MATHEMATICS HELP

1. For randomly selected Mombasa residents, the number of times they visit a clinic frequency distributions was obtained as follows

Using the table above:

i. Estimate mean, mode and median

ii. Estimate mean absolute deviation, variance and standard deviation

Question 2

A factory operates on two types of machines

There are more machines of type B than those of type A. Taking the number of machines of type A used as X and that of types B as Y, form the inequalities in X and Y. If the profit from using machine A is sh. 400 per hour and that from using machine B is sh. 600 per hour. Find graphically, the number of machines of each type that should be in use to give maximum profit per hour hence find the maximum profit.

Required

Develop a linear program and hence find the optimal solution for the problem.

Question 3

A market researcher investigating preference for 3 brands of beverages coffee, tea and cocoa in Kisumu city gathered the following information. From a sample of 800 consumers, 230 took coffee, 245 took tea and 325 took cocoa. 30 took all three beverages, 70 took coffee and cocoa, 110 took coffee only while 185 took cocoa only.

Required:

i. Present the above information in a venn diagram

ii. Find the number of customers who took tea only

iii. Find the number of customers who took tea and coffee only

iv. Find the number of customers who took none of the beverages.