Five-Minute Check (over Chapter 11) Mathematical Practices 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 Lesson Menu

Find the volume of a rectangular prism with length of 6 inches, width of 5 inches, and height of 4.5 inches. A. 159 in3 B. 145 in3 C. 135 in3 D. 120 in3 5-Minute Check 1

Find the volume of a cone with slant height of 4 Find the volume of a cone with slant height of 4.3 centimeters and radius of 3.5 centimeters. A. 85.8 cm3 B. 64.5 cm3 C. 32.0 cm3 D. 15.05 cm3 5-Minute Check 2

Find the volume of a hemisphere with radius of 6 meters. A. 339.3 m3 B. 360.4 m3 C. 421.5 m3 D. 452.4 m3 5-Minute Check 3

Find the volume of a cylinder with radius of 8 feet and height of 12 feet. A. 84 ft3 B. 603.2 ft3 C. 1005.3 ft3 D. 2412.7 ft3 5-Minute Check 4

What is the density of a cube that has a side length of 8 centimeters and a mass of 950 grams? Round to the nearest tenth. A. 1.6 g/cm3 B. 1.9 g/cm3 C. 5.4 g/cm3 D. 14.8 g/cm3 5-Minute Check 5

The volume of a sphere is 24,429 cubic inches The volume of a sphere is 24,429 cubic inches. What is the radius of the sphere? A. 8.7 in. B. 18.0 in. C. 19.8 in. D. 76.4 in. 5-Minute Check 6

Mathematical Practices 1 Make sense of problems and persevere in solving them. 2 Reason abstractly and quantitatively. Content Standards Preparation for S.CP.9 (+) Use permutations and combinations to compute probabilities of compound events and solve problems. MP

You calculated experimental probability. Use lists, tables, and tree diagrams to represent sample spaces. Use the Fundamental Counting Principle to count outcomes. Then/Now

multi-stage experiment Fundamental Counting Principle sample space tree diagram two-stage experiment multi-stage experiment Fundamental Counting Principle Vocabulary

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, B R, B B, R Example 1

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. Example 1

Represent a Sample Space Tree Diagram Example 1

One yellow token and one blue token are placed in a bag 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 Example 1

The sample space is the result of 4 stages. ● Dressing (F, R, or BC) MultiStage 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. Example 2

MultiStage Tree Diagrams Answer: Example 2

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? A. 3 B. 4 C. 5 D. 6 Example 2

Concept

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 possible color color outcomes 11 7 5 3 6 4 3 83,160 × = Answer: So, a consumer can create 83,160 different possible cars. Example 3

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? A. 3,888 B. 3,912 C. 4,098 D. 4,124 Example 3