Math Answers

The table below shows data collected in a research on the relationship

between monthly income and monthly expenditure of citizens in town Q.

Use it to answer the following questions.

Earner A B C D E F G H I J

Income usd . 44 65 50 57 96 94 110 34 79 65

Expenditure usd.“ 41 60 40 50 80 68 84 30 55 48

(a) Fit the regression line of expenditure on income using least squares

method.

(b) Using the regression line obtained in (a) above, estimate the expected

amount of expenditure of a Kenyan whose monthly income is usd.

75,000.

For a group of 20 items, sum of X = 1452, sum of x ² = 144800 and mode = 67,

find the Karl Pearson’s coefficient of skewness and interpret the results.

Tigist wishes to mix two types of food C and D in such a way that the vitamin contents of the mixture contain at least 8 units of vitamin C and 11 units of vitamin D. Food C costs $ 60/kg and Food D costs $80/kg. Food C contains 3 units/kg of Vitamin A and 5 units / kg of Vitamin B while food D contains 4 units/kg of Vitamin A and 2 units/kg of vitamin B. Determine the minimum cost of the mixture by graphic model.

2. A trader has 62 % chance of making a sale to each client. Given that the

behavior of successive clients is independent find the probability that the

trader will make a sale if two clients Lynn and Faith enter the trader’s

premises.

The results of the nationwide aptitude test in mathematics are normally distributed with a mean of 80 and a standard deviation of 15. Find the raw score such that 70% of the cases are below it.

Prove or disprove that the polynomial 21x^3 - 3x^2 + 2x + 9 is irreducible over Z2 , but not over Z3. Justify your answer.

The probability density function of a continuous random variable X is given below:

𝑓(𝑥) = {

1.25(1 − 𝑥

4

) , 0 < 𝑥 < 1

0 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒

a. Find P(0.4< X<0.9)

b. Compute the expected value and variance of X.

Draw Dienes block to show how to find the solution to 78 + 56