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Pachacha [2.7K]
3 years ago
5

a rectangle swimming pool is 4 ft deep. one side of the pool is 2.5 times longer than the other. the amount of water needed to f

ill the swimming pool is 1960 cubic feet. find the dimensions of the pool. (find largest and smallest)
Mathematics
1 answer:
mojhsa [17]3 years ago
8 0

Find the are of the pool by dividing the volume by the depth:

1960 / 4 = 490

The pool is 490 square feet.


Area is found by multiplying the length by the width.

Let the width = X

We are told the length is 2.5X ( 2.5 times longer)


So we now have 2.5x * x = 490


2.5x * x = 2.5x^2


Now we have 2.5x^2 = 490


Divide both sides by 2.5:

x^2 = 490/2.5

x^2 = 196

find X by taking the square root of 196:

x = √196

x = 14


The width is 14 feet

The length is 2.5 * 14 = 35 feet

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We can find the individual probabilities and we got:

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Step-by-step explanation:

For this case we have the following density function:

f(x) = \frac{27}{13} (\frac{1}{3})^x , x=1,2,3

In order to satisfty that this function is a probability mass function we need to check two conditions:

1) f(x_i) \geq 0, \forall x_i

2) sum_{i=1}^n P(X_i) =1

We can find the individual probabilities and we got:

f(1)= \frac{27}{13} (\frac{1}{3})^1 =0.6923

f(2)= \frac{27}{13} (\frac{1}{3})^2 =0.2307

f(3)= \frac{27}{13} (\frac{1}{3})^3 =0.0770

And the sum of the 3 values 0.6923+0.2307+0.0770= 1 so then we satisfy all the conditions and we can conclude that f(x) is a probability distribution.

And if we want to find the following probabilities:

P(X \leq 1) = P(X=1) =0.6923

P(X>1) = P(X=2) +P(X=3) = 0.2307+0.0770=0.3077

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