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Evaluate 16*85/272*((-93)/15)/(33/11).\n
-31/3\n
ibivibiv/math_instruct
Suppose 16*g - 12*g + 20 = 0. What is the second biggest value in 5, -2/5, g?\n
-2/5\n
ibivibiv/math_instruct
What is next in 931, 1877, 2823?\n
3769\n
ibivibiv/math_instruct
What is the next term in 6507, 6518, 6537, 6564, 6599, 6642?\n
6693\n
ibivibiv/math_instruct
Does 1140 divide 30842430?\n
False\n
ibivibiv/math_instruct
Which is the nearest to 3/7? (a) -2/9 (b) -4 (c) 7\n
a\n
ibivibiv/math_instruct
Let g be ((0 - -4) + 280/(-80))*34. Let l(q) = q**3 - 5*q**2 + 4. Let n be l(5). Suppose 36 = 4*b + n*a, -3*b - 4*a + g = -13. List the prime factors of b.\n
2, 3\n
ibivibiv/math_instruct
In base 13, what is cca + 126?\n
1123\n
ibivibiv/math_instruct
Find l such that -4*l**5/5 + 16*l**4 + 4924*l**3/5 - 6280*l**2 + 5280*l = 0.\n
-30, 0, 1, 5, 44\n
ibivibiv/math_instruct
What is the value of -10 + -8 + (-7 - -11) - 7?\n
-21\n
ibivibiv/math_instruct
Let j be 2/(-2 - 114/(-58)). Let x be (-188)/j - 3/1. Let g = -163/435 + x. Which is the nearest to -1? (a) g (b) -2/3 (c) 2\n
b\n
ibivibiv/math_instruct
Sort 0, -124.73, -0.6.\n
-124.73, -0.6, 0\n
ibivibiv/math_instruct
Let u = -61 - 10. Let q = 115 + u. Suppose -h + 2*k + 52 = 6*k, -h - 2*k + q = 0. Does 36 divide h?\n
True\n
ibivibiv/math_instruct
Which is the fourth smallest value? (a) 549 (b) 1/6 (c) 0.8 (d) -2/7\n
a\n
ibivibiv/math_instruct
Suppose 59 = a + 4*x, -29 = 5*a - 4*x - 348. Let j = -39 + 60. What is the highest common factor of a and j?\n
21\n
ibivibiv/math_instruct
Does 222 divide 253731570?\n
True\n
ibivibiv/math_instruct
Suppose 3*r + 2*w - 7*w = 31, -3*r - 2*w - 4 = 0. Solve 6*y - 4 = r*y for y.\n
1\n
ibivibiv/math_instruct
Which is smaller: -0.23 or -183/32?\n
-183/32\n
ibivibiv/math_instruct
What is -10614 divided by -183?\n
58\n
ibivibiv/math_instruct
Calculate the remainder when 3715 is divided by 286.\n
283\n
ibivibiv/math_instruct
Solve 5*h + 5 = 3*t, -2*t + 6 = 2*h - 8 for t.\n
5\n
ibivibiv/math_instruct
Let 2*f**4 - 20*f**3 + 72*f**2 - 108*f + 54 = 0. Calculate f.\n
1, 3\n
ibivibiv/math_instruct
Put -34, 4, -1 in decreasing order.\n
4, -1, -34\n
ibivibiv/math_instruct
How many seconds are there in one twentieth of a day?\n
4320\n
ibivibiv/math_instruct
Evaluate (-44)/11*(-25)/20.\n
5\n
ibivibiv/math_instruct
Let r(g) = -43*g. Let s(p) = 2*p**2 - 57*p - 14210. Determine s(r(w)).\n
3698*w**2 + 2451*w - 14210\n
ibivibiv/math_instruct
What is the closest to -0.9 in -18, -1/3, 3?\n
-1/3\n
ibivibiv/math_instruct
What is (16/32)/((-10)/(-25))?\n
5/4\n
ibivibiv/math_instruct
Which is the second smallest value? (a) 2 (b) 0.1 (c) -1/32\n
b\n
ibivibiv/math_instruct
What is the product of 2.3 and -210?\n
-483\n
ibivibiv/math_instruct
Is 34 a factor of 24990?\n
True\n
ibivibiv/math_instruct
Calculate the remainder when 1810707 is divided by 218.\n
217\n
ibivibiv/math_instruct
Factor 5*c**2 - 25752990*c + 103011880.\n
5*(c - 5150594)*(c - 4)\n
ibivibiv/math_instruct
Which is the nearest to -1/5? (a) -57 (b) -193 (c) -0.5\n
c\n
ibivibiv/math_instruct
Write an educational piece suited for college students related to the following text snippet: "# Definition of limit inferior - paradox We define the limit inferior and limit superior of a sequence $$(A_n:n\in \mathbb N)$$ of subsets of a set $$X$$ by setting (1) $$\begin{split}\lim \inf _{n\rightarrow\infty} A_n&=\b...
