Math Answers

An interest rate of 14.90% per year compounded every three months is equivalent to a weekly compounded compounded interest rate of

BAT Industries is a manufacturer of orange juice in Jamaica. In 2022 it sold a bottle of orange juice to wholesalers for $100 and its variable costs is $40 and fixed costs is $100,000 monthly:

Using the information provided. 

i. How many bottles of orange juice must the company sell in order to break even and what is the breakeven revenue? (4 marks)

ii. If the company sold 1,500,000 bottles of orange juice for the year 2022, what was its profit? (4 marks)

iii. Due to inflation, in 2023 fixed costs are expected to rise to $175,000 monthly. What will be the NEW break-even quantity and revenue? (4 marks)

iv. If the company will sell the same number of orange juice as it did in 2022 and it wants to make the same profit as in 20222, what price should they sell each bottle of orange Juice for in 2023? (5 marks)

Let X be a binomial(5, 0.2) random variable. Let Y be a discrete random variable that is independent of X, such that Y = 1 with probability 0.2 and Y = 0 with probability 0.8. What is the probability that the sum of X and Y is less than or equal to 3?

Find a general solution of the following differential equation

dy/dx - 5y = (xe^-2x)*y^-2

Solve the given initial value problem.

dy/dx = y(2x^2 +y^2)/2x^3

subject to y(1) = 1.

In a study of life expectancy of 400 people in a certain geographic region, the mean age death was 70 years, and the standard deviation was 5.1 years. If a sample of 50 people from this region is selected, what is the probability that he mean life expectancy will be less than 68 years?

(d^3-5d^2+7d-3)y=0

Lindiwe decides that she would like to buy her daughter,Mbali, a car when she turns 21 in six years time. She deposits R6000 each month into an account earning 8,94% interest per year, compounded monthly. The amount that Lindiwe ( rounded to the nearest rand ) will have available six years from now is

A firm uses three local hotels to provide accommodations for its clients. From past experience, it is known that 20% of its client are assigned rooms at Hotel A, 45% at Hotel B and 35% at Hotel C. It is also known that the probabilities of Hotel A, Hotel B and Hotel C facing water problems are 0.02, 0.01 and 0.03 respectively.

(a)Draw a tree diagram for the above data

(b)What is the probability that a client will be assigned a room without water problem?

A university has analyzed the results of 1,000 students after the first year examinations. The result of the analysis is summarized below

Types of sponsorship

Examination results

Government

Private

Church

Students who were to be discontinued

155

150

105

Students who passed the examination

180

195

170

Students who were to sit for a supplementary paper

20

5

20

Required

The probability that a student was discontinued or was required to sit for a supplementary paper                                                                                                           

The probability that a student was a government sponsored           

The probability that a privately sponsored student passed the examination     

The probability that a student was church sponsored and was required to sit for a supplementary paper