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If 6 were red than 4 were orange, then the fraction of orange lamps to total lamps is 4/10, which simplifies to 2/5.

What can i multiply to get -32 and add to get -4?  

The numbers are –8 and +4.  

Check answer:    Multiply     (4) • (–8)  =  –32  

                            Add          (4) + (–8)  =  –4  

_.

If you are going to use Stirling's approximation, then you got it backwards!

what is 9223372036854775806! ==10^(10^(10^1.306055539958))

At t= 1      height =  10 - 1.86 = 8.14   m

at t= 3      height = 30- 16.74 = 13.26

       (13.26 - 8.14)/2 = 2.56 m / s                       (   I think you performed   height 1 - height 3 ) / 2    

Write as an equation: \(36+x = 4x\)

Subtract \(x\) from both sides:

\(36 = 3x\)

Divide each side by \(3\)

This means that after \(\color{brown}\boxed{12}\) seconds, both the adults and the children ran \(\color{brown}\boxed{48}\) meters.

Multiply:

First, simplify the mixed numbers to a fraction. This can be accomplished by multiplying the whole number by the number beneath the fraction sign and adding it to the number on top of the fraction sign. This number would now be your numerator over the original denominator. For example, \(1 {1 \over 2}\) would be \((1 \times 2) + 1\). This means that the improper fraction, in this case, the product would be \({3 \over 2}\). 

Repeat this to the other number, so you would have \(9 \over 4\). To multiply fractions, you multiply the numerators and the denominators. So, in this case, \({ 3 \over 2 }\times {9\over4} =\color{brown}\boxed{{ 27\over 8}}\).

To divide fractions, you need to multiply by the reciprocal. To get the reciprocal, you swap the numerator and the denominator of the SECOND fraction ONLY. In this case, \({3 \over 2 } \div {9\over4}={3\over2}\times {4\over9}\). To multiply both these fractions, you do as stated above, and you recieve \(12 \over 18\) or \(\color{brown}\boxed{2 \over3}\)

10 - 3r - 5g = 2 pencils are yellow       2 out of 10   =   2/10 = 1/5 are yellow

To divide a fraction BY a fraction ....flip the denominator and MULTIPLY

1 1/2 = 3/2       2 1/4 = 9/4

3/2  /  9/4     =    3/2  *   4/ 9   = 12/18 = 2/3

-32 x = -4      diviede both sides of the equation by - 32

x = 4/32 = 1/8

listfor(n, 1, 100, floor(2#n)) ==(1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 10)==625

The only possibilities are: 69,78,87,96. Of these, the only one that works is 69. nice :)

(10 - 9) / 10

1 / 10

0.1

10%

it is all the intervals of which the value of the function either goes up(increases) or goes down(decreases)

Your answer is incorrect guest. You need to account for the side lengths OQ and PO, each of which have a side length of 15. 

The circumference of a complete circle would be \(30\pi\), so the circumference of \(3 \over 4\) of the circle would be \(22.5\pi\)

We also have to add 30 to the circumference, so the circumference is \(\color{brown}\boxed{22.5\pi+30}\)

I am not smart enough yet to make AIME, but when I saw this problem I definitely got a little suspicious, as I knew one of my friends was taking the test and it was happening at that time. Later confirmed it was a real AIME problem. I wish good luck to everyone who attempted AIME this year PROPERLY, cheaters get nowhere in life. Hope to make it next year myself though!

There are lots of wrong answers on here.   

This is a super old question, are you seriously interested?

It is up to the askers whether or not they accept any particular answer.

Anyway,  I have now answered it,

Simon's favorite factoring trick? (SFFT) / FOIL

-1+3t=5+4s

3t=4s+6

6t=8s+12 (1)

-2-2t=sk

-2t=sk+2

-6t=6+3sk  (2)

add

0=18+8s+3sk

-18=s(8+3k)

\(8+3k\ne0\\ k\ne \frac{-8}{3}\)

The ENTIRE perimeter of the complete circle would be 2πr (30π) so three-quarters of it will be 30π * 3 / 4 = 90π/4 = 45π/2

I don't know how he can cheat...?

Us here have cameras that show computer screen... 

I knew people would try to ask for help. 

1. 'Answers' here might not always be right, it's better to do it YOURSELF.

2. 'Mock AIME'. What do you mean Mock AIME. This was the #3 question from this years' AIME 1. 

3. Do not ask questions from tests. 

Good luck to everyone who took the AIME this year :). 

x==5 and  y == - 21

You have to use the "Extended Euclidean Algorithm", which is a long process:

(164 * 5) + (39 * -21) = 1

0.806 :)

The sum of the complex solutions is 508.