31.On a world globe, the distance between New York and Cairo, two cities that are actually
5619 mi apart, is 8.5 in. On this same globe, how far apart are Madrid and Rio de Janeiro,
two cities that are actually 5045 mi apart? Round your answer to the nearest tenth.
(Sources:Author’s globe, The World Almanac and Book of Facts.)
32.On a world globe, the distance between San Francisco and Melbourne, two cities that are
actually 7856 mi apart, is 11.875 in. On this same globe, how far apart are Mexico City and
Singapore, two cities that are actually 10,327 mi apart? Round your answer to the nearest
tenth. (Sources:Author’s globe, The World Almanac and Book of Facts.)
33.During the 2008 – 2009 school year, the
average ratio of teachers to students in
public elementary and secondary schools
was approximately 1 to 15. If a public
school had 846 students, how many
teachers would be at the school if this ra-
tio was valid for that school? Round your
answer to the nearest whole number.
(Source:U.S. National Center for Educa-
tion Statistics.)
34.On January 6, 2010, the eventual NBA champion L.A. Lakers were in first place in the
Western Conference of the NBA, having won 28 of their first 34 regular season games. If
the team continued to win the same fraction of its games, how many games would the
Lakers win for the complete 82-game season? (Source:www.nba.com)
35.To estimate the deer population of a forest preserve, wildlife biologists caught, tagged,
and then released 42 deer. A month later, they returned and caught a sample of 75 deer
and found that 15 of them were tagged. Based on this experiment, approximately how
many deer lived in the forest preserve?
36.Suppose that in the experiment in Exercise 35,only 5 of the previously tagged deer were
collected in the sample of 75. What would be the estimate of the deer population?
37.Biologists tagged 500 fish in a lake on January 1. On February 1, they returned and col-
lected a random sample of 400 fish, 8 of which had been previously tagged. On the basis
of this experiment, approximately how many fish does the lake have?
38.Suppose that in the experiment of Exercise 37,10 of the previously tagged fish were col-
lected on February 1. What would be the estimate of the fish population?
39.Bruce Johnston’s Shelby Cobra uses 5 gal of gasoline to drive 156 mi. He has 3 gal of
gasoline in the car, and he wants to know how much more gasoline he will need to drive
300 mi. If we assume that the car continues to use gasoline at the same rate, how many
more gallons, to the nearest tenth, will he need?
40.Mike Love’s T-bird uses 6 gal of gasoline to drive 141 mi. He has 4 gal of gasoline in the
car, and he wants to know how much more gasoline he will need to drive 275 mi. If we as-
sume that the car continues to use gasoline at the same rate, how many more gallons, to
the nearest tenth, will he need?
404 CHAPTER 7 Rational Expressions and Functions
A
B
C
4 6
2 x + 1 D
E
F
6 9
2 x + 5
41.Solve for x, using the given proportion to find the lengths of the third sides of the triangles.
In geometry, two triangles with corresponding angle measures equal, called similar triangles,
have corresponding sides proportional. For example, in the figure, angle ,
, and , so the triangles are similar. Then the following
ratios of corresponding sides are equal.
4
6
=
6
9
=
2 x+ 1
2 x+ 5
angle B=angle E angle C=angle F
A=angle D