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Mathematics Quick Checks and Sample Space Representations

Practice finding volumes of cones and hemispheres, surface area of cones, and exploring sample spaces for various experiments. Understand the Fundamental Counting Principle and its applications in real-life scenarios.

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Mathematics Quick Checks and Sample Space Representations

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

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

  3. A B C D Find the surface area of a cone with slant height of 8.5 yards and radius of 3.5 yards. 131.9 yd2 5-Minute Check 5

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

  5. Represent sample spaces. • Use the Fundamental Counting Principle to count outcomes. Then/Now

  6. 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 Example 1

  7. 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

  8. Represent a Sample Space Tree Diagram Example 1

  9. A B C D A.B. C.D.Y, Y; B, B; Y, B 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. Example 1

  10. 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. Example 2

  11. Multi-Stage Tree Diagrams Answer: Example 2

  12. A B C D 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? 5 Example 2

  13. Concept

  14. exterior interior seat engine computer wheels doors possible color color outcomesexterior interior seat engine computer wheels doors possible color color outcomes 11 7 5 3 6 4 3 83,160 × × × × × × = 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. Answer:So, a consumer can create 83,160 different possible cars. Example 3

  15. A B C D 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? 3,888 Example 3

  16. End of the Lesson

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