Homework Answers

With the help of Venn diagram and membership table prove:

(AUB)-C = (A-C)U(B-C)

In a large population, 58% of the people have been vaccinated. If 5 people are randomly selected, what is the probability that at least one of them has been vaccinated?

An amount of money is invested at 8% interest per year, compounded quarterly. After a number of years, the

accumulated amount in the account is R7 365,00. The investment earned R2 000,00 interest in this period.

If the accumulated amount is left in the account (the interest rate remains the same) for another period that

is one year longer than the first period, the accumulated amount in the account will then be

A sum of R8 000,00 is lent in the beginning of a year at a certain simple rate of interest. After eight months,

in a different loan, a sum of R1 164,00 more is lent but at the simple interest rate twice the former. At the

end of the year, R903,00 is earned as simple interest from both the loans. The original simple yearly rate of

interest, rounded to two decimal places, is

A local high school needs to hire several cafeteria workers and bus drivers. Cafeteria workers earn R13 800

per month and bus drivers earn R17 250 per month. The school board gave the school permission to spend

no more than R345 000 on the salaries per month, but must hire more than 15 people.

Let B represent the number of bus drivers hired.

Let C represent the number of cafeteria workers hired.

For every bus driver hired there must be at least two cafeteria workers hired. The number of cafeteria

workers must at most be three more than twice the number of bus drivers.

Write a system of linear inequalities that the school could use to determine the number of cafeteria workers

and bus drivers they can hire

x - 3y + 6z = 21

3x + 2y - 5z = - 30

2x - 5y + 2z = -6

The sum of values of x

x, y

y, and z

z of the solution is