Finite math

Please answer all the questions and give a detailed explanation for each. (see attached)

1. Use the echelon method to solve the system
2. Use the Gauss-Jordan method to solve the system of equations
3. A cable TV company charges $23 for the basic service plus $5 for each movie
channel. Let C(x) be the total cost in dollars of subscribing to cable TV, using x
movie channels. Write a cost function for the problem.
4. In deciding whether or not to set up a new manufacturing plant, analysts for a
popcorn company have decided that a linear function is a reasonable estimation for
the total cost C(x) in dollars to produce x bags of microwave popcorn. They
estimate the cost to produce 10,000 bags as$5480 and the cost to produce 15,000
bags as $7780. Find the marginal cost of the bags of microwave popcorn to be
produced in this plant.
5. Find inverse, if it exists, for the matrix.
6. Solve the matrix equation AX = B for X by finding A to power
7. Maximization Problem. Use simplex Method to solve from Initial Tableau.
The initial tableau of a linear programming problem is given
8. Find Compound Amount for the deposit: $6980 at11% compounded
semiannually for 8 years.
9. Find Effective rate corresponding to the given nominal rate 18% compounded
quarterly.
10. Southwest Dry Cleaners believes that it will need new equipment in 10 years.
The equipment will cost $26,000. What lump sum should be invested today at
8% compounded semiannually, to yield $26,000?
11. Find expected value for the random variable.
A business bureau gets complaints as shown in the following table.
Find the expected number of complaints per day.
12. An insurance company says that at age 50 one must choose to take
$10,000 at age 60, $30,000 at 70, or $50,000 at 80 ($0 death benefit).
The probability of living from 50 to 60 is .87, from 50 to 70, .69, and
from 50 to 80, .43. Find the expected value at each age.
13. List the requirements for a binomial experiment. Describe an experiment which is
binomial and explain how the experiment satisfies the requirements.
14. The table summarizes the total incomes in the year 2000 of the residents of a
particular town. Only those residents with full-time employment are included.
Estimate the mean income for fully employed residents of the town in 2000.
15. Solve the problem. Round to nearest hundreds, if necessary.
The following data gives the number of applicants that applied for a job
at a given company each month of 1999:
63,72,69,75,84,77,80,85,81,69,65,63.
a) What is the mean?
b) Find the mode or modes.
c) Find the median.