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thanks to you, too jimkey!

Here it is in latex. Rationalize the denominator of \(\displaystyle \frac{1}{\sqrt[3]{3} - \sqrt[3]{2}}\). With your answer in the form \(\displaystyle \frac{\sqrt[3]{A} + \sqrt[3]{B} + \sqrt[3]{C}}{D}\), and the fraction in lowest terms, what is A + B + C + D?

When copy and pasting things with latex you need to paste it in the search bar copy it then post it in the question because otherwise the latex doesn't show up and then nobody can help you.

20.  The center cube on each edge and each corner. 

The 12 center cubes on the edges are red on two sides.

The   8 corner cubes are red on three sides. 

The   6 center squares on each face are red on one side. 

The   1 cube on the inside did not get painted. 

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In poker, how many 5-card hands are three-of-a-kind?   

There are 13 card values, ace through king.  There are four of each of those values. 

So it seems obvious, if simplistic, that the possibility is 13 different 3-of-a-kind hands. 

Edited to add:   This assumes that we aren't using any wild cards e.g., Jokers. 

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Thank you for the help!

Minus times plus is always minus. 

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We know one of the numbers is negative and another is positive. Negative x positive number always results in a negative number. Therefore the sign of the product is minus.

Good work.  You have a persuasive argument about the "selected simultaneously" condition, so I won't even address that, much less dispute it.  I said I didn't know how to figure probabilities.  But compare the answers we got... yours was 5/7 and mine was 25/36.  If mine were 25/35 instead, we would have the same answer since 25/35 reduces to 5/7.  I don't know what this signifies, if anything.   

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Which classes do you go to on AOPS because these look like AOPS homework well anyways I'll help

I did!  I have a lot of homework and over the past week these are the ones I needed help with.  I posted them all in the same post because I couldn't figure them out and the only responses I got was the guest giving me rong answers.

so he rides at 15*5280 feet per hour and there are 3600 seconds in an hour so we ahve the equation 15*5280/3600 feet per second=22 feet per second.

well the negtive and positive cancel out to become (2^-1)/(2^1)= (1/2)/2=4 so our final answer is 4

we find that the triangles made with 2 pieces is the same area as the square so the area is (10*2)^2/5=20^2/5=400/5=80

Thank you!

140/360*18*18π where 140/360*18=7 so it is 7*18π=126π

so we divide by 2 every time so 64/2^x=2 we then solve that 64=2^6 so 6-1=5 so we need to do this 5 times.

so from 6 feet to 15 feet is 9 feet so we have 9/6 for the percent and 9/6=3/2=1.5=150% so it grew 150%

well we could just put 3 dot's like this ... to represent a repeating decimal

I agree that you're going to make it to 2000 likes!

Yeah I agree that you sould only put 1-2 question at a time

we know that the sums of the angles in a pentagon is 540 and the other angles add up to 108+125+98+98=429 so 2x+11=540-429 and 2x+11=111 so 2x=111-11=100  and x=50 then we know that the exterior angles add up to 180 so we have y+8=180-111 and y=180-111-8 so that means y=61

for example x is the price of rice so the price of rice is 100% while the price of wheat is 120%x so we have the equaiton 100%/120%=100/120=8 1/3 which is 83 1/3 percent or 83.333...

qwertyzz, it's okay if you need help but dumping 4 questions for someone to do in a post is a bit too much. 1-2 is fine. From here it's clear that these are pretty much homework problems you need to submit before a due date.