Asurvey of magazine subscribers showed that 45.8% rented a car during the past 12 months for business reasons, 54% rented a car during the past 12 months for personal reasons, and 30% rented a car during the past 12 months for both business and personal reasons. what is the probability that a subscriber rented a car during the past 12 months for business or personal reasons? what is the probability that a subscriber did not rent a car during the past 12 months for either business or personal reasons?

There is a 69.8% probability that a subscriber rented a car during the past 12 months for business or personal reasons.

There is a 30.2% probability that a subscriber did not rent a car during the past 12 months for either business or personal reasons.

Step-by-step explanation:

We can solve this problem by building the "Venn Diagram" of these probabilities.

I am going to say that A is the probability that a magazine subscriber rented a car for business reasons.

B is the probability that a magazine subscriber rented a car for personal reasons.

C are those who did not rent a car for either of these reasons.

We have that:

In which a are those who only rented for business reasons and are those who rented both for business and personal reasons.

By the same logic, we have that

In which b are those who only rented for personal reasons.

The sum of the probabilities is 1, so:

We start finding the values from the intersection of these sets.

30% rented a car during the past 12 months for both business and personal reasons. So .

45.8% rented a car during the past 12 months for business reasons

This means that .

And

54% rented a car during the past 12 months for personal reasons

This means that .

And

What is the probability that a subscriber rented a car during the past 12 months for business or personal reasons?

That is the probability that someone rented a car for only one of these reasons, or both. So:

There is a 69.8% probability that a subscriber rented a car during the past 12 months for business or personal reasons.

What is the probability that a subscriber did not rent a car during the past 12 months for either business or personal reasons?

This is the value of C

We have that:

[tex]C = 0.302[tex]

There is a 30.2% probability that a subscriber did not rent a car during the past 12 months for either business or personal reasons.

the final amount you will pay is $68.04.

the tip is determined by the pre-tax amount, so we calculate the tip based on the original bill, not after we've added sales tax.

to find the tip:

we can divide 54.00 by 100 to get 1% of 54. then we multiply that by 18.

54 / 100 = .54

.54 x 18 = 9.72

tip = 9.72$

to find the tax:

we can divide 54.00 by 100 to get 1% of 54. then we can multiply that by 8 to get 8%.

54 / 100 = .54

.54 x 8 = 4.32

tax= 4.32

now we can add the tip and tax to the bill to get our total.

54 + 9.72 + 4.32 = 68.04

total: $68.04

step-by-step explanation:

answer:   (s+1)(s+4)

step-by-step explanation:

factor s2+5s+4

s2+5s+4

=(s+1)(s+4)