Math Answers

On the menu list of a restaurant, there are 4 vegetables, 3 salads and 2 types of bread. If a customer wants one vegetable, one salad and one bread, how many possible choices are there for him?

How many ways can 3 cars and 4 trucks be selected from 8 cars and 11 trucks to be tested for a safety inspection?

Three sets of twins are to pose for photographs. How many photographs are possible if each set of the twins are to stand close to each other?

A passenger on a steamboat with a water wheel (see picture) notices an object that has become stuck on one of the paddles of the water wheel. She begins to keep track of its position above the water when it is at a point that is 7 m from the surface. The object then moved upwards to its highest point, 16 m above the surface of the water, then, 6 s later, to its lowest point 4 m below the surface of the water. a) Sketch a graph that represents the height of an object above the water, relative to the distance it has traveled for 2 rotations of the water wheel. Graph on the Separate Paper to. b) Determine an equation of the function, represented by this graph.

Television advertisers value the well-known Radio and TV awards scheme RTP as a measure of a TV/Radio show’s popularity among viewers. The RTP rating of a certain TV program is an estimate of the proportion of viewers, expressed as a percentage, who watch the program on a given day. In one survey, the RTP ratings team found that 101 out of 165 sampled families watched “The KSM Show” on the night of its premiere (the first time it is shown on television). In a separate survey several years later, the RTP ratings team found that 97 out of 180 sampled families watched “Music Music on TV3” on its premiere.

(a) Let p2 be the true proportion of all TV-viewing families who watched the premiere of “Music Music on TV3”. Estimate p1 − p2 and obtain a 95% confidence interval for p1 − p2.

(b) From the results in part (a), can you tell whether the premiere of “The KSM Show” was more popular that the premiere of “Music Music on TV3”? Give a brief justification of your answer.

Television advertisers value the well-known Radio and TV awards scheme RTP as a measure of a TV/Radio show’s popularity among viewers. The RTP rating of a certain TV program is an estimate of the proportion of viewers, expressed as a percentage, who watch the program on a given day. In one survey, the RTP ratings team found that 101 out of 165 sampled families watched “The KSM Show” on the night of its premiere (the first time it is shown on television). In a separate survey several years later, the RTP ratings team found that 97 out of 180 sampled families watched “Music Music on TV3” on its premiere.

(a) Estimate the true proportion p1 of all TV-viewing families who watched the premiere of “The KSM Show” and obtain a 95% confidence interval for p1.

(b) Briefly explain what this 95% confidence interval means.

(c) If the RTP team wanted to guarantee that all proportions are estimated to within ±0.05 with 95% confidence, how large should their samples be?

If a normal population of overpayments by National Health Insurance Authority to a private health service

provider is known to have a population standard deviation equal to GHC5, how large a sample would we

take in order to be 95% confident that the sample mean overpayment will not differ from the population

mean overpayment by more than ±0.80?

In a sample of 50 turnings from an automatic lathe 8 were found to be outside specifications. The cutting

bits were then changed and the machine restarted. A new sample of 50 contained 3 defective turnings.

Find a 90% confidence interval for the decrease in the proportion defective after changing bits.

The manager of AllNeeds supermarket wants to estimate µ,, the average amount of money spent per week

for groceries by each student, assuming this amount of money follows approximately a normal distribution.

A random sample of 90 is taken, of which the mean and standard deviation of the amount of money spent

per week for groceries are GHC81.50 and GHC10.36 respectively.

(a) Calculate a 99% confidence interval for µ.

(b) Based on your result in (i), would you say on average a student spends more than GHC30?

(c) How many students must be surveyed if the manager wanted to estimate the true average spending

of students within a margin of .10 with probability .95?

The directors of Thor Limited have appointed you as their financial consultant. They are considering new investment projects and need you to calculate the cost of capital for the company. The present capital structure is as follows; 2 000 000 ordinary shares with a par value of R1.00 per share. These shares are currently trading at R2.50 per share and the latest dividend paid is 40 cents. An average dividend growth of 9% is maintained. 1 500 000 8% R2.00 preference shares, with a market value of R1.80 per share. R10 000 000 non-distributable reserves R2 000 000 7% debentures due in 6 years time and the current yield to maturity is 10%, and R1 000 000 15% bank loan. Additional information: The company has a beta of 2.1 a risk free rate of 7% and a return of market of 16%. The company tax rate is 30%. Required 3.1 Calculate the weighted average cost of capital using Gordon growth model to calculate the cost of equity. (7) 3.2