instruction_seed stringlengths 5 2.9k | response_seed stringlengths 3 9.55k | input stringclasses 1
value | _source stringclasses 1
value |
|---|---|---|---|
Calculate the remainder when 18322 is divided by 3723.\n | 3430\n | ibivibiv/math_instruct | |
Simplify (q**(-2/27))**(2/47)*(q*q*q**(1/2)/q*q)/q**(-2/39) assuming q is positive.\n | q**(84073/32994)\n | ibivibiv/math_instruct | |
Factor -188772*z**2 - 62948*z - 8.\n | -4*(3*z + 1)*(15731*z + 2)\n | ibivibiv/math_instruct | |
What is the hundreds digit of 1613?\n | 6\n | ibivibiv/math_instruct | |
Let u be (-11)/(-6) - 8/(-48). Let o(q) = 2 - 11*q**2 + 20*q**u - 3 + 0*q - 10*q**2 + q. Let c(m) = -10*m**3 - 10*m**2 + 10*m - 10. Calculate c(r) - 10*o(r).\n | -10*r**3\n | ibivibiv/math_instruct | |
(((-704)/(-1760))/(1/(-60)))/(-3)\n | 8\n | ibivibiv/math_instruct | |
Let n = -130 - -132. Let t(y) = y**2 + 5*y - 3. Let q be t(-6). Let d be 1/n + q/(-2) - -1600001. Round d to the nearest 1000000.\n | 2000000\n | ibivibiv/math_instruct | |
Collect the terms in 670*l**3 + 8*l**2 + 10*l**2 - 18*l**2.\n | 670*l**3\n | ibivibiv/math_instruct | |
Let w = -497 - -507. Suppose 5*o = -4*y + 17, -3*y - 4*o + 4 = -8. What is the least common multiple of y and w?\n | 40\n | ibivibiv/math_instruct | |
Product of 4 and 364.\n | 1456\n | ibivibiv/math_instruct | |
Let w(t) = 3*t + 16. Let c be w(-7). Let s(r) = 10*r**2 + 4*r**3 + r - 23*r**2 + 16 - 3*r**3 + 18*r**2. Let m be s(c). Solve -4*q + 3 - m = 0 for q.\n | -2\n | ibivibiv/math_instruct | |
Let v = 72 + -35. Suppose -m + 49 = v. Calculate the greatest common factor of m and 48.\n | 12\n | ibivibiv/math_instruct | |
Let s(w) = 2*w**2 - 39289*w + 706565. What is s(18)?\n | 11\n | ibivibiv/math_instruct | |
What is next in 5, 17, 43, 89, 161?\n | 265\n | ibivibiv/math_instruct | |
Let s = -354.8 - -365.8. Put -2, s, -0.5, 1/3 in descending order.\n | s, 1/3, -0.5, -2\n | ibivibiv/math_instruct | |
Let b(c) = 56209*c + 14501955. Calculate b(-258).\n | 33\n | ibivibiv/math_instruct | |
What is the value of 3 + 1 - 1 - 4 - 7?\n | -8\n | ibivibiv/math_instruct | |
Which is the nearest to 6/7? (a) 0 (b) -0.4 (c) 309 (d) 7 (e) 5\n | a\n | ibivibiv/math_instruct | |
Solve 13*o + 5*l - 15 = 11*o, 4*o + l = 21 for o.\n | 5\n | ibivibiv/math_instruct | |
Is 19304849 prime?\n | True\n | ibivibiv/math_instruct | |
Simplify (2 + -1*sqrt(48))**2 + -4 + (sqrt(147) + -2 - sqrt(147)).\n | -16*sqrt(3) + 46\n | ibivibiv/math_instruct | |
b"What is the rth term of 62, 103, 144, 185?\n" | 41*r + 21\n | ibivibiv/math_instruct | |
Solve -27 = -67*i + 40 for i.\n | 1\n | ibivibiv/math_instruct | |
Which is smaller: -46/3 or -16?\n | -16\n | ibivibiv/math_instruct | |
Find the third derivative of -2*u**6 - 125745*u**4 + 4*u**3 - 6598096*u**2.\n | -240*u**3 - 3017880*u + 24\n | ibivibiv/math_instruct | |
