Mary's car will go 261 miles on 14.5 gallons of gasoline in highway driving.

Mathematics

1 answer:

suter [353]3 years ago

3 0

Answer:

a) 91 1/6 gallons

b) 2502 miles

Step-by-step explanation:

You are given a number of miles and a number of gallons for the car. The ratio of these numbers is ...

(261 mi)/(14.5 gal) = 18 mi/gal

We presume this value is constant for this car. Then the questions can be answered by forming and solving a proportion:

a) 1641 miles/(gallons) = 18 mi/(1 gal)

Multiplying by gallons and dividing by 18 mi/gal, we get

1641/18 gal = (gallons) = 91 1/6 gal

It will take 91 1/6 gallons of gasoline for Mary to drive to her friend's house.

___

b) Same deal, but the miles are unknown.

(miles)/(139 gal) = (18 mi)/(1 gal)

Multiplying by 139 gal gives ...

(18 mi)·139 = (miles) = 2502 mi

139 gallons of gasoline will let Mary drive 2502 miles.

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A survey conducted for the Northwestern National Life Insurance Company revealed that 70% of American workers say job stress cau

Bad White [126]

Answer:

a) The expected number is 5.

b) 0.25% probability that none of the workers say they will burn out in the near future

c) 97.93% probability that at least two of the workers say they will burn out in the near future

Step-by-step explanation:

For each person, there are only two possible outcomes. Either they said they will burnout in the near future, or they did not. The probability of a person saying that they will burnout in the near future is independent of any other person. So the binomial probability distribution is used to solve this question.

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 combinations 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.

33 % said they expected to burn out in the job in the near future.

This means that $p = 0.33$

15 workers

This means that $n = 15$

a. Suppose a random sample of 15 American workers is selected. What is the expected number of these sampled workers who say they will burn out in the near future?

The expected number of the binomial distribution is given by the following formula:

$E(X) = np$