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sum(12358, 12385, 12538, 12583, 12835, 12853, 13258, 13285, 13528, 13582, 13825, 13852, 15238, 15283, 15328, 15382, 15823, 15832, 18235, 18253, 18325, 18352, 18523, 18532, 21358, 21385, 21538, 21583, 21835, 21853, 23158, 23185, 23518, 23581, 23815, 23851, 25138, 25183, 25318, 25381, 25813, 25831, 28135, 28153, 28315, 28351, 28513, 28531, 31258, 31285, 31528, 31582, 31825, 31852, 32158, 32185, 32518, 32581, 32815, 32851, 35128, 35182, 35218, 35281, 35812, 35821, 38125, 38152, 38215, 38251, 38512, 38521, 51238, 51283, 51328, 51382, 51823, 51832, 52138, 52183, 52318, 52381, 52813, 52831, 53128, 53182, 53218, 53281, 53812, 53821, 58123, 58132, 58213, 58231, 58312, 58321, 81235, 81253, 81325, 81352, 81523, 81532, 82135, 82153, 82315, 82351, 82513, 82531, 83125, 83152, 83215, 83251, 83512, 83521, 85123, 85132, 85213, 85231, 85312, 85321)==Total permutations ==120==Total sum==5,066,616

There are 120 ways to arrange these 5-digit positive integers. That means that the digits will be added 24 times in each digit of the sum. Therefore, our sum would be equal to:
5(24(10000 + 20000 + 30000 + 50000+80000) + 24(1000 + 2000 + 3000 + 5000 + 8000) + ... + 24(1 + 2 + 3 + 5 + 8)))

We know that this is equal to:

120(11111 + 22222 + 33333 + 55555 + 88888) 

= 25333080

Guest, I don't think computing the avlues would be a great idea. We could take a more less bashy approach with C and P. But that works too! :D

Minor issue, Guest. We are looking for the product and not the sum. :)

The answer would be 9 * 3 * 2 = 54. 

Combining liking terms gives us:

ax^2 + 18x + 9 

We know that if we factor this out, we get:
\((\sqrt{a} + 3)^2\)

Since we know that 6sqrt(a) = 18

We know that sqrt(a) = 3 

a = 9. 

H(4, b) = (4 + 2sqrt(b) + b)/3.

In order for this to be a postive integer b has to be a perfect square and the numberator has to be divisble by 3. The smallest perfect square that outputs a postive integer is b = 25. 

[2^10 * 3^18 * 5^4] / 150 ==1,652,994,086,400==2^9 × 3^17 × 5^2

Number of divisors ==[9 +1] * [17 +1] * [2 + 1] ==10 x 18 x 3 ==540 divisors.

345600 = 2^9 * 3^3 * 5^2

a + b + c==9 + 3 + 2 ==14

What is the prime factorization of 6300? How can we use the prime factorization to solve for the odd divisors? Remember, odd x odd is odd. :) 

A very interesting problem, indeed. Since we know that Dmitri and Ivan are next to Fyodor, who do you think is diagonally across Fyodor? What is the length of the diagonal of this rectangular room? Can you go from here? :)

Note that 150 is equal to 2 * 3 * 5^2.

This means that our divisors need at least 1 2, 1 3, and 2 5s. 

That means that we can select any power of 2 from 1 - 10. This gives us 10 ways. 

In addition, we can select any power of 3 from 1 - 18. This gives us 18 ways.

Finally, since we need 2 5s, we can choose any power of 5 from 2-4. This counts as 3 ways.

We multiply all of these together to receive 540 ways. 

Set the length equal to x. What would the length of the width be?

Can you find an expression for the perimeter in terms of x?

From the first equation, we get:

-z + x = 8 - y

And the third equation gievs us:

z - x = 10 - 2y.

Since we know that -z + x is -1 times z - x, we know that:

8 - y = 2y - 10

This gives us: y = 6

Substiting this value into the first two equations gives us:

x = 7, z = 5

From here, we get 210 as our answer. 

Try divisibility tricks! See what you can find and what postie integers divide into that number :)

It seems that the centers of the circles form a triangle. Can you find the lengths of this triangle using radii? How can we find the area after finding the lengths of a triangle?

Liz's babysitting rate is common to both Zander and Ailey. If we assign her charge as \(x\) we can represent both Zander and Ailey's rates as \(\frac{7}{4}x\). We know that Ailey worked \(2\) hours to earn \(47\) dollars. Do you think we can find \(x\), which is Liz's rate now? After that, can you find Zander and Ailey's rates?

You should be able to solve the problem now. 

You're obviously trolling. The wording of this question makes it hard to interpret. We don't know if you're asking for

\(\frac{(1-32)}{100}\), or 1 - \(\frac{32}{100}\)

Besides, this is an incredibly simple problem. It's disappointing that you would try to cheat on basic schoolwork.

The answer is 3.

there are more teaching answers now. thank goodness.

just solve for the numerator and then you get the answer. I'm not sure if this is a troll post...

1-32= -31

that's your denominator. i hope you can do the rest on your own because it's simple fractions. 

if Sally finished right after 90%, wouldn't that mean that she would be 91%? Then, 9% would be greater, right?

what have you done to start this problem? this is a relatively simple math question involving fractions. Perhaps you could show your work?

NICE JOB guest!