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3 years ago

7

The cost to rent a jet ski is $80 per hour. in addition there also includes fee for a lesson on how to use the jet ski. Steve re

nted a jet ski for 3 hours and the total bill was $265. Write the equation for the total cost of renting a jet ski y for x hours.

1 answer:

melomori [17]3 years ago

8 0

Answer:

$y=80x+25$

Step-by-step explanation:

Let

x ----> the number of hours

y ---> the total cost of renting a jet ski in dollars

we know that

The linear equation in slope intercept form is equal to

$y=mx+b$

where

m is the slope or unit rate of the linear equation

b is the y-intercept or initial value

In this problem we have

The slope is equal to

$m=\$80\ per\ hour$

we have the ordered pair (3,265)

substitute in the linear equation

$265=80(3)+b$

solve for b

$265=240+b$

$b=265-240$

$b=\$25$ ----> fee for a lesson on how to use the jet ski

substitute

$y=80x+25$

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Step-by-step explanation:

For each container, there are only two possible outcomes. Either it is undefilled, or it is not. This means that we can solve this problem using the binomial probability distribution.

Binomial probability distribution:

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinatios of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

In this problem

There are 10 containers, so $n = 10$ .

A food-packaging apparatus underfills 10% of the containers, so $p = 0.1$ .

a) This is P(X = 1)

$P(X = 1) = C_{10,1}.(0.1)^{1}.(0.9)^{9} = 0.38742$

b) This is P(X = 3)

$P(X = 3) = C_{10,3}.(0.1)^{3}.(0.9)^{7} = 0.05740$

c) This is P(X = 9)

$P(X = 9) = C_{10,9}.(0.1)^{9}.(0.9)^{1} = 0.00000$

d) This is $P(X \geq 5)$ .

Either the number is lesser than five, or it is five or larger. The sum of the probabilities of each event is decimal 1. So:

$P(X < 5) + P(X \geq 5) = 1$

$P(X \geq 5) = 1 - P(X < 5)$

In which

$P(X < 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)$

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$P(X = 0) = C_{10,0}.(0.1)^{0}.(0.9)^{10} = 0.34868$

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$P(X = 2) = C_{10,2}.(0.1)^{2}.(0.9)^{8} = 0.1937$

$P(X = 3) = C_{10,3}.(0.1)^{3}.(0.9)^{7} = 0.05740$

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Finally

$P(X \geq 5) = 1 - P(X < 5) = 1 - 0.99837 = 0.00163$

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