ANSWERS TO SELECTED EXERCISES - Cengage

1 CHAPTER 1 exercise SET distance is EXERCISES 33 39, only one possible answer is given. Your ANSWERS may vary from the given 1 and even, but is does not work for : the utility stock; Jose: the automotive stock;Anita: the technology stock; Tony: the oil : stamps; Chicago: baseball cards; Philadelphia: coins; Seattle: comic , bookstore, supermarket, creditunion, home; or home, credit union, supermarket, bookstore, , because the first letter of Nine is SET , 14, 36, 68, are 56 cannonballs in the sixth pyramid and 84 cannonballs in the seventh eighth pyramid has eight levels of cannonballs. The number of cannonballs in the nth level is given by the nth number in the sequence 1, 3, 6, 10, 15, 21, 28, 36.

2 Thus the total number of cannonballs in the eighth pyramid is 17. cuts produce six pieces and six cuts produce 7 prediction is not close compared to the results obtained for the inner ; ; ; Ifnis an even number, then the ratio is slightly less than exercise SET $ : 1, C: 9, D: 36, E: 84, F: 126, G: 126, H: F is the fifth region from the left and region G is the fifth region from the right. For any path from A to F, the ball makes anumber of left or right turns. If the turns are reversed, right turns instead of left turns and left turns instead of right turns, then the ball ends up in region G. Thus for each path from A to F, there is exactly one symmetrical path, about a central vertical line, from A to G.

3 Also,from each path from A to G, there is exactly one symmetrical path from A to F. Thus there are the same numbers of paths to both ducks, 14 , , 4096 .FnFn 1Fn Fn 1 Fn 3 Fn 4Fn 2Fn 1 Fn 2 Fn 102,334,155F30 832,040,F20 6765,a3 7, a4 9, a5 11an n 136 3 6 10 15 21 28 an 2nan n2 n 132, 5, 212, 18, 552n 4 4 n3n 4 2n n 46n 82 3n 46n 81 31 3x 3x 12x 12 131517A1 ANSWERS TO SELECTED EXERCISES25. , 484, and billion; billion; to 200231. number of theatre admissions in 2003 was less thanthe number of admissions in more sisters than 11th four coins on the left balance pan and the other four on the right balance pan. The pan that is the highercontains the fake coin. Take the four coins from the higher pan and use the balance scale to compare the weight of two of these coins to theweight of the other two.

4 The pan that is the higher contains the fake coin. Take the two coins from the higher pan and use the balance scaleto compare the weight of one of these coins to the weight of the other. The pan that is the higher contains the fake coin. This procedureenables you to determine the fake coin in three three of the coins on one of the balance pans and another threecoins on the other. If the pans balance, then the fake coin is one of the two remaining coins. You can use the balance scale to determinewhich of the remaining coins is the fake coin because it will be lighter than the other coin. If the three coins on the left pan do not balancewith the three coins on the right pan, then the fake coin must be one of the three coins on the higher pan.

5 Pick any two coins from thesethree and place one on each balance pan. If these two coins do not balance, then the one that is the higher is the fake. If the coins balance,then the third coin (the one that you did not place on the balance pan) is the fake. In any case, this procedure enables you to determine thefake coin in two 1600. Sally likes perfect 64. Each number is the cube of a term in thesequence 1,2,3,4,5, born in 1980 will be 45 in , because people born in 2070will be 46 in will 1 REVIEW EXERCISES page [Sec ] [Sec. ] [Sec. ] [Sec. ] a counterexample because and 0 is not greater than 0. [Sec. ] a counterexample because which is not an even number. [Sec. ] a counterexample becausebut [Sec.]

6 ] and Then However,[Sec. ]9. [Sec. ]10. [Sec. ]11.[Sec. ]12.[Sec. ]13.[Sec. ]14.[Sec. ]15.[Sec. ]16.[Sec. ] feet by 1600 feet [Sec. ]18.[Sec. ] skyboxes [Sec. ] the first trip the rancher takes the rabbit across the river. The rancher returns alone. Therancher takes the dog across the river and returns with the rabbit. The rancher next takes the carrots across the river and returns alone. Onthe final trip the rancher takes the rabbit across the river. [Sec. ]21.$300 [Sec. ] [Sec. ] will vary. [Sec. ] will vary. [Sec. ] : biology major; Clarissa: businessmajor; Reggie: computer science major; Ellen: chemistry major [Sec. ] : drug store; Pirates: supermarket;Tigers: bank; Giants: service station [Sec.