Four letters picked without replacement from lslguggddl. What is prob of sequence ldug?\n | 1/280\n | ibivibiv/math_instruct | |
What is 592 minutes before 1:43 PM?\n | 3:51 AM\n | ibivibiv/math_instruct | |
Find the third derivative of -1433236311*k**3 + 667196349*k**2 wrt k.\n | -8599417866\n | ibivibiv/math_instruct | |
What is -45b (base 15) in base 2?\n | -1111011010\n | ibivibiv/math_instruct | |
Let v(r) = -274*r**2. Let a(t) = -3*t + 9. What is v(a(f))?\n | -2466*f**2 + 14796*f - 22194\n | ibivibiv/math_instruct | |
Suppose -269273 = -107*v + 183016. Does 10 divide v?\n | False\n | ibivibiv/math_instruct | |
Suppose 10*q = 668 + 3082. What is the hundreds digit of q?\n | 3\n | ibivibiv/math_instruct | |
Let h = -329 - -274056/833. Suppose 23*w + 7*w = 12*w - 22*w. Is w at least as big as h?\n | True\n | ibivibiv/math_instruct | |
What is the sixth root of 3615532 to the nearest integer?\n | 12\n | ibivibiv/math_instruct | |
Calculate -31 - 0.42.\n | -31.42\n | ibivibiv/math_instruct | |
In base 15, what is -3 + -d4?\n | -d7\n | ibivibiv/math_instruct | |
Rearrange -19*d - 34 + 64*d + 33 + 30*d + (8 - 2 + 1)*(0 + d + 0) to z*d + x and give x.\n | -1\n | ibivibiv/math_instruct | |
Let m(c) = -2*c**3 - c + 3. Determine m(-3).\n | 60\n | ibivibiv/math_instruct | |
What is the square root of 797206140 to the nearest integer?\n | 28235\n | ibivibiv/math_instruct | |
Let b(n) = -9*n - 17. Calculate b(4).\n | -53\n | ibivibiv/math_instruct | |
Is 8376619 composite?\n | False\n | ibivibiv/math_instruct | |
Let p = -63 - -64. Sort -91, 0.2, p in descending order.\n | p, 0.2, -91\n | ibivibiv/math_instruct | |
b"What is the lth term of -12158, -24319, -36480, -48641, -60802?\n" | -12161*l + 3\n | ibivibiv/math_instruct | |
Put 4, -0.1, 2/9 in decreasing order.\n | 4, 2/9, -0.1\n | ibivibiv/math_instruct | |
Find the second derivative of 824*h**3 + 949*h**3 - 341*h**3 - 212*h**3 - 2057*h wrt h.\n | 7320*h\n | ibivibiv/math_instruct | |
Calculate the remainder when 1521 is divided by 15.\n | 6\n | ibivibiv/math_instruct | |
Three letters picked without replacement from mhhhhhahmahehmvuahh. What is prob of picking 1 e, 1 v, and 1 h?\n | 10/969\n | ibivibiv/math_instruct | |
What is next in 33, 138, 237, 330, 417, 498?\n | 573\n | ibivibiv/math_instruct | |
Let u(y) be the first derivative of y**2/2 + 1. Let o = 2 - 0. Let h(v) = 2*v**o - 5*v**2 + 2*v**2 + 0*v**2. What is h(u(b))?\n | -b**2\n | ibivibiv/math_instruct | |
-42000442 (base 7) to base 6\n | -203353104\n | ibivibiv/math_instruct | |
Multiply 1.54908 and 0.1.\n | 0.154908\n | ibivibiv/math_instruct | |
Solve 373*n - 228 = 335*n for n.\n | 6\n | ibivibiv/math_instruct | |
Solve -8697*l = -8732*l - 560 for l.\n | -16\n | ibivibiv/math_instruct | |
Let k(r) = 4*r + 10. Let g be ((-3)/2)/((-8)/(-16)). Determine k(g).\n | -2\n | ibivibiv/math_instruct | |
