Mathematical Applications for the Management, Life, and Social Sciences 11th Edition by Ronald J. Ha
b. $–53,000
c. $–37,000
d. $53,000
e. $323,000
ANSWER: b
84. Suppose that the cost C (in dollars) of removing p percent of the particulate pollution from the smokestacks of an industrial plant is given by . Find the domain of this function. Recall that p represents the percent pollution that is removed.
a.
b.
c.
d.
e.
ANSWER: d
85. If a test that has reliability r is lengthened by a factor , the reliability R of the new test is given by
If the reliability is r = 0.5, the equation becomes . When the test length is unchanged, the reliability r = R(1) = 0.5. If the length of the test is doubled, the reliability r = R(2). What percent improvement is there in the reliability when the test length is doubled?
a. 25.0%
b. 33.3%
c. 75.0%
d. 66.7%
e. 16.7%
ANSWER: b
86. If 140 feet of fence is to be used to fence in a rectangular yard, then the resulting area of the fenced yard is given by A = x(70-x), where x is the width of the rectangle. Is A a function of x?
a. Yes
b. No
ANSWER: Yes
87. If a box with a square cross section is to be sent by a delivery service, there are restrictions on its size such that its volume is given by the function , where x is the length of each side of the cross section (in inches). What restrictions must be placed on x (the domain) so that the volume makes physical sense?
a. 0 < x < 66
b. -66 < x < 0
c. 0 < x < 22
d. 0 < x < 3
e. -3 < x < 3
ANSWER: c
88. For many species of fish, the weight W is a function of the length L that can be expressed by
Suppose that for a particular species k = 0.03 and that for this species the length (in centimeters) is a function of the number of years t the fish has been alive, and that this function is given by
Find in order to express W as a function of the age t of the fish.
a.
b.
c.
d.
e.
ANSWER: e
89. Suppose that a company’s revenue is a function g of the number of customers C. Suppose also that the amount spent on advertising A affects the number of customers so that is a function f of A. The function is defined, since . Is defined?
a. Yes
b. No
ANSWER: No
90. Two of the processes (functions) used by a manufacturer of factory-built homes are sanding (denote this as function p) and painting (denote this as function s). Choose the correct explanation for the functional expression .
a. painting the door and then sanding
b. sanding the door and then painting
c. sanding the door twice
d. sanding the door and then painting
e. painting the door twice
ANSWER: d
91. A shipping crate has a square base with sides of length x feet, and it is half as tall as it is wide. If the material for the bottom and sides of the box costs $2.25 per square foot and the material for the top costs $1.25 per square foot, express the total cost (in dollars) of material for the box as a function of x.
a.
b.
c.
d.
e.
ANSWER: a
92. A company handles an apartment building with 50 units. Experience has shown that if the rent for each of the units is $380 per month, then all of the units will be filled; however, one unit will become vacant for each $30 increase in the monthly rate. If x represents the number of $30 increases, express the revenue R from the building as a function of x.
a. R(x) = 380+30x
b. R(x) = (380+30x)(50-x)