Math120 Final Review Exercises

Math120 Final Review Exercises

1. Find the perimeter of given figure.

a)b)c) d)

1. Find the areas of given figure.

a) b) c)

1. a) If a tree casts a shadow 12 feet long and at the same time a person who is 5 feet 10 inches tall casts a shadow of 5 feet, find the height of the tree.

b) The two triangles shown are similar. Find the length of side AC.

1. Evaluate each expression:

1. 8!
2. 8P2
3. 7P5
4. 3C3
5. 9C7

1. a) The letters A, B, C, D, and E are to be used in a four-letter ID card. How many different cards are possible if letters are allowed to be repeated? How many cards are possible if each letter can only be used once?

b) How many different ways can a pledge class with 20 members choose a president, vice president, and Greek Council representative? (No pledge can hold two offices.)

c) How many different ways can seven types of laser printer be displayed on a shelf in a computer store?

d) Out of a group of eight students serving on the student government association, how many different ways can a president, a vice president, and a treasurer be selected?

e) How many combinations of four objects are there taken two at a time?

f) While studying abroad one semester, Tran is required to visit 10 different cities. He plans to visit 3 of the 10 over a long weekend. How many different ways can he choose the 3 to visit? Assume that distance is not a factor.

1. A single die is rolled. Find the probability of getting

1. A 2.
2. A number less than 5.
3. An odd number.

1. Two coins are flipped. Find the probability of getting

1. Two heads.
2. At least one head.
3. At most one head.

1. A card is drawn from an ordinary deck. Find the probabilities of getting

1. A jack.
2. Not drawing the clubs.
3. A 3 or a diamond.

1. A card is drawn from an ordinary deck. Find the probabilities of getting

a) Both cards are redb) Both cards are ace

1. A card is drawn from a standard deck of 52 cards.

1. Find the odds in favor of getting an ace.
2. Find the odds against getting an ace.

1. Suppose that your professor goes stark raving mad and chooses your final grade from A, B, C, D, F, or Incomplete totally at random. Find the probability of getting an A given that you get a letter grade higher than D.
2. Find the probability that a red card was picked given that the number on the card was an odd number.
3. Find the probability that a number less than 5 was picked given that the card was a black card.

1. You pay a dollar to roll two dice. If you roll 5 or 6, you get your dollar back plus two more just like it. If not, you get nothing and like it. Find the expected value of playing this game 100 times.
2. The prize in a raffle is a flat-screen TV valued at $350, and 1,000 tickets are sold. What's the expected value if you buy 1 ticket?

1. Find the mean, median, mode, range, and standard deviation of given data.

a)

b)

1. Find the area under the standard normal distribution

1. Between z = 1.55 and z = 2.25.
2. Between z = −0.60 and z = −1.35.
3. Between z = 1.50 and z = −1.75.
4. To the right of z = 1.70.
5. To the right of z = −0.95.

1. If the weights of Oreos in a package are normally distributed with mean 518 grams and standard deviation 4 grams, find the percentage of packages that will weigh less than 510 grams.
2. Based on data in the 2012 Statistical Abstract of the United States, the average American generates 1,570 pounds of garbage per year. Let's estimate that the number of pounds generated per person is approximately normally distributed with standard deviation 200 pounds. Find the probability that a randomly selected person generates

1. Between 1,250 and 2,050 pounds of garbage per year.
2. More than 2,050 pounds of garbage per year.

Table: Area Under a Normal Distribution Curve Between z = 0 and a Positive Value of z