Math Answers

Find the power set of each of these sets, where a and b are distinct elements.

a) {a} b) {a, b} c) {∅, {∅}}

Company ABC limited capital structure as December 31st 2020 was as follows.

Amount

Ordinary share 80,000@sh 10 sh 800,000

12.5% preference shares@sh 15 sh 900,000

10% debentures @sh 100 sh 600,000

14% bank loan sh 500,000

Retained earnings sh 450,000

Additional information

The market value of the Equity is sh 15 and firm pays 10% dividend whereas the growth rate was 5% pa.

The market price of preference was sh 25 and the debenture market value was sh 90.

The equity flotation fee per share was sh 1 and corporation tax was 30%.

Required

Compute the cost of each source of fund

Answer these questions for the poset ({3, 5, 9, 15, 24, 45}).

a) Find the maximal elements.

b) Find the minimal elements.

c) Is there a greatest element?

d) Is there a least element?

e) Find all upper bounds of { 5, 9}.

f ) Find the least upper bound of { 5, 9}, if it exists.

g) Find all lower bounds of {15, 24}.

h) Find the greatest lower bound of {15, 24}, if it exists.

Use generating functions to solve the recurrence relation an = 4a_n−1 − 4a_n−2 +n²

, where a₀ = 2, a₁ = 5.

A researcher is interested in learning how strong is the association between the sodium intake and systolic blood pressure of 12 individuals and how well can he predict blood pressure from sodium intake. He obtained the following data from these 12 individuals:

Person

1

2

3

4

5

6

7

8

9

10

Sodium

6.8

7.0

6.9

7.2

7.3

7.0

7.0

7.5

7.3

7.1

6.5

6.4

BP

154

167

162

173

190

158

166

195

189

186

148

140

a.) Obtain the equation of the regression line and estimate the blood pressure of a person if his sodium intake is 6.6.

b.) Test H0: b= 0 at the 0.01 level of significance.

c.) Use the analysis of varianve technique to test if there is a significant linear relationship between sodium intake and blood pressure.

d.) Compare the results of (b) and (c)

An experiment was conducted to study the effect of pesticides on plant species that are exposed to them. Different dosages of pesticides were administered to 4 groups of 4 mice. The 16 mice were females of similar age and condition. One group received no pesticides. The response Y was measure of brain activity. It was postulated that brain activity (Y in moles/liters per minute) would decrease with an increase in dosage (X in mg/kg body weight)

Dose (X)

0.0, 0.0, 0.0, 0.0, 2.5, 2.5, 2.5, 2.5

Activity (Y)

10.6, 10.4, 10.8, 11.0, 11.0, 11.3, 10.3, 9.9

Dose (X)

5.0, 5.0, 5.0, 5.0, 7.5, 7.5, 7.5, 7.5

Activity (Y)

9.5, 9.2, 9.7, 8.6, 8.2, 8.0, 8.4, 7.8

a) test if there is a significant linear relationship between the dose and the brain activity by constructing an analysis of variance table for the above data.

b) compute r and interpret the result.

Determine the probability of getting the sum 6 exactly 3 times in 7 throws with a pair of fair dice

((D-3D'-2)^3)z=6(e^2x)sin(3x+y)

Use Cayley hamilton theorem to find the values of the matrix

A^8-5A^7+7A^6-3A^5+8A^4-5A^3+8A^2-2A+I

A box with a square base is taller than it is width. In order to send the box through the

PH mail, the height of the box and the perimeter of the base can sum to no more than

108 in. What is the maximum volume for such a box?