instruction_seed stringlengths 5 2.9k | response_seed stringlengths 3 9.55k | input stringclasses 1
value | _source stringclasses 1
value |
|---|---|---|---|
Calculate 2 divided by -974.\n | -1/487\n | ibivibiv/math_instruct | |
Let x = 163 - 160. Sort x, -7, 5, 2.\n | -7, 2, x, 5\n | ibivibiv/math_instruct | |
What is the tens digit of (-4 - 0) + (-14 + 0)*-11?\n | 5\n | ibivibiv/math_instruct | |
What is the next term in -15429299, -30858601, -46287903, -61717205?\n | -77146507\n | ibivibiv/math_instruct | |
Calculate (-4)/18*(-72)/8.\n | 2\n | ibivibiv/math_instruct | |
Solve -87*y - 58 = -5*x - 86*y + 114, 126 = 4*x + 5*y for x.\n | 34\n | ibivibiv/math_instruct | |
1846629576.363 - 0.243\n | 1846629576.12\n | ibivibiv/math_instruct | |
Calculate the common denominator of 89/180 and 4*6/18*(787/180 + -4).\n | 540\n | ibivibiv/math_instruct | |
9/(-6)*(-8)/6\n | 2\n | ibivibiv/math_instruct | |
How many minutes are there between 9:28 PM and 8:09 AM?\n | 641\n | ibivibiv/math_instruct | |
Suppose -2*w - 25 + 29 = 0. Let m(p) = 4*p - 2*p**2 + 149*p**3 - w*p**2 + 148*p**3 + 3 - 298*p**3. What is m(-4)?\n | -13\n | ibivibiv/math_instruct | |
Solve 36*y - 160 = -f, 4*f = f - 7*y + 9*y - y + 44 for f.\n | 16\n | ibivibiv/math_instruct | |
Let s(r) = r. Let u(q) = -7*q + 75. Let w(x) = -22*x + 226. Let o be 12/(-4)*((-256)/(-12))/4. Let y(f) = o*u(f) + 5*w(f). Give s(y(h)).\n | 2*h - 70\n | ibivibiv/math_instruct | |
Round 0.00000392706443 to seven decimal places.\n | 0.0000039\n | ibivibiv/math_instruct | |
Find the third derivative of 104036*q**3 + 188822*q**2.\n | 624216\n | ibivibiv/math_instruct | |
-8 + (2 - 1) + -71 + 78\n | 0\n | ibivibiv/math_instruct | |
Simplify (f**(9/4)/((f*f**7*f)/f))**(-3/35)/(f**(-1/2)/f**(-2))**3 assuming f is positive.\n | f**(-561/140)\n | ibivibiv/math_instruct | |
Let s(f) = -4*f**2 + 4*f - 6. Let c be s(6). Let m be (-82)/c + 2/(-9). Sort 2/17, 0.1, m in decreasing order.\n | m, 2/17, 0.1\n | ibivibiv/math_instruct | |
Two letters picked without replacement from {h: 1, e: 3, g: 5, u: 6}. What is prob of picking 1 g and 1 e?\n | 1/7\n | ibivibiv/math_instruct | |
Write an educational piece suited for college students related to the following text snippet:
"# Find a smooth function $f:\mathbb{R}\to\mathbb{R}$ such that $|f'(x)| < 1$ and $f(x) \neq x$ for all $x\in\mathbb{R}$
Exercise: Find a smooth function $f:\mathbb{R}\to\mathbb{R}$ such that $|f'(x)| < 1$ and $f(x) \neq x$ f... | In this educational piece, we will delve into the world of real analysis and explore a problem posed in the book "Curso de Análise: volume 1" by Elon Lages Lima. The objective is to find a smooth function \( f:b{R} o {R} \) that adheres to two conditions simultaneously:
1. Its derivative's absolute value should be ... | ibivibiv/math_instruct | |
(-18)/105*(-35)/15\n | 2/5\n | ibivibiv/math_instruct | |
Add 444 and -3.\n | 441\n | ibivibiv/math_instruct | |