Let v = 6.3 + -1.3. Which is the third smallest value? (a) 5/3 (b) 3/8 (c) v (d) -2/13\n | a\n | ibivibiv/math_instruct | |
Let y = -52 - -31. Let f = -17 - y. Solve -5*o + f*u = -3*o + 6, 5*u = -o + 25 for o.\n | 5\n | ibivibiv/math_instruct | |
Let d = -58 - -200. Calculate the remainder when d is divided by 24.\n | 22\n | ibivibiv/math_instruct | |
Let w(d) be the third derivative of -d**7/70 - 7*d**5/12 + 2287*d**4/24 + 49*d**2 + 3. Find the second derivative of w(i) wrt i.\n | -36*i**2 - 70\n | ibivibiv/math_instruct | |
Two letters picked without replacement from {i: 4, f: 3, r: 2, l: 1, q: 1}. What is prob of sequence lq?\n | 1/110\n | ibivibiv/math_instruct | |
Evaluate 44*14/672*12.\n | 11\n | ibivibiv/math_instruct | |
What is the greatest common divisor of 1068034 and 102168?\n | 946\n | ibivibiv/math_instruct | |
Solve 73 = -2*w - 74*a + 79*a, 0 = -95*w + 94*w + 2*a - 30 for w.\n | -4\n | ibivibiv/math_instruct | |
Differentiate 5 - 55 - 3 - 59*q**2 with respect to q.\n | -118*q\n | ibivibiv/math_instruct | |
Solve 0 = 4*q - 0*q + 4, 0 = 2*t - 5*q - 15 for t.\n | 5\n | ibivibiv/math_instruct | |
Let a = -2 + 0. Let y = a - -8. Is 6 a factor of y?\n | True\n | ibivibiv/math_instruct | |
Let z = 403 + -221. Let o = z + 287. Is o a prime number?\n | False\n | ibivibiv/math_instruct | |
What is one fifth of a meter in centimeters?\n | 20\n | ibivibiv/math_instruct | |
What is the difference between -52638704 and 132?\n | 52638836\n | ibivibiv/math_instruct | |
Is 693460 a multiple of 65?\n | False\n | ibivibiv/math_instruct | |
Which is bigger: 0.094 or -1409?\n | 0.094\n | ibivibiv/math_instruct | |
Let l(i) = -80*i**3 - 6*i**2 + 11*i + 6. Let t(r) = 80*r**3 + 5*r**2 - 9*r - 5. What is -5*l(d) - 6*t(d)?\n | -80*d**3 - d\n | ibivibiv/math_instruct | |
Let z(a) = a. Let n(p) = -p**2 - 2. Let v(w) = -n(w) - 2*z(w). Let h(r) = -r. Let q be h(-2). Let d be v(q). Solve b + d = -1 for b.\n | -3\n | ibivibiv/math_instruct | |
Sort 4, 6143, 11, 8, 2, -4 in descending order.\n | 6143, 11, 8, 4, 2, -4\n | ibivibiv/math_instruct | |
Factor -3*o**2/2 - 411*o/2 - 603.\n | -3*(o + 3)*(o + 134)/2\n | ibivibiv/math_instruct | |
Let p(b) = -4*b + 5. Let q be p(10). Does 15 divide (-10)/q + (-418)/(-7)?\n | True\n | ibivibiv/math_instruct | |
Evaluate (12/(-385))/((-6402)/(-5335)).\n | -2/77\n | ibivibiv/math_instruct | |
Solve -264 = -4*p - 62*z, -4*p - 28*z + 8 = -30*z for p.\n | 4\n | ibivibiv/math_instruct | |
Let l = -3.776 + 3.7. What is l rounded to 2 decimal places?\n | -0.08\n | ibivibiv/math_instruct | |
Suppose -3*w = -n + 35 - 101, 2*w - 5*n - 44 = 0. Let t(l) = l**2 - 16*l + 57. Let g be t(4). Suppose g*z = -2*z + w. Solve z*c + 2 = -4 for c.\n | -3\n | ibivibiv/math_instruct | |
Let g = 361.3 + -361. Let j = -0.1 + 0.6. Which is the third smallest value? (a) j (b) 0.2 (c) g\n | a\n | ibivibiv/math_instruct | |
