See Problem 4.

Weather Use inductive reasoning to make a prediction about the weather.

31. Lightning travels much faster than thunder, so you see lightning before you hear thunder. If you count 5 s between the lightning and thunder, how far away is the storm?

    

32. The speed at which a cricket chirps is affected by the temperature. If you hear 20 cricket chirps in 14 s, what is the temperature?

    Number of Chirps per 14 Seconds	Temperature ( ° F ) open degrees cap f close
    5	45
    10	55
    15	65

See Problem 5.

Find one counterexample to show that each conjecture is false.

33. ∠ 1 angle 1  and ∠ 2 angle 2  are supplementary, so one of the angles is acute.
34. Δ ABC cap delta  is a right triangle, so ∠ A angle eh  measures 90.
35. The sum of two numbers is greater than either number.
36. The product of two positive numbers is greater than either number.
37. The difference of two integers is less than either integer.

B Apply

Find a pattern for each sequence. Use inductive reasoning to show the next two terms.

38. 1, 3, 7, 13, 21,…
39. 1, 2, 5, 6, 9,…
40. 0.1, 0.01, 0.001,…
41. 2, 6, 7, 21, 22, 66, 67,…
42. 1, 3, 7, 15, 31,…
43. 0 , 1 2 , 3 4 , 7 8 , 15 16 , … 0 comma . 1 half , comma , 3 fourths , comma , 7 eighths , comma , 15 over 16 , comma dot dot dot

Predict the next term in each sequence. Use your calculator to verify your answer.

44. 12345679 × 9 = 111111111 12345679 × 18 = 222222222 12345679 × 27 = 333333333 12345679 × 36 = 444444444 12345679 × 45 =   table with 5 rows and 3 columns , row1 column 1 , 12345679 , times , column 2 9 equals , column 3 111111111 , row2 column 1 , 12345679 , times , column 2 18 equals , column 3 222222222 , row3 column 1 , 12345679 , times , column 2 27 equals , column 3 333333333 , row4 column 1 , 12345679 , times , column 2 36 equals , column 3 444444444 , row5 column 1 , 12345679 , times , column 2 45 equals , column 3 table with 1 row and 1 column , row1 column 1 , , end table , end table
45. 1 × 1 = 1 11 × 11 = 121 111 × 111 = 12321 1111 × 1111 = 1234321 11111 × 11111 =   table with 5 rows and 3 columns , row1 column 1 , 1 times , column 2 1 , column 3 equals 1 , row2 column 1 , 11 times , column 2 11 , column 3 equals 121 , row3 column 1 , 111 times , column 2 111 , column 3 equals , 12321 , row4 column 1 , 1111 , times , column 2 1111 , column 3 equals , 1234321 , row5 column 1 , 11111 , times , column 2 11111 , column 3 equals , table with 1 row and 1 column , row1 column 1 , , end table , end table

46. Patterns Draw the next figure in the sequence. Make sure you think about color and shape.

    

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