What is the factored form of 216p^3+125q^3?

1 answer:

7 0

Notice that 216 is a perfect cube and so is 125.
You have the sum of two cubes which is factorable and follows the pattern:

$a^3 + b^3 = (a + b)(a^2 - ab + b^2)$

$216p^3 + 125q^3 =$

$= (6p)^3 + (5q)^3$

$= (6p + 5q)(36p^2 - 30pq + 25q^2)$

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You take a three-question true or false quiz. You guess on all the questions. What is the probability that you will get a perfec

elena-14-01-66 [18.8K]

The probability that you will guess the first answer correctly = 1/2 = 0.5
The probability that you will guess the second answer correctly = 1/2 = 0.5
The probability that you will guess the third answer correctly = 1/2 = 0.5

The probability that you will guess all three answers correctly is

(0.5) x (0.5) x (0.5) = 0.125 = 12.5% .

============================

Here are all the ways your answer sheet could wind up:
(R = a right answer. W = a wrong answer.)

W W W
W W R
W R W
W R R
R W W
R W R
R R W
R R R

Number of possible ways to score 0 right out of 3 questions: 1 way
Number of possible ways to score 1 right out of 3 questions: 3 ways
Number of possible ways to score 2 right out of 3 questions: 3 ways
Number of possible ways to score 3 right out of 3 questions: 1 way

Statistically, if your answers are all pure guesses,
then on the average, the score you expect is

(0 + 33-1/3 + 33-1/3 + 33-1/3 + 66-2/3 + 66-2/3 + 66-2/3 + 100) / 8

= 400 / 8

= 50% .

If you're happy with that score, great !
Go to the movies the night before the test,
and start guessing.

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A new park was designed to contain two circular gardens. Garden A had a diameter 50 m, anf garden B has a diameter of 70 m. If t

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Which is greater, 1/4 or 9/20

Zina [86]

9/20

You need to have the same denominator so multiply it by 5 on the bottom and top to get 5/20 then you can compare it 5/20 < 9/20

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