# Mathematics - Algebra

See attachment

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.

One-tenth of the undergraduate students

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 as there are graduate

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?

https://brainmass.com/math/basic-algebra/mathematics-algebra-203756

#### Solution Summary

Complete, Neat and Step-by-step Solutions are provided in the attached file.