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Making linear equations out of word problems.

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1. Assume that you do not know how many people from your contact list will call you this week. Let's call this number z.
a. What would this z be called in mathematics? A variable
b. If you know that on the week of your birthday you will get 2.3 times the number of calls as normal, write an expression that writes this in terms of z.
2.3z=x
c. If z is the number of calls you got in module 1, calculate the number of calls you will get during your birthday week. Assume you got 10 calls in module 1. Z = 1
2. Assume that every week after the week you counted your number of contacts you add another person to the list. Assuming 150 contacts.
a. Write an equation that will tell you how many people will be on your list in x number of weeks.
b. Figure out how many people will be on your list in 12 weeks.
c. Figure out how many weeks it will take to have 200 people on your list.
3. Draw a coordinate system. On the x-axis place time measured in number of weeks, and on the y-axis the number of people in your contact list.
a. Assume week 1 is the week when you originally counted the number of contacts. Draw a point on the coordinate system that corresponds to the number of contacts at week 1.
b. Draw another point that corresponds to the number of people you calculated would be on your list in 12 weeks.
c. Draw a line that represents the equation you wrote in 2.a. Does this line go through the 2 points you drew in part 3 a and b? Why or why not?

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This solution provides step-by-step instructions for determining and graphing linear equations from word problems in 537 words.

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Linear Equations, Linear Programming, Word Problems and Measures of Central Tendency

Show your work.

1. (3 points) Find the equation of the line shown:

2. (6 points) A bank loaned $15,000, some at an annual rate of 16% and some at an annual rate of 10%. If the income from these loans was $1800, how much was loaned at 10%?

3. (3 point) Write the augmented matrix of the system:

2x1 -3x2 + x3 = 0 x1 - x2 - 2x3 = -2 -5x1 + x2 = -4

4. (3 point) Perform the row operation R2 = (-2)r1 + r2 on the matrix

5. (3 point) Indicate whether the reduced row-echelon form of each augmented matrix has one solution, no solution, or infinitely solutions.

a. b. c.

6. (4 points) Find: .

7. (4 points) Find: .

8. (6 Points) Find the inverse of: .

9. (8 points) Maximize P = x1 + 2x2 + 3x3 using the simplex method.
subject to the constraints
2x1 + x2 + x3 < 25
2x1 + 3x2 + 3x3 < 30
x1 > 0, x2 > 0, x3 > 0,

10. (8 points) A company makes three products, A, B, and C. There are 500 pounds of raw material available. Each unit of product A requires 2 pounds of raw material, each unit of product B requires 2 pounds of raw material, and each unit of product C requires 3 pounds. The assembly line has 1,000 hours of operation available. Each unit of product A requires 4 hours, while each unit of products B and C requires 5 hours. The company realizes a profit of $500 for each unit of product A, $600 for each unit of product B, and $1,000 for each unit of product C. Formulate (but don't solve) a linear program to determine how many units of each of the three products the company should make to maximize profits.

11. (3 point) What is the ending balance from an initial deposit of $4,250 at 12% compounded quarterly for 6 years?

12. (3 points) Find the present value of $5,000 in 5 years at 10% compounded annually.

13. (4 points) Find the value of an annuity in which $1,100 is deposited at the end of each year for 5 years, at an interest rate of 11.5% compounded annually.

14. (4 points) Determine the amount of each payment to be made to a sinking fund in order to pay off a $120,000 loan in 8 1/2 years when the funds earn interest at a rate of 10% compounded semiannually.

15. (4 points) Find the present value of an ordinary annuity with annual payments of $1,000, for 6 years, at 10% interest compounded annually.

16. (2 points) In a marketing survey, consumers are asked to give their first three choices, of 9 different drinks. In how many different ways can they indicate their choices?

17. (6 points) A class consists of 15 students. The instructor wants to pick a group of 4 to work on a special project.
a. How many different groups of 4 can he choose?
b. If the class consists of 10 girls and 5 boys, how many different groups
of 4 are made up of 2 boys and 2 girls?

18. (4 points) How many license plates can a state have if each license plate has 2 letters followed by 4 digits, if the first digit cannot be zero?

19. (6 points) Two cards are drawn at random from an ordinary deck of playing cards. The first is not replaced before the second is drawn. What is the probability that:
a. Both cards are aces?
b. At least one card is black?

20. (16 points) Using the following sample: 28, 30, 24, 30, 32, 40, 22, 25, 26, 34
a. Find the mean.
b. Find the median.
c. Find the mode.
d. Find the standard deviation.
e. Find the z-score for 30. (Assuming a normal distribution)
f. Find the range.

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