A Few Destroyer QR Questions

[tawaqul]

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1) On #34, it says: The dimensions of a rectangular box w/ a square base are all positive integers. If the volume is a prime number, what must be the area of the square base? Answer: 1.
I don't really understand the soln here, can anyone try to explain it to me in more detail/or maybe less detail, lol.

2) On #45, it says: Simplify the following: (x^-2/ y^-2) times (y/x)^3 . What I'm wondering here is why don't you get the correct answer if you simply take (x^-2 times y^3) all divided by (y^-2 times x^3). But if you do that and subtract the exponents accordingly, you get x times y^5....why? What am I doing that isn't allowed with my math?

3) On #64, it says: The weatherman tells you there is a 70% chance of rain each day for the next 3 days. What is the probability it will rain 2 out of the 3 days? Answer: 441/1000. I'm just not understanding how to do the problem with any sort of logic. Is the only way to do it, to memorize the formula given in the soln??

To all those that respond, thank you very much!

 

[klutzy1987]

1) On #34, it says: The dimensions of a rectangular box w/ a square base are all positive integers. If the volume is a prime number, what must be the area of the square base? Answer: 1.
I don't really understand the soln here, can anyone try to explain it to me in more detail/or maybe less detail, lol.

2) On #45, it says: Simplify the following: (x^-2/ y^-2) times (y/x)^3 . What I'm wondering here is why don't you get the correct answer if you simply take (x^-2 times y^3) all divided by (y^-2 times x^3). But if you do that and subtract the exponents accordingly, you get x times y^5....why? What am I doing that isn't allowed with my math?

3) On #64, it says: The weatherman tells you there is a 70% chance of rain each day for the next 3 days. What is the probability it will rain 2 out of the 3 days? Answer: 441/1000. I'm just not understanding how to do the problem with any sort of logic. Is the only way to do it, to memorize the formula given in the soln??

To all those that respond, thank you very much!

3) you use the sucess failure formula. NcR * (prob success)^#of success * (prob failure)^#failure

3C2 * .7^2 * .3^1=.441 or 441/1000

 

[klutzy1987]

2) You can just multilpy it out to get (X^-2 * Y^3)/(X^3 * Y^-2)

Simlpifying this gives Y^5/X^5.

 

[klutzy1987]

1) In order for a volume, which is 3 numbers multiplied, to be a prime number it has to have 2 sides being 1. Otherwise it is impossible for the volume to be prime.

 

[Andre3k]

1.) Prime number is a number divisible by 1 and itself.
The rectangular box has a square base so you know that the length and the width of the base have to be equal. But the height can be any positive integer.
V = L x W x H
So the volume has to be 1 times some number
If you use any other number except 1 for the length and the width the volume wont be prime.
V = (2)x(2)x H= 4H cant be prime
V = (3)x(3)x H= 9H cant be prime
V = (4)x(4)x H= 16H cant be prime
However
if V = (1)x(1)x H= 1H Can be Prime
So L x W of the base has to be 1

2) Is the answer y^5/x^5 ??

3) No clue

 

[klutzy1987]

2) Is the answer y^5/x^5 ??

The answer is Y^5/X^5.

 

[klutzy1987]

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