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# Algebra, Mth 112 Chapter 8 Worked Out Homework

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Worked Out Homework
Chapter 8
Section 8.1
33. a. A set of four ordered pairs in which each of the least corrupt countries corresponds to a corruption rating is; (Iceland,9.7),Finland,9.6),(New Zealand,9.6),(Denmark,9.5). b. The relation in part (a) is a function because each country corresponds to only one corruption rating. c. A set of four ordered pairs in which corruption ratings for the least corrupt countries correspond to countries; (9.7,Iceland),(9.6,Finland),(9.6,New Zealand),(9.5,Denmark) d. The relation in part (c) is a not a function because 9.6 corresponds to both Finland and New Zealand.
Section 8.2
47. a. f(x)=.013(80)+56.46=57.50
F(80) represents (80,57.5) on the graph. This states that in 1980, the average temp. was 57.50 degrees. b. The graph shows 57.50 as the average temp. in 1980 which is overestimated by .10 degrees as the average temp in 1980 was actually 57.40 degrees.
49. a. f(x) = 1.27(50)+305=368.5 (50,367.5) f50 on the graph represents the average atmospheric concentration of carbon dioxide in parts per million as 368.5 in the year 2000.
b. g(x)=.01(50)^2+.65(50)+310=367.50 parts per million was the average carbon dioxide concentration in 2000.
51. f(x)=.4(20)^2-36(20)+1000 (20,440) .4(400)-720+1000 160-720+1000 There are 440 accidents per 50 miles for 20 year old drivers.
53. (45,190) The value of x is 45 and the value of y is 190 when the graph is at its lowest point. .4(45)^2-36(45)+1000 .4(2025)-1620+1000 810-1620+1000=190
The minimum number of accidents occurs with 45 year old drivers at 190 accidents per 50 million miles driven.

55. f3 on this graph is (3,.78). This represents that it will cost \$0.78 to mail a first class letter weighing 3 ounces.
57. It will cost \$0.61 to mail a first class letter weighing 1.5 ounces.
Section 8.3
63. a. (M+F)(X) (1.54x+114.6)+(1.48x+120.6) 3.02x+235.2 b. 3.02(10)+235.2 265.4 The book shows the answer as 295.6 but I keep getting 265.4 c. the results from part B are underestimated by 32.6mm.
65. a. (M/F)(X)= 1.54x+114.6 ---------------- 1.48x+120.6

(M/F)(5)= 1.54(5)+114.6 122.30 ----------------- --------- 1.48(5)+120.6 128 b. 122.30/128 = .955
c. This is an underestimated number. The actual ratio of men vs women in 2000 is .965.
Section 8.4
61. a. f reflects the discount off the original price and g reflects the percentage of the original price, in this case g is 75% of the original price. b. (fog)(x)=f(g(x))= x-400 .75x-400 c. (gof)(x)=.75(x-400) d. I have to say .75x-400 and .75x-400 should be the same. e. x-400 y=.75x-400 x=.75y-400 400+ x=.75y-400+400 X+400/.75=Y F^1(x)=x+400
F^1 represents the original sale price of the item while x represents the price after the \$400 discount.

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