_instruct | |
Solve 85*k - 3 + 237 = -359 - 427 for k.\n | -12\n | ibivibiv/math_instruct | |
Calculate (194 - 175) + (-12 - 1).\n | 6\n | ibivibiv/math_instruct | |
List the prime factors of 5750.\n | 2, 5, 23\n | ibivibiv/math_instruct | |
Let n(h) = -h**3 + 3*h - 7*h**2 - 4 - 2*h - 5. Let k be n(-8). Suppose -3*w - 2 = -k. Is w a multiple of 15?\n | True\n | ibivibiv/math_instruct | |
Let z = -6 + 8. Does 12 divide 43/z*(3 - 1)?\n | False\n | ibivibiv/math_instruct | |
Sum -33798.3506 and 0.0314.\n | -33798.3192\n | ibivibiv/math_instruct | |
Suppose -3*p + 4 = -v, -2*p - v - 12 = 2*v. Suppose -6/7*f**2 + 4/7*f**3 + 6/7*f**4 - 4/7*f + p = 0. Calculate f.\n | -1, -2/3, 0, 1\n | ibivibiv/math_instruct | |
What is the third derivative of -1972*s**5 + 55*s**2 + 2*s wrt s?\n | -118320*s**2\n | ibivibiv/math_instruct | |
Let y(u) = 2*u**2 - 4*u + 3. Let l = -13 + 15. Calculate y(l).\n | 3\n | ibivibiv/math_instruct | |
Evaluate 1 + (-2 + 8 - 1).\n | 6\n | ibivibiv/math_instruct | |
Find the second derivative of 1071*n**3 - 5273*n.\n | 6426*n\n | ibivibiv/math_instruct | |
Which is the closest to 5? (a) -1/5 (b) 1/2 (c) -1.81 (d) -1\n | b\n | ibivibiv/math_instruct | |
Round 13706840 to the nearest 1000.\n | 13707000\n | ibivibiv/math_instruct | |
Let r be ((-3)/138)/(69/(-3174)). Put -8, r, -605 in ascending order.\n | -605, -8, r\n | ibivibiv/math_instruct | |
What is 453 minutes after 2:00 AM?\n | 9:33 AM\n | ibivibiv/math_instruct | |
What is the first derivative of -18305722*j**4 - 16304523?\n | -73222888*j**3\n | ibivibiv/math_instruct | |
Let h(t) = 4205*t**2 + 2639. Let d(a) = -166*a**2 - 104. Let u(q) = 203*d(q) + 8*h(q). Let j(c) = -2*c. Calculate j(u(i)).\n | 116*i**2\n | ibivibiv/math_instruct | |
Let i = -2209 + 2210.009. Let c = i + -0.232. Let h = c - 0.107. Round h to 1 dp.\n | 0.7\n | ibivibiv/math_instruct | |
What is 4826081 (base 9) in base 8?\n | 11764655\n | ibivibiv/math_instruct | |
Which is the second biggest value? (a) -9626 (b) -2/9 (c) 0.3\n | b\n | ibivibiv/math_instruct | |
What is the closest to 207/5 in 0, 0.054, -1/7, 2?\n | 2\n | ibivibiv/math_instruct | |
Expand -2*f**4 - 3*f**4 + 2*f**4 + (-4 + 4 + 2)*(-f**4 - 6*f**4 + 5*f**4).\n | -7*f**4\n | ibivibiv/math_instruct | |
What is prob of picking 4 y when four letters picked without replacement from {z: 7, y: 5}?\n | 1/99\n | ibivibiv/math_instruct | |
Let b(g) = -4*g**2 - 5*g**2 + 11*g**2 + 3*g**2 - 7*g**2 + 3*g. Let y(n) = -2*n**2 + 4*n. Give 3*b(i) - 2*y(i).\n | -2*i**2 + i\n | ibivibiv/math_instruct | |
Let a(k) = -5*k. Let c = 17 - 13. Suppose i + 3*x = -c*i - 11, 3*i + 11 = -4*x. Let s(v) = 1. Let q(l) = 2*l**2 - 4. Let w(p) = i*q(p) - 4*s(p). Give a(w(t)).\n | 10*t**2\n | ibivibiv/math_instruct |
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