week 8 review

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1.

Write the following set in builder notation form


2.
Determine whether the equation defines y as a linear function of x. If so, write it in the form y = mx + b. 8x = 5y + 9

y = x +

 


y = x –

 


y = –x –

 


y = –x +

 


3.

Determine whether the system of linear equations has one and only one solution, infinitely many solutions, or no solution. Find all solutions whenever they exist.

one and only one solution


one and only one solution


one and only one solution


infinitely many solutions


4.
Find the present value of $40,000 due in 4 years at the given rate of interest 8%/year compounded monthly.


5.
Find the interest rate needed for an investment of $4,000 to grow to an amount of $5,000 in 4 yr if interest is compounded continuously. Please round the answer to the nearest hundredth of percent.


6.

Find the pivot element to be used in the next iteration of the simplex method.


7.

Indicate whether the matrix is in row-reduced form.


8.

In a poll conducted among 180 active investors, it was found that 100 use discount brokers, 122 use full-service brokers, and 54 use both discount and full-service brokers. How many investors use only discount brokers?


9.
If the line passing through the points (2, a) and (5, – 3) is parallel to the line passing through the points (4, 8) and (- 5, a + 1) , what is the value of a?


10.
Find the simple interest on a $400 investment made for 5 years at an interest rate of 7%/year. What is the accumulated amount?


11.

Metro Department Store’s annual sales (in millions of dollars) during 5 years were

Annual Sales, y

5.8

6.1

7.2

8.3

9

Year, x

1

2

3

4

5

Plot the annual sales (y) versus the year (x) and draw a straight line L through the points corresponding to the first and fifth years and derive an equation of the line L.





12.

The following breakdown of a total of 18,686 transportation fatalities that occured in 2007 was obtained from records compiled by the U.S. Department of Transportation (DOT).

Mode of Transportation

Car

Train

Bicycle

Plane

Number of Fatalities

16,525

842

698

538

What is the probability that a victim randomly selected from this list of transportation fatalities for 2007 died in a train or a plane accident? Round answer to two decimal places.


13.
A system composed of two linear equations must have at least one solution if the straight lines represented by these equations are nonparallel.


14.

Use Venn diagrams to illustrate the statement.


15.
A survey of 900 subscribers to the Los Angeles Times revealed that 700 people subscribe to the daily morning edition and 400 subscribe to both the daily and the Sunday editions.How many subscribe to the Sunday edition?


16.

Solve the linear programming problem by the simplex method.


17.

Write the equation in the slope-intercept form and then find the slope and y-intercept of the corresponding line.


18.

Maximize

P= 10x + 12y

subject to


19.

Check that the given simplex tableau is in final form. Find the solution to the associated regular linear programming problem.


20.

Let .

Are the events F and G mutually exclusive?


21.

Solve the system of linear equations using the Gauss-Jordan elimination method.


22.

Solve the linear system of equations

Unique solution:


Unique solution:


Infinitely many solutions:


23.
If a merchant deposits $1,500 annually at the end of each tax year in an IRA account paying interest at the rate of 10%/year compounded annually, how much will she have in her account at the end of 25 years? Round your answer to two decimal places.


24.
An experiment consists of tossing a coin, rolling a die, and observing the outcomes. Describe the event “A head is tossed and an odd number is rolled.”


25.
What is the probability of arriving at a traffic light when it is red if the red signal is flashed for 30 sec, the yellow signal for 5 sec, and the green signal for 40 sec?