Find the correlation coefficient.
63)
Consider the data points with the following coordinates:
x 57 53 59 61 53 56 60
y 156 164 163 177 159 175 151
63)
A)
–0.0783
B)
–0.0537
C)
0.2145
D)
0.1085
64)
The test scores of 6 randomly picked students and the number of hours they prepared are as
follows:
Hours 510 4 6 10 9
Score 64 86 69 86 59 87
64)
A)
0.6781
B)
–0.6781
C)
0.2242
D)
–0.2242
Solve the problem.
65)
The change in a certain engineer’s salary over time can be approximated by the linear equation
y = 1500x + 47,500 where y represents salary in dollars and x represents number of years on the job.
According to this equation, after how many years on the job was the engineer’s salary $55,000?
65)
A)
7 years
B)
4 years
C)
6 years
D)
5 years
Find an equation in slope–intercept form (where possible) for the line.
66)
The line with x–intercept 5 and perpendicular to 7x – y =9
66)
A)
y = – 1
7x + 5
B)
y = – 7x + 35
C)
y =1
7x +5
7
D)
y = – 1
7x +5
7
Find the correlation coefficient.
67)
Consider the data points with the following coordinates:
x 62 53 64 52 52 54 58
y 158 176 151 164 164 174 162
67)
A)
0.7537
B)
–0.0810
C)
–0.7749
D)
0
Find an equation in slope–intercept form (where possible) for the line.
68)
Through (5, 2), m = – 5
6
68)
A)
y =5
6x +25
6
B)
y = – 5
6x +25
6
C)
y =5
6x –37
6
D)
y = – 5
6x +37
6
Write a cost function for the problem. Assume that the relationship is linear.
69)
Marginal cost, $50; 50 items cost $2900 to produce
69)
A)
C(x) =50x + 2900
B)
C(x) =8x + 400
C)
C(x) =8x + 2900
D)
C(x) =50x + 400
Find the equation of the least squares line.
70)
The paired data below consist of the costs of advertising (in thousands of dollars) and the number
of products sold (in thousands).
Cost (x) 9 2 3 4 2 5 9 10
Number (y) 85 52 55 68 67 86 83 73
70)
A)
y = 26.4 + 1.42x
B)
y = – 26.4 – 1.42x
C)
y = 55.8 + 2.79x
D)
y = 55.8 – 2.79x
Solve the problem.
71)
The paired data below consist of the test scores of 6 randomly selected students and the number of
hours they studied for the test. Use the equation of the least squares line to predict the score on the
test of a student who studies 5 hours.
Hours (x) 5 10 4 6 10 9
Score (y) 64 86 69 86 59 87
71)
A)
72.7
B)
77.7
C)
74.8
D)
67.7
Find the equation of the least squares line.
72)
Two different tests are designed to measure employee productivity and dexterity. Several
employees of a company are randomly selected and asked to complete the tests. The results are
below.
Dexterity (x) 23 25 28 21 21 25 26 30 34 36
Productivity (y) 49 53 59 42 47 53 55 63 67 75
72)
A)
y = 5.05 + 1.91x
B)
y = 2.36 + 2.03x
C)
y = 75.3 – 0.329x
D)
y = 10.7 + 1.53x
Solve the problem.
73)
A meteorologist in the Upper Peninsula of Michigan predicts an overnight low of –14° Fahrenheit.
What would a Canadian meteorologist predict for the same location in Celsius?
73)
A)
–7.8°
B)
–25.6°
C)
–46°
D)
–14°
74)
For some reason the quality of production decreases as the year progresses at a light bulb
manufacturing plant. The following data represent the percentage of defective light bulbs
produced at a light bulb manufacturing plant in the corresponding month of the year.
month (x) 2 3 5 7 8 9 12
% defective (y) 1.3 1.6 2.0 2.4 2.6 2.8 3.1
Use the equation of the least squares line to predict in which month the percentage of defective light
bulbs would be 1.83%.
74)
A)
May
B)
February
C)
March
D)
April
75)
For some reason the quality of production decreases as the year progresses at a light bulb
manufacturing plant. The following data represent the percentage of defective light bulbs
produced at a light bulb manufacturing plant in the corresponding month of the year.
month (x) 2 3 5 7 8 9 12
% defective (y) 1.3 1.6 2.0 2.4 2.6 2.8 3.1
Use the equation of the least squares line to predict the percentage of defective bulbs in June.
