Search & Filtering
Find the dimensions of a right circular cone of minimum volume V that can be
circumscribed about a sphere of radius 8 inches.
Consider the following product mix problem:
Three machine shops A, B, C produces three types of products X, Y, Z respectively. Each product involves operation of each of the machine shops. The time required for each operation on various products is given as follows:
Machine shops
Products
A
B
C
Profit per unit
X
10
7
2
Birr 12
Y
2
3
4
Birr 3
Z
1
2
1
Birr 1
Available Hours
100
77
80
Make the Mathematical model of the above primal problem to maximise the profit and then make the dual problem
A work shop contains four persons available for work on the four jobs. Only one person can work on any one job. The following table shows the cost of assigning each person to each job. The objective is to assign person to jobs such that the total assignment cost is a minimum.
Jobs
1
2
3
4
A
20
25
22
28
Persons
B
15
18
23
17
C
19
17
21
24
D
25
23
24
24
show that p ↔ q and (p^q) v (¬p ^ ¬q) are logically equivalent.
A fast-food chain decided to carry out an experiment to assess the influence of advertising expenditure on sales. Different relative changes in advertising expenditure, compared to the previous year, were made in eight regions of the country, and resulting changes in sales levels were observed. The accompanying table shows the results
Increase in advertising expenditure (%) 0 4 14 10 9 8 6 1
Increase in sales (%) 2.4 7.2 10.3 9.1 10.2 4.1 7.6 3.5
a. Estimate the least-squares the linear regression of the increase in sales on increase in advertising expenditure
b. Find a 90% confidence interval for the slope of the population regression line
Use a Venn diagram to illustrate the subset of even integers in the set of all positive integers not exceeding 15.
Is the average amount spent on textbooks per semester by accounting majors significantly different from the average amount spent on text books per semester by management majors? Answer this question with a 90% confidence interval using the following data from random samples of students majoring in accounting or management. Discuss the assumptions
Accounting majors Management major
Mean $340 $285
Standard deviation 20 30
Sample size 40 50
Heights of the students in a class are given in the distribution below:
5' - 5'2" 10
5'2" - 5'4" 40
5'4" - 5'6" 25 .
Find:
1. Central Tendency
2. Dispersion
3. Skewness and kurtosis
A study is conducted in a company that employs 800 engineers. A random sample of 50 engineers reveals that the average sample age is 34.3 years. Historically, the population standard deviation of the age of the company’s engineers is approximately 8 years. Construct a 98% confidence interval to estimate the average age of all the engineers in this company
A researcher wanted to estimate the difference between the percentages of users of two tooth pastes who will never switch to another tooth paste. In a sample of 500 users of Toothpaste A taken by this researcher, 100 said that they will never switch to another toothpaste. In a sample of 400 users of Toothpaste B taken by the same researcher 68 said that they will never switch to another toothpaste.
(i) Let p1 and p2 be the populations of all users of Toothpastes A and B, respectively who will never switch to toothpaste. What is the point of p1-p2?
(ii) Construct a 98% confidence interval for the difference between the proportions of all users of the two toothpastes who will never switch