What comes next: -1260, -2505, -3758, -5025, -6312, -7625?\n | -8970\n | ibivibiv/math_instruct | |
What is 0.000009156 rounded to six decimal places?\n | 0.000009\n | ibivibiv/math_instruct | |
In base 13, what is -2ca9a + -11?\n | -2caab\n | ibivibiv/math_instruct | |
Let m(c) = -6*c + 15. Let k be m(7). Let b = k + 32. Factor 2*i - 7*i**3 + 0*i**4 - 5*i**3 + b*i**2 + 16*i**3 + i**4.\n | i*(i + 1)**2*(i + 2)\n | ibivibiv/math_instruct | |
Solve 788*i + 586 + 831 - 3495 = 21562 for i.\n | 30\n | ibivibiv/math_instruct | |
Let n = -184.530629 + 184.54. What is n rounded to four dps?\n | 0.0094\n | ibivibiv/math_instruct | |
Calculate the remainder when 2262313 is divided by 1268.\n | 201\n | ibivibiv/math_instruct | |
Simplify (i/(i**(-3/7)/i))**2/((((i**(-18)/i)/i)/i)/i**(8/5)) assuming i is positive.\n | i**(961/35)\n | ibivibiv/math_instruct | |
Suppose 4 = -2*v + 2*n, v + n - 7 = -5. Let c(f) = f - 6. Let h(b) = -b**2 - 7*b + 2. Let o be h(-6). Let y be c(o). Solve y*q + q = v for q.\n | 0\n | ibivibiv/math_instruct | |
Put -0.2, -7, 4/3, 1/6, -21/4 in decreasing order.\n | 4/3, 1/6, -0.2, -21/4, -7\n | ibivibiv/math_instruct | |
Calculate the remainder when 991 is divided by 98.\n | 11\n | ibivibiv/math_instruct | |
Let v(l) = l**3 + 3*l**2 - 4*l - 2. Let t be v(-3). Solve -3*x - 4*h = -h - 9, -t = -2*h for x.\n | -2\n | ibivibiv/math_instruct | |
What is 410.3405 decades in millennia?\n | 4.103405\n | ibivibiv/math_instruct | |
Let g = 13 + -9. Let o(w) = w**2 - 6*w + 3. Let s be o(6). Let d(l) = 5 + 1 - l - g*l - 6*l**2 - l**s. Determine d(-5).\n | 6\n | ibivibiv/math_instruct | |
Collect the terms in 2*z - 421*z**3 + 333*z**3 + 983*z**3.\n | 895*z**3 + 2*z\n | ibivibiv/math_instruct | |
What is the units digit of 4974?\n | 4\n | ibivibiv/math_instruct | |
Four letters picked without replacement from ooooodoodoooddododd. Give prob of picking 1 d and 3 o.\n | 385/969\n | ibivibiv/math_instruct | |
What is the value of (11/((-154)/(-4))*(-126)/(-36))/(1/(-13))?\n | -13\n | ibivibiv/math_instruct | |
Solve 0 = -0*n + 5*n - 5*d + 20, -15 = 5*n - 4*d for n.\n | 1\n | ibivibiv/math_instruct | |
Sort 64, 0, 4, -2 in descending order.\n | 64, 4, 0, -2\n | ibivibiv/math_instruct | |
Rearrange (3*r + 2*r**2 - 3*r - 1)*(33 + 37 - 40) to the form y + l*r + n*r**2 and give n.\n | 60\n | ibivibiv/math_instruct | |
Suppose 0 = 7*l - 4*l - 12. Suppose 8*z = l*z + 12. Solve -a - 4*q = -16, 5*a - z*q = 2 + 9 for a.\n | 4\n | ibivibiv/math_instruct | |
What is the closest to -1295 in -4, 2, 0.5, 1/5?\n | -4\n | ibivibiv/math_instruct | |
What is -146306 (base 9) in base 5?\n | -10334131\n | ibivibiv/math_instruct | |
Calculate the greatest common factor of 13252 and 16.\n | 4\n | ibivibiv/math_instruct | |
Sort 5, -11, 4, 114, -14, 1, -5.\n | -14, -11, -5, 1, 4, 5, 114\n | ibivibiv/math_instruct | |
How many minutes are there between 11:44 AM and 5:11 PM?\n | 327\n | ibivibiv/math_instruct | |
