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.

  1. Find how much interest is found in the account after 7 years.
  1. 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

  1. Find the monthly payment
  2. 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

  1. with no repeated digits and no lead zero
  2. with no repeated digits but lead zero is allowed
  1. with repeated digits allowed including a lead zero
  1. 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