Algebra Find the probability that coordinate x of a point chosen at random on A K ¯ eh k bar  satisfies the inequality.

33. 2 ≤ x ≤ 8 2 less than or equal to . x less than or equal to 8
34. 2 x ≤ 8 2 x less than or equal to 8
35. 5 ≤ 11 − 6 x 5 less than or equal to . 11 minus 6 x
36. 1 2 x − 5 > 0 1 half , x minus . 5 greater than 0
37. 2 ≤ 4 x ≤ 3 2 less than or equal to . 4 x less than or equal to 3
38. − 7 ≤ 1 − 2 x ≤ 1 negative 7 less than or equal to . 1 minus . 2 x less than or equal to 1
39. One type of dartboard is a square of radius 10 in. You throw a dart and hit the target. What is the probability that the dart lies within 10 square root of 10  in. of the square's center?

40. Games To win a prize at a carnival game, you must toss a quarter, so that it lands entirely within a circle as shown below. Assume that the center of a tossed quarter is equally likely to land at any point within the 8-in. square.

    

    1. What is the probability that the quarter lands entirely in the circle in one toss?
    2. Reasoning On average, how many coins must you toss to win a prize? Explain.
41. Traffic Patterns The traffic lights at Fourth and State Streets repeat themselves in 1-min cycles. A motorist will face a red light 60% of the time. Use this information to estimate how long the Fourth Street light is red during each 1-min cycle.
42. You have a 4-in. straw and a 6-in. straw. You want to cut the 6-in. straw into two pieces so that the three pieces form a triangle.
    1. If you cut the straw to get two 3-in. pieces, can you form a triangle?
    2. If the two pieces are 1 in. and 5 in., can you form a triangle?
    3. If you cut the straw at a random point, what is the probability that you can form a triangle?
43. Target Game Assume that a dart you throw will land on the 12 in.-by-12 in. square dartboard and is equally likely to land at any point on the board. The diameter of the center circle is 2 in., and the width of each ring is 1 in.

    

    1. What is the probability of hitting either the blue or yellow region?
    2. What is the probability the dart will not hit the gray region?

C Challenge

• 44. Graphing Calculator A circular dartboard has radius 1 m and a yellow circle in the center. Assume you hit the target at a random point. For what radius of the yellow center region would P(hitting yellow) equal each of the following? Use the table feature of a calculator to generate all six answers. Round to the nearest centimeter.
  1. 0.2
  2. 0.4
  3. 0.5
  4. 0.6
  5. 0.8
  6. 1.0
• You and your friend agree to meet for lunch between 12 P.M. and 1 P.M. Each of you agrees to wait 15 min for the other before giving up and eating lunch alone. If you arrive at 12:20, what is the probability you and your friend will eat lunch together?

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