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# Algebra 2

## Educators

### Problem 1

State whether the events are independent or dependent.
choosing the color and size of a pair of shoes

Elizabeth X.

### Problem 2

State whether the events are independent or dependent.
choosing the winner and runner-up at a dog show

Elizabeth X.

### Problem 3

An ice cream shop offers a choice of two types of cones and 15 flavors of ice cream. How many different 1-scoop ice cream cones can a customer order?

Elizabeth X.

### Problem 4

A bookshelf holds 4 different biographies and 5 different mystery novels. How many ways can one book of each type be selected?
A. 1
B. 9
C. 10
D. 20

Elizabeth X.

### Problem 5

Lance’s math quiz has eight true-false questions. How many different choices for giving answers to the eight questions are possible?

Elizabeth X.

### Problem 6

Pizza House offers three different crusts, four sizes, and eight toppings. How many different ways can a customer order a pizza?

Elizabeth X.

### Problem 7

For a college application, Macawi must select one of five topics on which to write a short essay. She must also select a different topic from the list for a longer essay. How many ways can she choose the topics for the two essays?

Elizabeth X.

### Problem 8

State whether the events are independent or dependent.
choosing a president, vice-president, secretary, and treasurer for Student Council, assuming that a person can hold only one office

Elizabeth X.

### Problem 9

State whether the events are independent or dependent.
selecting a fiction book and a nonfiction book at the library

Elizabeth X.

### Problem 10

State whether the events are independent or dependent.
Each of six people guess the total number of points scored in a basketball game. Each person writes down his or her guess without telling what it is.

Elizabeth X.

### Problem 11

State whether the events are independent or dependent.
The letters A through Z are written on pieces of paper and placed in a jar. Four of them are selected one after the other without replacing any of them.

Elizabeth X.

### Problem 12

State whether the events are independent or dependent.
Tim wants to buy one of three different books he sees in a book store. Each is available in print and on CD. How many book and format choices does he have?.

Elizabeth X.

### Problem 13

State whether the events are independent or dependent.
A video store has 8 new releases this week. Each is available on videotape and on DVD. How many ways can a customer choose a new release and a format to rent?

Elizabeth X.

### Problem 14

State whether the events are independent or dependent.
Carlos has homework in math, chemistry, and English. How many ways can he choose the order in which to do his homework?

Elizabeth X.

### Problem 15

State whether the events are independent or dependent.
The menu for a banquet has a choice of 2 types of salad, 5 main courses, and 3 desserts. How many ways can a salad, a main course, and a dessert be selected to form a meal?

Elizabeth X.

### Problem 16

State whether the events are independent or dependent.
A baseball glove manufacturer makes gloves in 4 different sizes, 3 different types by position, 2 different materials, and 2 different levels of quality. How many different gloves are possible?

Elizabeth X.

### Problem 17

State whether the events are independent or dependent.
Each question on a five-question multiple-choice quiz has answer choices labeled A, B, C, and D. How many different ways can a student answer the five questions?

Elizabeth X.

### Problem 18

Abby is registering at a Web site. She must select a password containing six numerals to be able to use the site. How many passwords are allowed if no digit may be used more than once?

Elizabeth X.

### Problem 19

How many ways can you arrange the science books?

Elizabeth X.

### Problem 20

Since the science books are to be together, they can be treated like one book and arranged with the music books. Use your answer to Exercise 19 and the Counting Principle to find the answer to the problem in the comic.

Elizabeth X.

### Problem 21

Refer to the information about telephone area codes at the left.
How many area codes were possible before 1995?

Elizabeth X.

### Problem 22

Refer to the information about telephone area codes at the left.
In 1995, the restriction on the middle digit was removed, allowing any digit in that position. How many total codes were possible after this change was made?

Elizabeth X.

### Problem 23

How many ways can six different books be arranged on a shelf if one of the books is a dictionary and it must be on an end?