7 ]27. ANSWERS will The countries of India, Bangladesh,and Myanmar all share borders with each of the other two countries. Thus at least three colors are needed to color the map. [Sec. ]28. following figure shows a route that passes over each bridge once and only [Sec. ] square inch; 4 square inches; 25 square inches [Sec. ]30. [Sec. ] represents 1, B represents 9, and D represents 0. [Sec. ] [Sec. ] [Sec. ] [Sec. ] [Sec. ]230 1,073,741,824210 1024 North BaySouth Bay315 14,348,907an 5n 1an n2 3n 2an n2 3n 4an 3na25 31,125a5 225a4 108,a3 39,a2 6,a1 3,a20 1578a5 93,a4 58,a3 31,a2 12,a1 1, 768 72a3 b3 13 13 2. a b 3 1 1 3 23 1 1 2 16 17. 1 4 2 25,x 1 4 3 5 4 66 15,x 404 0x 0 2116 462 2025 452 112 inchesA2 ANSWERS to SELECTED ExercisesAnswers to SELECTED [Sec.

8 ]2n 6 6 2n4n 122 2n 64n nickel is worth 5 cents. Thus 2004 nickels are worth cents, or $ [Sec. ]38. to [Sec. ]39. times as times as many [Sec. ]40. [Sec. ] [Sec. ] are no narcissistic numbers. [Sec. ]43. [Sec. ]44. is the product of 387,420,489 nines. Atone multiplication per second, this computation would take about years. [Sec. ]CHAPTER 1 TEST page [Sec. ] [Sec. ] [Sec. ] [Sec. ] [Sec. ] , 1, 2, 3, 5, 8, 13, 21, 34, 55 [Sec. ]7. [Sec. ] , 1,6,and [Sec. ] , 212, 343 [Sec. ] the problem. Devise a plan. Carry out the plan. Review the solution. [Sec. ] [Sec. ] [Sec. ] [Sec. ]14.$672 [Sec. ] [Sec. ] [Sec. ] is 13, Ramiro is 5, Shakira is 15, and Sasha is 7.

9 [Sec. ] [Sec. ] acounterexample because division by zero is undefined. [Sec. ]20. to ,000 [Sec. ]x 4 5460 10, 3,an 3n 1an 4n9 99 99 387,420, 5 10,020 CHAPTER 2 exercise SET , nickel, dime, , , G. H. W. Bush, Clinton, G. W. EXERCISES 13 19, only one possible answer is set of days of the week that begin with the letter set consisting of the two planets in our solar system that areclosest to the set of single-digit natural set of natural numbers less than or equal to ;but is not an element ; has one element, whereas has ; the word good is ; 0 is an element of the first set, but 0 is not an element of thesecond EXERCISES 31 39, only one possible answer is a multiple of 5 and the name of a month that has 31 the name of a state that begins with the letter a season that starts with the letter , , Arizona, Florida, , 2002, , , October, , 1986, 1987, , 1990, 1991, 1992, 1993, 1995, well well well well will vary.

10 However, the setof all real numbers between 0 and 1 is one example of a set that cannot be written using the roster SET different sets of coins can have the same , I , II , III , I, II , I, III , II, III , I, II, III , , , , 0, 2, 4, 6, 8 0, 7, 8 U 0, 1, 2, 3, 4, 5, 6, 7, 8 0, 1, 3, 5, 8 A BA B x x x x x x4 x 16 x x x x N and x 13 0 a, b, c . b b a, b, c , 7 5, 4, 3, 2, 1 A4 ANSWERS to SELECTED Exercises57. only three elements, namely 1, 2, and 3. Because is not equal to 1, 2, or 3, is not a set,so it cannot be a given set has the elements 1 and Because there are exactly two elements in 59. a. A, B, C , A, B, D , A, B, E , A, C, D , A, C, E , A, D, E , B, C, D , B, C, E , B, D, E , C, D, E , A, B, C, D , A, B, C, E , A, B, D, E , A, C, D, E , B, C, D, E , A, B, C, D, E b.