Factor 2492*o**2 - 58976*o/3 - 41024.\n | 4*(7*o + 12)*(267*o - 2564)/3\n | ibivibiv/math_instruct | |
What is the second derivative of 94225503*f**4 + 1781264*f + 24?\n | 1130706036*f**2\n | ibivibiv/math_instruct | |
What is the square root of 907253 to the nearest integer?\n | 952\n | ibivibiv/math_instruct | |
Let k(d) = -3*d**2 + 4*d + 5. Let a(r) = -r**2 + 2*r + 2. What is -7*a(l) + 3*k(l)?\n | -2*l**2 - 2*l + 1\n | ibivibiv/math_instruct | |
Calculate prob of sequence yy when two letters picked without replacement from lyyf.\n | 1/6\n | ibivibiv/math_instruct | |
b"What is the pth term of 40, -39, -178, -407, -756, -1255?\n" | -5*p**3 - 44*p + 89\n | ibivibiv/math_instruct | |
Let l(m) be the first derivative of m**4/48 + m**3/4 + 5*m**2/8 - m - 13. Let i(v) be the first derivative of l(v). Let i(g) = 0. Calculate g.\n | -5, -1\n | ibivibiv/math_instruct | |
Find r such that 14*r**2/19 + 26*r/19 = 0.\n | -13/7, 0\n | ibivibiv/math_instruct | |
b"What is the ith term of 3057, 3132, 3339, 3744, 4413, 5412, 6807?\n" | 11*i**3 - 2*i + 3048\n | ibivibiv/math_instruct | |
What is the product of 0.33139 and 560?\n | 185.5784\n | ibivibiv/math_instruct | |
Simplify 5 + (1 + -6*(-5 + sqrt(38)/sqrt(72) + 1 + (sqrt(931) - sqrt(19)))*5)**2.\n | -44770*sqrt(19) + 664921\n | ibivibiv/math_instruct | |
What is 43c (base 15) in base 2?\n | 1110111101\n | ibivibiv/math_instruct | |
What is 318.24814 rounded to the nearest one hundred?\n | 300\n | ibivibiv/math_instruct | |
Simplify sqrt(1539) + (sqrt(1539) - (sqrt(1539) + 0))**2 + -3.\n | -3 + 9*sqrt(19)\n | ibivibiv/math_instruct | |
What is next in 22728, 22750, 22794, 22872, 22996?\n | 23178\n | ibivibiv/math_instruct | |
Which is the closest to -0.5? (a) -0.08 (b) -15 (c) -3 (d) 0.5\n | a\n | ibivibiv/math_instruct | |
Which is smaller: 551 or 552?\n | 551\n | ibivibiv/math_instruct | |
Sort 2/7, -0.09, -2/379 in ascending order.\n | -0.09, -2/379, 2/7\n | ibivibiv/math_instruct | |
Let g = 706.1 + -685.1. What is the third biggest value in g, 5, 13?\n | 5\n | ibivibiv/math_instruct | |
Four letters picked without replacement from {n: 4, d: 6, i: 5, p: 1}. What is prob of sequence pnnd?\n | 3/1820\n | ibivibiv/math_instruct | |
Convert 129 (base 11) to base 12.\n | 108\n | ibivibiv/math_instruct | |
Four letters picked without replacement from {t: 13, w: 3}. What is prob of sequence twtt?\n | 33/280\n | ibivibiv/math_instruct | |
(-2)/(-12)*-3*2\n | -1\n | ibivibiv/math_instruct | |
Simplify (n**(1/4)*n)**(5/13)*(n**3)**(1/60) assuming n is positive.\n | n**(69/130)\n | ibivibiv/math_instruct | |
Let i = 1028.962 + -1065. Let b = 36.074 + -0.074. Let r = i + b. What is r rounded to 2 dps?\n | -0.04\n | ibivibiv/math_instruct | |
Simplify (5 + ((sqrt(320) - (sqrt(320) - (sqrt(320) + -1*sqrt(320)*2))) + (2 + sqrt(320))*4 - -3*(2 + 1 + sqrt(320))))**2.\n | 2112*sqrt(5) + 12004\n | ibivibiv/math_instruct | |