The concept of limits inferior and superior is fundamental in analysis and sets theory. These concepts allow us to examine the behavior of sequences of sets as we move further along the index. This discussion focuses on the limit inferior and its definition, providing insights into why the given formulation works desp...
ibivibiv/math_instruct
What is 353947.1 micrometers in millimeters?\n
353.9471\n
ibivibiv/math_instruct
What are the prime factors of 72674221?\n
19, 1831, 2089\n
ibivibiv/math_instruct
What is the highest common factor of 1068297 and 255?\n
51\n
ibivibiv/math_instruct
Let y = -2565 + 2562. Suppose -2*c - 5*u = -0*c - 84, 4*c - u = 190. Sort c, y, 4.\n
y, 4, c\n
ibivibiv/math_instruct
Suppose 4*k + 11 = 4*m + 3, -5*k + 6 = -m. Suppose -2*n = 5*n - 21. Suppose 2*x + 2 - 6 = n*c, 0 = 5*x - 25. Solve -c*s + 15 = 6*i - i, i - m*s = -19 for i.\n
1\n
ibivibiv/math_instruct
What is (-45 - -12) + 14 - -16?\n
-3\n
ibivibiv/math_instruct
What is -1069276 rounded to the nearest one thousand?\n
-1069000\n
ibivibiv/math_instruct
Suppose 4*j - 543 = -2*t - 43, 4*j + t - 502 = 0. Calculate the greatest common factor of 18 and j.\n
18\n
ibivibiv/math_instruct
Does 9 divide 36379?\n
False\n
ibivibiv/math_instruct
Let j(t) = -2*t**2 + 7547*t + 758818. Determine j(-98).\n
4\n
ibivibiv/math_instruct
In base 7, what is -461213 - 23?\n
-461236\n
ibivibiv/math_instruct
List the prime factors of 16820.\n
2, 5, 29\n
ibivibiv/math_instruct
Suppose -2*h + 0 = -4*c + 12, -3*h = -5*c + 13. Find the common denominator of 902/495 + 2/c and (10 - 139/10)*10/(-18).\n
18\n
ibivibiv/math_instruct
Let x = -42.1 + -10.9. Let t = x - -54.02. Let d = -0.02 + t. Which is the closest to 1? (a) d (b) -3/2 (c) 2/17\n
a\n
ibivibiv/math_instruct
Let 72*l**5 - 428*l**4 + 932*l**3 - 912*l**2 + 400*l - 64 = 0. What is l?\n
4/9, 1/2, 1, 2\n
ibivibiv/math_instruct
Calculate the common denominator of -83/22 and 65/462.\n
462\n
ibivibiv/math_instruct
Collect the terms in 21*m**3 - 46*m**3 - 8*m**3 - 10*m**3.\n
-43*m**3\n
ibivibiv/math_instruct
Which is the third smallest value? (a) -0.4 (b) -0.2 (c) 48 (d) -235683\n
b\n
ibivibiv/math_instruct
What is 646 minutes before 4:10 PM?\n
5:24 AM\n
ibivibiv/math_instruct
Let g(c) be the third derivative of -c**6/120 + 4*c**5/15 - c**4/12 + 23*c**3/6 - 1099*c**2. Determine g(16).\n
-9\n
ibivibiv/math_instruct
Let l = -12776 + 12779. Which is the second biggest value? (a) -4/5 (b) -2 (c) 17 (d) 4 (e) l\n
d\n
ibivibiv/math_instruct
