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2. +, -, *, / Rational #’s Theoretical Probability Experimental Probability Properties Vocabulary $100 $100 $100 $100 $100 $200 $200 $200 $200 $200 $300 $300 $300 $300 $300 $400 $400 $400 $400 $400 $500 $500 $500 $500 $500

3. Properties for $100 Name the Property shown below: b + 0 = b

4. Answer Identity Property of Addition Back

5. Properties for $200 Name the Property shown below: 7 + (3 + C) = (7 + 3) + C

6. Answer Associative Property of Addition Back

7. Properties for $300 Name the Property shown below: 2*b = b*2

8. Answer Commutative Property of Multiplication Back

9. Properties for $400 Name the Property shown below: 5(1/5) = 1

10. Answer Inverse Property of Multiplication Back

11. Properties for $500 Simplify the expression. Justify each step. 6x + 4(3 + 9x)

12. Answer 6x + 4(3 + 9x) 6x + 4*3 + 4 *9x => Distributive Property 6x + 12 + 36x => Multiplication 6x + 36x + 12 => Commutative Property of addition (6 + 36)x + 12 => Distributive Property 42x + 12 => Addition Back

13. Theoretical Probability for $100 If I roll a dice one time, what is the probability of rolling a one or a three? i.e. P(1 or 3) = ?

14. Answer Number of Items in Sample Space = 6 Sample Space {1 2 3 4 5 6} Probability = 2/6 or 1/3 Back

15. Theoretical Probability for $200 If I flip a coin 4 times, what is the probability of the same face showing up all 4 times? i.e. Either H-H-H-H or T-T-T-T

16. Answer Elements in Sample Space = 2*2*2*2 = 16 P(H-H-H-H) = 1/16 P(T-T-T-T) = 1/16 P(H-H-H-H OR T-T-T-T) = (1/16) + (1/16) = 2/16= 1/8 Back

17. Theoretical Probability for $300 Suppose you choose an m&m from a bag containing 5 blue m&m’s, 4 red m&m’s and 7 yellow m&m’s. You then pick another m&m. Find P(red then yellow)

18. Answer P(red then yellow) Number of Items in Sample Space: 16 Sample Space {b b b b b r r r r y y y y y y y} Event 1: P(red) = 4/16 = ¼ New Sample Space {b b b b b r r r y y y y y y y} Event 2: P(yellow) = 7/15 P(red then yellow) = ¼ * 7/15 = 7/60 Back

19. Theoretical Probability for $400 Draw the sample space for the following event: You flip a coin, and then spin the spinner shown below.

20. Answer } { H-O H-P H-Y H-G H-R T-O T-P T-Y T-G T-R Back

21. Theoretical Probability for $500 I spin the spinner shown below, and then roll a dice. Find P(Red and 2)

22. Answer Number of elements in sample space: 5 * 6 = 30 P(Red) = 1/5 P(2) = 1/6 P(Red and 2) = (1/5) * (1/6) = 1/30 Back

23. Experimental Probability for $100 If I draw 35 cards out of a bag, and 7 or them are hearts, what is the experimental probability of drawing a heart?

24. Answer 7/35 = 1/5 Back

25. Experimental Probability for $200 What is the experimental probability of thinking Mr. Paul is funny if out of 98 randomly chosen students, 2 thought he was funny?

26. Answer 2/98 = 1/49 = 2.04% Back

27. Experimental Probability for $300 I rolled a dice 12 times, and the results are shown below. What is the experimental probability of rolling a 6? 3, 5, 1, 5, 4, 6, 6, 3, 6, 3, 5, 3

28. Answer Items in Sample Space: 12 Sample Space: {3, 5, 1, 5, 4, 6, 6, 3, 6, 3, 5, 3} Favorable outcomes in sample space: 3 Experimental Probability= 3/12 = ¼ = 25% Back

29. Experimental Probability for $400 If I randomly pick 24 of the 66 eighth graders at AIS and find that 8 of them are eating pizza for lunch, how many of the 66 total eighth graders would we expect to be eating pizza?

30. Answer Experimental Probability = 8/24 = 1/3 Total 8th graders = 66 Total Students Eating Pizza Expected = (1/3) * 66 = 22 Students Back

31. Experimental Probability for $500 There are 452 dogs that live in district 1. If I randomly select 69 of the dogs, and find that 29 are small dogs, what is the experimental probability of a dog being small AND how many of the 452 dogs in district 1 would we expect to be small dogs?

32. Answer Experimental Probability = 29/69 Total Dogs in District 1 = 452 Total Small Dogs Expected = (29/69) * 452 = 190 Dogs Back

33. Vocabulary for $100 Define the following word: Coefficient

34. Answer Coefficient – The numerical factor of a term (a number, a variable, or the product of a number and one or more variables) Back

35. Vocabulary for $200 Define the following word: Matrix

36. Answer Matrix – a rectangular arrangement of numbers in rows and columns Back

37. Vocabulary for $300 Define the following word: Like Terms

38. Answer Like Terms – Terms (a number, a variable, or the product of a number and one or more variables) that have exactly the same variable factors Back

39. Vocabulary for $400 Define the following word: Sample Space

40. Answer Sample Space – The set of all possible outcomes of an event Back

41. Vocabulary for $500 Define the following word: Complement of an Event

42. Answer Complement of an Event – All of the possible outcomes not in the event. i.e. all of the items in the sample space that do not satisfy the given event Back

43. Operations on of Rational #’s for $100 Solve: 5 - -3 + 9*3

44. Answer 5 - -3 + 9*3 = 5 - -3 + 27 = 8+27 = 35 Back

45. Operations on of Rational #’s for $200 Solve: -3 *|3-5| -2

46. Answer -3 *|3-5| = -3 * 2 = -6 = 3 -2 -2 -2 Back

47. Operations on of Rational #’s for $300 Evaluate the following expression for b = -2.1 |3 – b| - 2(b + 6) + |b|

48. Answer |3 – b| - 2(b + 6) + |b| = |3 - -2.1| - 2(-2.1 + 6) + |-2.1| = |5.1| - 2(3.9) + |-2.1| = 5.1 – 7.8 + 2.1 = -0.6 Back

49. Operations on of Rational #’s for $400 Add the following two Matrices: -2.3 3.0 -5.3 2.1 9 1.2 5.4 -7.2 3.2 10.2 6.7 -0.3 -1.5 9.8 7.7 6.4 6.6 -1.6 3.3 -1 7.6 5.0 -7.1 0.1 2.5 3.4 -1.2 3.97.6 -4.3 -6.1 -2.7 4.4 4.6 -10 8.3-7.9 -8.2 -1.1 5.6 +

50. Answer The matrices can not be added because they are not the same size. The first is a 4x5, the second is a 5x4 Back