MTH 507 ASSIGNMENT SEMESTER 2, 2022

1. Explain what Gauss-Jordan elimination, with reference to an example, is. [2m]

2. Use Cramer's rule to solve the following system: x - 4y + z = 4

5x + 6y - 7z = 10

3x - 2y + z = 16

3. Graph the following system of linear inequalities:

2x - y 4

x + y 6

4. The given table shows the data of 10-point holders in a given class of 30. Find the probability that the student getting 10 point is a girl. 10 pointers Not 10 pointers Girl 3 8

Boy 6 13 5. Anna won a lottery, and immediately after winning, she decides to invest up to a total of $30,000 in two types of investments, Investment x that yields 10% per year and Investment y, which yields 8% per year. Furthermore, she believes that the amount invested in Investment x should be at most one-third of the amount invested in Investment y. What investment program should Anna pursue to maximize income? Clearly outline the objective function and the constraints. 6. To qualify for the university sprints squad, the athletes in the training squad must perform in the trials comprising speed tests. After the trials, it is observed that the individual times are normally distributed with mean of 13.2 seconds and a standard deviation of 3 seconds. If only the top 85% of the participating athletes are selected, find the cut-off time.

Hint: The top athletes will have the least times. 8. A red die and a white die are rolled. Event R is the event that the white die shows a number smaller than 3 and Event W is event that the sum of the numbers on both dice is greater than 9. What is the probability that events R or W occurs.