What is the closest to -13177/2 in -4.7, 0, -1/4?\n | -4.7\n | ibivibiv/math_instruct | |
Calculate prob of sequence oii when three letters picked without replacement from {o: 2, d: 1, i: 3, g: 3, q: 2, t: 3}.\n | 1/182\n | ibivibiv/math_instruct | |
Product of -0.7 and 47961877.\n | -33573313.9\n | ibivibiv/math_instruct | |
Convert 0.5552427ml to litres.\n | 0.0005552427\n | ibivibiv/math_instruct | |
Express -9*v**2 + 4 - 67*v**2 - 3 - 2 - 3 as u + t*v + q*v**2 and give u.\n | -4\n | ibivibiv/math_instruct | |
In base 7, what is 5465 - 105542?\n | -100044\n | ibivibiv/math_instruct | |
Let k = -425 - -476. What is the greatest common factor of k and 136?\n | 17\n | ibivibiv/math_instruct | |
Suppose -1 = 3*u - 4. Let g = u - 5. Let h(c) be the second derivative of -c**5/20 - 5*c**4/12 - 5*c**3/6 + c. What is h(g)?\n | 4\n | ibivibiv/math_instruct | |
Let q(s) = -s**2 + 5*s - 3. Let u be q(2). Let f be (1/u)/((-8)/120). Which is the closest to -0.1? (a) f (b) 0.1 (c) 2/11\n | b\n | ibivibiv/math_instruct | |
Factor a**3/5 + 2134*a**2/5 + 12777*a/5 + 19152/5.\n | (a + 3)**2*(a + 2128)/5\n | ibivibiv/math_instruct | |
Two letters picked without replacement from uueeueduud. What is prob of picking 1 d and 1 e?\n | 2/15\n | ibivibiv/math_instruct | |
Find the second derivative of 258*r**4 - 49*r - 1.\n | 3096*r**2\n | ibivibiv/math_instruct | |
What is the thousands digit of 6683632?\n | 3\n | ibivibiv/math_instruct | |
What is the greatest common divisor of 18 and 336?\n | 6\n | ibivibiv/math_instruct | |
Calculate the remainder when 1034 is divided by 323.\n | 65\n | ibivibiv/math_instruct | |
Let s(q) = 2*q**2 + 22*q + 71. Is s(22) a prime number?\n | True\n | ibivibiv/math_instruct | |
Let q = -6058360679.4908443087283 - -9093.4908459787283. Let u = 6058351463 + q. Let o = u - -123. Round o to seven dps.\n | 0.0000017\n | ibivibiv/math_instruct | |
Solve 3*y**5/5 - 444*y**4/5 + 348*y**3/5 + 13854*y**2/5 - 26991*y/5 + 2646 = 0.\n | -6, 1, 5, 147\n | ibivibiv/math_instruct | |
Write an educational piece suited for college students related to the following text snippet:
"### Home > INT3 > Chapter 9 > Lesson 9.2.1 > Problem9-98
9-98.
Imagine the graph $y = \text{sin}\left(x\right)$ shifted up $1$ unit.
1. Sketch what the graph would look like.
2. What do you have to change in the equation ... | We begin by addressing problem 9-98 from your provided textbook resource. This question covers several fundamental topics related to transformations of functions, specifically sine functions. Let's break down the problem into its constituent parts and address them systematically.
1. Shifting the Graph Vertically
Whe... | ibivibiv/math_instruct | |
Let g(f) be the third derivative of -f**6/40 + f**5/20 + f**4/4 + 4*f**2. Let g(y) = 0. What is y?\n | -1, 0, 2\n | ibivibiv/math_instruct |
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