Mat 119 Finite Mathematics
Department of Mathematics and Statistics
Arizona State University
Summer 2006, Final Exam Review Total Points 30
1. Solve the following system of linear equations:
2. Solve the following system of linear equations by matrix inverse method:
3. Find for the given matrices and .
4. Graph the system of inequalities and list all corner points of your feasible region.
5. Find the minimum value of the objective function , subject to the given constraints: Show complete work.
6. Suppose you invest some amount at simple interest for years. If the total amount is found as $5020 in the account find how much you have invested.
7. Suppose you invest $45000 at 5.03% compounded biweekly.
- Find how much interest is found in the account after 7 years.
- Find the effective rate of interest.
8. Find the number of years for which $3000 will be $6000 at interest compounded annually.
9. A $200,000 mortgage that has been financed over 30 years at 6% APR compounded monthly
- Find the monthly payment
- Find the equity after 20 years
10. How many license plates consisting of 2 letters (upper case) followed by 2 digits are possible?
11. The student relations committee of a college consists of 2 administrators, 3 faculty members, and 5 students. Four administrators, 8 faculty members, and 20 students are eligible to serve. How many different committees are possible?
12. Find the coefficient of in the expansion of
13. In tossing 2 fair dice, are the events, “sum is 2” and “sum is 12” mutually exclusive? What is the probability of obtaining either a sum 2 or a sum 12?
14. If two fair dice are thrown, what are the odds of obtaining a sum of 7?
15. For a 3-child family, find the probability of exactly 2 girls, given that the first child is a girl.
16. Given that , what is ? Are E and F independent?
17. Find the number of 7 digit telephone numbers
- with no repeated digits and no lead zero
- with no repeated digits but lead zero is allowed
- with repeated digits allowed including a lead zero
- the first digit can not be 0 or 9 and last digit is greater than 2 but less than or equal to 4.
18. Write down initial simplex tableau for the problem (if in standard form)
Max , subject to the following constraints
Also show one iteration using pivot element and write corresponding solution.
19. Show that 0! = 1