Five-Minute Check (over Chapter 12)

CCSS

Then/Now

New Vocabulary

Example 1:Represent a Sample Space

Example 2:Real-World Example: Multi-Stage Tree Diagrams

Key Concept: Fundamental Counting Principle

Example 3:Real-World Example: Use the Fundamental Counting Principle

Over Chapter 12

A. 159 in2

B. 145 in2

C. 135 in2

D. 120 in2

Find the surface area of a rectangular prism with length of 6 inches, width of 5 inches, and height of 4.5 inches.

Over Chapter 12

A. 85.8 cm3

B. 64.5 cm3

C. 32.0 cm3

D. 15.05 cm3

Find the volume of a cone with slant height of 4.3 centimeters and radius of 3.5 centimeters.

Over Chapter 12

A. 339.3 m3

B. 360.4 m3

C. 421.5 m3

D. 452.4 m3

Find the volume of a hemisphere with radius of 6 meters.

Over Chapter 12

A. 84 ft2

B. 603.2 ft2

C. 1005.3 ft2

D. 2412.7 ft2

Find the lateral area of a cylinder with radius of 8 feet and height of 12 feet.

Over Chapter 12

A. 93.4 yd2

B. 99.4 yd2

C. 131.9 yd2

D. 142.8 yd2

Find the surface area of a cone with slant height of 8.5 yards and radius of 3.5 yards.

Over Chapter 12

A. 8.7 in.

B. 18.0 in.

C. 19.8 in.

D. 76.4 in.

The volume of a sphere is 24,429 cubic inches. What is the radius of the sphere?

Content Standards

Preparation for S.CP.9 (+) Use permutations and combinations to compute probabilities of compound events and solve problems.

Mathematical Practices

1 Make sense of problems and persevere in solving them.

2 Reason abstractly and quantitatively.

You calculated experimental probability.

• Use lists, tables, and tree diagrams to represent sample spaces.

• Use the Fundamental Counting Principle to count outcomes.

• sample space

• tree diagram

• two-stage experiment

• multi-stage experiment

• Fundamental Counting Principle

Represent a Sample Space

One red token and one black token are placed in a bag. A token is drawn and the color is recorded. It is then returned to the bag and a second draw is made. Represent the sample space for this experiment by making an organized list a table, and a tree diagram.

Organized List

Pair each possible outcome from the first drawing with the possible outcomes from the second drawing.

R, R B, BR, B B, R

Represent a Sample Space

Table

List the outcomes of the first drawing in the left column and those of the second drawing in the top row.

Represent a Sample Space

Tree Diagram

One yellow token and one blue token are placed in a bag. A token is drawn and the color is recorded. It is then returned to the bag and a second draw is made. Choose the correct display of this sample space.

A. B.

C. D. Y, Y; B, B; Y, B

Multi-Stage Tree Diagrams

CHEF’S SALAD A chef’s salad at a local restaurant comes with a choice of French, ranch, or blue cheese dressings and optional toppings of cheese, turkey, and eggs. Draw a tree diagram to represent the sample space for salad orders.

The sample space is the result of 4 stages.

● Dressing (F, R, or BC)

● Cheese (C or NC)

● Turkey (T or NT)

● Eggs (E or NE)

Draw a tree diagram with 4 stages.

Multi-Stage Tree Diagrams

Answer:

A. 3

B. 4

C. 5

D. 6

BASEBALL GAME In the bleachers at a major league game you can purchase a hotdog, bratwurst, or tofu dog. This comes with the optional choices of ketchup, mustard, onions, and/or relish. How many stages are in the sample space?

Use the Fundamental Counting Principle

CARS New cars are available with a wide selection of options for the consumer. One option is chosen from each category shown. How many different cars could a consumer create in the chosen make and model?

Use the Fundamental Counting Principle.

exterior interior seat engine computer wheels doors possiblecolor color outcomes

11 7 5 3 6 4 3 83,160 × × × × × × =

Answer: So, a consumer can create 83,160 different possible cars.

A. 3,888

B. 3,912

C. 4,098

D. 4,124

BICYCLES New bicycles are available with a wide selection of options for the rider. One option is chosen from each category shown. How many different bicycles could a consumer create in the chosen model?