Elizabeth X.

### Problem 24

In how many orders can eight actors be listed in the opening credits of a
movie if the leading actor must be listed first or last?

Elizabeth X.

### Problem 25

How many different 5-digit codes are possible using the keypad shown at the right if the first digit cannot be 0 and no digit may be used more than once?

Elizabeth X.

### Problem 26

Use the Internet or other resource to find the configuration of letters and numbers on license plates in your state. Then find the number of possible plates.

Elizabeth X.

### Problem 27

Describe a situation in which you can use the Fundamental Counting Principle to show that there are 18 total possibilities.

Elizabeth X.

### Problem 28

Explain how choosing to buy a car or a pickup truck and then selecting the color of the vehicle could be dependent events.

Elizabeth X.

### Problem 29

The members of the Math Club need to elect a president and a vice president. They determine that there are a total of 272 ways that they can fill the positions with two different members. How many people are in the Math Club?

Elizabeth X.

### Problem 30

Use the information on page 684 to explain how you can count the maximum number of license plates a state can issue. Explain how to use the Fundamental Counting Principle to find the number of different license plates in a state such as Oklahoma, which has 3 letters followed by 3 numbers. Also explain how a state can increase the number of possible plates without increasing the length of the plate number.

Elizabeth X.

### Problem 31

How many numbers between 100 and 999, inclusive, have 7 in the tens place?
A. 90
B. 100
C. 110
D. 120

Elizabeth X.

### Problem 32

A coin is tossed four times. How many possible sequences of heads or tails are possible?
F. 4
G. 8
H. 16
J. 32

Elizabeth X.

### Problem 33

Prove that $4+7+10+\cdots+(3 n+1)=\frac{n(3 n+5)}{2}$ for all positive integers $n$.

Elizabeth X.

### Problem 34

Find the indicated term of each expansion.
third term of $(x+y)^{8}$

Elizabeth X.

### Problem 35

Find the indicated term of each expansion.
fifth term of $(2 a-b)^{7}$

Elizabeth X.

### Problem 36

Edison is located at (9, 3) in the coordinate system on a road map. Kettering is located at (12, 5) on the same map. Each side of a square on the map represents 10 miles. To the nearest mile, what is the distance between Edison and Kettering?

Elizabeth X.

### Problem 37

Solve each equation by factoring.
$x^{2}-16=0$

Elizabeth X.

### Problem 38

Solve each equation by factoring.
$x^{2}-3 x-10=0$

Elizabeth X.

### Problem 39

Solve each equation by factoring.
$3 x^{2}+8 x-3=0$

Check back soon!

### Problem 40

Solve each matrix equation.
$\left[\begin{array}{ll}{x} & {y}\end{array}\right]=\left[\begin{array}{ll}{y} & {4}\end{array}\right]$

Elizabeth X.

### Problem 41

Solve each matrix equation.
$\left[\begin{array}{l}{3 y} \\ {2 x}\end{array}\right]=\left[\begin{array}{l}{x+8} \\ {y-x}\end{array}\right]$

Elizabeth X.

### Problem 42

Evaluate each expression.
$\frac{5 !}{2 !}$

Elizabeth X.

### Problem 43

Evaluate each expression.
$\frac{6 !}{4 !}$

Elizabeth X.

### Problem 44

Evaluate each expression.
$\frac{7 !}{3 !}$

Elizabeth X.

### Problem 45

Evaluate each expression.
$\frac{6 !}{1 !}$

Elizabeth X.

### Problem 46

Evaluate each expression.
$\frac{4 !}{2 ! 2 !}$

Elizabeth X.

### Problem 47

Evaluate each expression.
$\frac{6 !}{2 ! 4 !}$

Elizabeth X.

### Problem 48

Evaluate each expression.
$\frac{8 !}{3 ! 5 !}$

Elizabeth X.
$\frac{5 !}{5 ! 0 !}$