Two letters picked without replacement from ykyyeykwewywyywy. Give prob of picking 1 e and 1 w.\n | 1/15\n | ibivibiv/math_instruct | |
b"What is the wth term of 32582, 65044, 97456, 129818, 162130, 194392, 226604?\n" | -25*w**2 + 32537*w + 70\n | ibivibiv/math_instruct | |
Sort -3, -54, -5, 2, -4.\n | -54, -5, -4, -3, 2\n | ibivibiv/math_instruct | |
Four letters picked without replacement from nhhnnhnnnnhnnn. What is prob of sequence nnnh?\n | 120/1001\n | ibivibiv/math_instruct | |
Let i(a) = a**2. Let m(t) = 2*t**2 + 6. Let d(l) be the third derivative of -l**3/6 + 2*l**2. Let g(c) = -6*d(c) - m(c). Calculate i(g(k)).\n | 4*k**4\n | ibivibiv/math_instruct | |
Let v = 230/11 + -932/33. Let r be 1 - (163/21 + 1). Let n = r - v. Sort n, 0.1, -5 in decreasing order.\n | 0.1, n, -5\n | ibivibiv/math_instruct | |
What are the prime factors of 5434?\n | 2, 11, 13, 19\n | ibivibiv/math_instruct | |
Calculate the highest common factor of 80 and 1040.\n | 80\n | ibivibiv/math_instruct | |
Is 18 a factor of 8951760?\n | True\n | ibivibiv/math_instruct | |
Let y(z) = -z**3 + 11*z**2 - 14*z + 38. Let c be y(10). Find the common denominator of (c - (-169)/65) + 518/120 and 85/48.\n | 48\n | ibivibiv/math_instruct | |
Solve 0 = 4*b - h - 6, -12403*b + 12403*b - 88 = 4*h for b.\n | -4\n | ibivibiv/math_instruct | |
Collect the terms in 13 - 2286*i + 1096*i + 1087*i - 22 + 9.\n | -103*i\n | ibivibiv/math_instruct | |
Rearrange -i**3 + 53*i**4 + 3*i**3 - 44*i**4 + 33*i - 21*i**4 to q*i**4 + w + s*i**2 + g*i + z*i**3 and give s.\n | 0\n | ibivibiv/math_instruct | |
Let c be (-1)/4 - 1044/(-16) - 3. Let p = 64 - c. Let q(t) = -t**3 - 2*t**2 - 2*t + 2. Let y(d) = d**3 - d + 1. Determine p*y(x) - q(x).\n | 3*x**3 + 2*x**2\n | ibivibiv/math_instruct | |
Let b(i) = 23*i + 6. Let w be b(-7). Let x = -87 - w. Let s = -1120 - -1137. What is the greatest common factor of s and x?\n | 17\n | ibivibiv/math_instruct | |
Let v(d) = -67*d**2 + 11*d - 64*d**2 + 2 + 130*d**2 + 5. Determine v(6).\n | 37\n | ibivibiv/math_instruct | |
In base 5, what is 311421324 + -1202?\n | 311420122\n | ibivibiv/math_instruct | |
Is 26325 a multiple of 13?\n | True\n | ibivibiv/math_instruct | |
Solve h - 3 = -0*h - x, 5*x = h + 21 for h.\n | -1\n | ibivibiv/math_instruct | |
Let o = -128 - -163. Find the first derivative of o + 41 + 7*r**4 + 37*r**4 wrt r.\n | 176*r**3\n | ibivibiv/math_instruct | |
Is 486 a factor of 225408744?\n | True\n | ibivibiv/math_instruct | |
Calculate the common denominator of -41/147 and 25/189.\n | 1323\n | ibivibiv/math_instruct | |
Let w = -1 + -1. Let q = 0 + 1. Let t be 2/4*(-2)/3. What is the nearest to q in w, 2/5, t?\n | 2/5\n | ibivibiv/math_instruct | |
Solve 524*i + 71 + 453 = 0 for i.\n | -1\n | ibivibiv/math_instruct | |
Suppose 3*f - 6 = 9. Let l(d) = 167 - 59 + 7*d - 61 - d**2 - 51. Give l(f).\n | 6\n | ibivibiv/math_instruct |
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