Find the second derivative of 52936508*z**5 + 47872921*z + 2 wrt z.\n
1058730160*z**3\n
ibivibiv/math_instruct
What is prob of picking 2 p when two letters picked without replacement from ppppp?\n
1\n
ibivibiv/math_instruct
Let z = 64 - 34. What is the least common multiple of z and (3 + (-45)/10)*-22?\n
330\n
ibivibiv/math_instruct
Suppose -8*l + 18 = -5*l. What is the units digit of l?\n
6\n
ibivibiv/math_instruct
Evaluate -61 + 17 + 82 + -60.\n
-22\n
ibivibiv/math_instruct
How many hours are there in seven halves of a day?\n
84\n
ibivibiv/math_instruct
Convert -35a (base 11) to base 2.\n
-110101100\n
ibivibiv/math_instruct
Express 3*c + 2*c - 8*c in the form r*c + y and give r.\n
-3\n
ibivibiv/math_instruct
-23 + 3080/(-462) + (-4)/3\n
-31\n
ibivibiv/math_instruct
Calculate the remainder when 28078859 is divided by 163249.\n
31\n
ibivibiv/math_instruct
Suppose -2*a + 4*c = -52, 0*a - 4*c + 200 = 5*a. Suppose 97 = 5*i + 3*u - a, -5*u - 20 = 0. List the prime factors of i.\n
29\n
ibivibiv/math_instruct
Which is the closest to -1/475? (a) 0.3 (b) 586 (c) 7\n
a\n
ibivibiv/math_instruct
What comes next: -28873, -113714, -255109, -453052, -707537, -1018558, -1386109, -1810184?\n
-2290777\n
ibivibiv/math_instruct
Calculate -50 divided by -1802.\n
25/901\n
ibivibiv/math_instruct
What comes next: 8, 17, 34, 65, 116, 193?\n
302\n
ibivibiv/math_instruct
(-1)/(-3)*(-2)/(-3)\n
2/9\n
ibivibiv/math_instruct
Which is the nearest to 0.2? (a) -5 (b) 0 (c) 3 (d) -154 (e) 18\n
b\n
ibivibiv/math_instruct
What is the closest to 1 in -0.2, -2/5, 0.09, 2?\n
0.09\n
ibivibiv/math_instruct
Suppose -653 = -4*i - 77. Suppose -2*w - 3*h = -9, -w + 1 = -3*h + h. Suppose -w*f + 431 = 2*j, -f + j + i = 2*j. Is f prime?\n
False\n
ibivibiv/math_instruct
Let l(r) = -2 + 11*r + 7 - 3 - 1 + 2*r. Let g(y) = 52*y + 4. Calculate -2*g(m) + 9*l(m).\n
13*m + 1\n
ibivibiv/math_instruct
Let b(z) = -z**3 + 4*z**2 + 3*z - 6. Let h = 30 - 26. Calculate b(h).\n
6\n
ibivibiv/math_instruct
Which is smaller: 14193 or 1?\n
1\n
ibivibiv/math_instruct
Simplify ((sqrt(684)*3 + sqrt(684))**2 - (sqrt(95)/sqrt(5) + 2)) + (1 + sqrt(1216))**2*4*-6.\n
-18266 - 385*sqrt(19)\n
ibivibiv/math_instruct
What is 176 minutes after 11:05 AM?\n
2:01 PM\n
ibivibiv/math_instruct
Suppose 4*f = 2*f - 10, -2*o = 5*f + 21. Factor 4/3*y + 4/9*y**4 - 4/3*y**3 + 4/9*y**o - 8/9.\n
4*(y - 2)*(y - 1)**2*(y + 1)/9\n
ibivibiv/math_instruct
Factor -3*l**2/5 - 60943086*l/5 + 60943089/5.\n
-3*(l - 1)*(l + 20314363)/5\n
ibivibiv/math_instruct
