I need help with the following 8 Pre-Statistic Problem

1. If the universal set is the set of the days of the week, A = {Tuesday, Wednesday, Thursday, Friday} and B = {Friday, Saturday, Sunday}, draw/shade a Venn diagram to represent the situation and find:

a) (A B)

b) (A U B)'

2. A survey of a group of 265 high school seniors was taken. The survey showed the following:

150 plan to go to college.

70 plan travel.

25 plan to go to college and travel but not work

80 plan to go to college and work but not travel

18 plan to travel and work but not go to college

15 plan to go to college, travel and work.

5 have no plan to travel, go to college or work

a) Sketch and properly label the Venn Diagram to

represent this situation (in the space to the right).

b) How many plan to work only?

3. A public college in Georgia guarantees that you'll earn a HOPE SCHOLARSHIP covering 80% of your tuition if you earn a 3.0 cumulative GPA in high school and maintain 3.0 cumulative GPA each year in college.

Let p represent "you earn a 3.0 cumulative GPA in high school"

Let q represent "you earn a 3.0 cumulative GPA in college"

Let r represent "A public college in Georgia awards you a HOPE SCHOLARHIP covering 80% of your tuition "

a) ~q (in words)

b) Write p -> r (in words).

c) Write the guarantee symbolically (not in words, use p, q, r)

4. The difference between a country's exports and imports is called the country's trade balance. If one country had a

trade balance of -$75 billion in 1990, $14 million in 1984, and -$27 trillion in 1989, what was the total trade balance for these years?

5. Museum officials expect that 10,000 people will visit the new exhibit in its first week and that the number of visitors will drop by 200 people per week after the first week during the first six months.

a) Writeequation to represent the total number of visitors in terms of weeks. Be sure to clearly define your variables.

b) Find the total number of visitors expected in the exhibit's first 9 weeks.

6. A flat rectangular piece of aluminum has a perimeter of 104 inches. The length is 18 inches longer than the width. Find the width. (Sketch and label a diagram.)

a) Write equation to determine the length and width (in terms of one variable).

b) Determine the LENGTH and WIDTH.

c) What is the area of the rectangular piece of aluminum?

7. The sum of the angles in a triangle is 180. Find the three angles of the triangle if one angle is four times the smallest angle and the third angle is 360 greater than the smallest angle.

8. How many different license plates can be made using 3 letters followed by 2 digits then followed by 2 letters.

Numbers are selected from the digits 0 through 9. The letters cannot repeat; the numbers may repeat.

9. A pair of fair, six-sided dice is rolled. (draw out the table.)

Find the following:

a. What is the probability of rolling a product of 20?

b. What is the probability of rolling at least a product of 20?

c. What is the probability of rolling a product of 1?