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# Mathematics - Algebra

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Section 6,1:

120. Toxic pollutants. The annual cost in dollars for removing
p% of the toxic chemicals from a town's water supply is
given by the formula
c(p) =
b) Use the formula to find C(99.5) and C(99.9).
c) What happens to the cost as the percentage of
pollutants removed approaches 100%?

Section 6,2:

82. Driving marathon. Felix drove 800 miles in x hours on
Monday.
a) Write a rational expression for his average speed.
b) On Tuesday he drove for 6 hours at the same average
speed. Write a rational expression for his distance on
Tuesday.

Section 6,4:

90. Barn painting. Melanie can paint a certain barn by herself
in x days. Her helper Melissa can paint the same barn by
herself in 2x days. Write a rational expression for the fraction
of the barn that they complete in one day by working
together. Evaluate the expression for x = 5.

Section 6,5:

64. Commuting students. At a well-known university, _

_ of the undergraduate students commute,
and 1/3 of the graduate students commute.
drive more than 40 miles daily, and 1/6
of the graduate students drive more than 40 miles
daily. If there are twice as many undergraduate
students, then what fraction of the commuters drive more
than 40 miles daily?

6.6:

68. Telephoto lens. Use the formula to find
the image distance i for an object that is 2,000,000 mm from
a 250-mm telephoto lens.

6.7:

30. Rise and run. If the rise is 3/2
and the run is 5, then what is
the ratio of the rise to the run?

46. Fast food. If four out of five doctors prefer fast food,
then at a convention of 445 doctors, how many prefer fast
food?

62. Bear population. To estimate the size of the bear
population on the Keweenaw Peninsula, conservationists
captured, tagged, and released 50 bears. One year later, a
random sample of 100 bears included only 2 tagged bears.
What is the conservationist's estimate of the size of the
bear population?

6.8:

36. Upstream, downstream. Junior's boat will go 15 miles per
hour in still water. If he can go 12 miles downstream in the
same amount of time as it takes to go 9 miles upstream,
then what is the speed of the current?

64. Filling a tank. A water tank has an inlet pipe and a drain
pipe. A full tank can be emptied in 30 minutes if the drain
is opened and an empty tank can be filled in 45 minutes
with the inlet pipe opened. If both pipes are accidentally
opened when the tank is full, then how long will it take to
empty the tank?