Is 1099800 a multiple of 312?\n
True\n
ibivibiv/math_instruct
Let t be 6/(-20)*20/(-15). Which is the nearest to t? (a) 3 (b) -0.5 (c) -0.3\n
c\n
ibivibiv/math_instruct
Sort -3, -220, 13, 6, 3 in decreasing order.\n
13, 6, 3, -3, -220\n
ibivibiv/math_instruct
What comes next: 322, 1701, 3992, 7189, 11286?\n
16277\n
ibivibiv/math_instruct
Calculate the remainder when 21235 is divided by 2735.\n
2090\n
ibivibiv/math_instruct
Let g = 6.3 + -1.3. Let y = -0.98 + -0.02. What is the closest to 0 in y, -2, g?\n
y\n
ibivibiv/math_instruct
Rearrange ((-3*t + 3*t - 5*t**2)*(4 + 0 - 3) - 13 + 13 - 7*t**2)*(32*t - 30*t + 54*t) to the form i*t**3 + o*t + l*t**2 + k and give l.\n
0\n
ibivibiv/math_instruct
Let x(s) = s**3 + 12*s**2 - 17*s + 785. Calculate the remainder when x(-16) is divided by 21.\n
12\n
ibivibiv/math_instruct
Suppose -2*u + 14 - 2 = 0. Suppose 5*y + 4*o - 8 = 0, 2*y + u = 4*y + 3*o. Suppose 3*d + y*d = 6. Solve 15 = -5*s + d*n, -2*s - 5*n = -2*n - 13 for s.\n
-1\n
ibivibiv/math_instruct
Solve -2/9*p**3 + 4/3 - 4/3*p**2 + 2/9*p = 0.\n
-6, -1, 1\n
ibivibiv/math_instruct
What is the second smallest value in 332, 0.5, -5/2?\n
0.5\n
ibivibiv/math_instruct
Let x = -2 - -4. Suppose 3 = -5*v + 3*s, -v = x*v + 3*s - 3. Suppose -18 = -2*o - v*o. List the prime factors of o.\n
3\n
ibivibiv/math_instruct
Write an educational piece suited for college students related to the following text snippet: "Prove that $n^k+1$ has a prime divisor $>2k$ Let $$n\ge3$$ & $$k\ge2$$. Show that $$n^k +1$$ has a prime divisor $$>2k$$. • Where did you find this problem? It's quite interesting. – Carl Schildkraut Oct 20 '18 at 17:12 By...
This mathematical statement is an application of Zsigmondy's theorem, which deals with primality conditions in certain arithmetic sequences. Before diving into the details of the problem, let us first establish some definitions and background knowledge. **Prime number:** A natural number greater than 1 that cannot be...
ibivibiv/math_instruct
In base 4, what is -302101 - -10232?\n
-231203\n
ibivibiv/math_instruct
Express (-5 + 5 - 2*b)*(2 + 6*b - 2) in the form j*b + x + d*b**2 and give d.\n
-12\n
ibivibiv/math_instruct
Let j(i) = 3*i**2 - 3*i - i**2 + 0*i**2 - 4*i**2 - 4 - i**3. Suppose 3*m - 7 = 2*x, 0*x - 2*x - 3*m = -23. What is the remainder when j(-3) is divided by x?\n
2\n
ibivibiv/math_instruct
What is the hundreds digit of 378?\n
3\n
ibivibiv/math_instruct
Simplify (3*sqrt(68)*-3*-3)**2.\n
49572\n
ibivibiv/math_instruct