75)
A)
2.20%
B)
2.15%
C)
2.0%
D)
2.3%
Find the correlation coefficient.
76)
Consider the data points with the following coordinates:
x 121 101 128 160 154 126 134
y 171 152 168 157 164 169 160
76)
A)
–0.0781
B)
0.0537
C)
0.2245
D)
0.5370
Solve the problem.
77)
On a summer day, the surface water of a lake is at a temperature of 20° Celsius. What is this
temperature in Fahrenheit?
77)
A)
20°
B)
68°
C)
36°
D)
52°
Find an equation in slope–intercept form (where possible) for the line.
78)
Through (5, 7), parallel to –9x + 7y = – 31
78)
A)
y = – 5
7x –31
7
B)
y = – 9
7x –4
7
C)
y =9
7x +4
7
D)
y =7
9x –7
9
Find the correlation coefficient.
79)
The following are the temperatures on randomly chosen days and the amount a certain kind of
plant grew (in millimeters):
Temp 77 88 85 61 64 72 73 63 74
Growth 39 17 12 22 15 29 14 25 43
79)
A)
0.0396
B)
–0.0953
C)
–0.3105
D)
0
Explanation:
Solve the problem.
80)
The following data show the list price, x, in thousands of dollars, and the dealer invoice price, y,
also in thousands of dollars, for a variety of sport utility vehicles. Find a linear equation that
approximates the data, using the points (16.5, 16.1) and (20.0, 18.3).
List Price Dealer Invoice Price
16.5 16.1
17.6 17.0
20.7 18.2
23.1 19.3
20.0 18.3
24.6 21.0
80)
A)
y = 1.59x – 9.11
B)
y = 1.59x – 10.2
C)
y = 0.629x + 5.73
D)
y = 0.629x + 6.38
Explanation:
Graph the equation.
25
Explanation:
81)
y = – 2x –4
81)
A)
B)
C)
D)
Write a cost function for the problem. Assume that the relationship is linear.
82)
A cable TV company charges $28 for the basic service plus $8 for each movie channel. Let C(x) be
the total cost in dollars of subscribing to cable TV, using x movie channels.
82)
A)
C(x) =28x – 8
B)
C(x) =8x + 28
C)
C(x) =8x – 28
D)
C(x) =28x + 8
Find an equation in slope–intercept form (where possible) for the line.
83)
Through (–3, –8) and (–1, –17)
83)
A)
y =9
2x +11
2
B)
y = – 9
2x –43
2
C)
y = – 9
2x –22
3
D)
y = – 2
9x –26
3
Explanation:
Solve the problem.
84)
Suppose that the demand and price for a certain model of graphing calculator are related by
p = D(q) =100 –4.25q, where p is the price (in dollars) and q is the demand (in hundreds). Find the
demand for the calculator if the price is $32. Round to the nearest whole number if necessary.
84)
A)
400 calculators
B)
1600 calculators
C)
27,200 calculators
D)
16 calculators
Explanation:
Explanation:
Find the slope of the line.
85)
85)
A)
2
3
B)
3
2
C)
–2
3
D)
–3
2
Solve the problem.
86)
Regrind, Inc. regrinds used typewriter platens. The cost per platen is $1.20. The cost to regrind 100
platens is $400. Find the linear cost function to regrind platens. If reground platens sell for $8.80
each, how many must be reground and sold to break even?
86)
A)
C(x) =1.20x + 280
break–even =288
B)
C(x) =1.20x + 400
break–even =41
C)
C(x) =1.20x + 280
break–even =37
D)
C(x) =1.20x + 400
break–even =54
87)
Assume that the sales of a certain appliance dealer can be approximated by a straight line. Suppose
that sales were $11,500 in 1982 and $87,500 in 1987. Let x = 0 represent 1982. Find the equation
giving yearly sales S.
87)
A)
S =15,200x + 87,500
B)
S =76,000x + 87,500
C)
S =15,200x + 11,500
D)
S =76,000x + 11,500
Find the slope of the line.
88)
A line parallel to 4y + 3x =7
88)
A)
7
3
B)
–4
3
C)
3
4
D)
–3
4
Solve the problem.
89)
A shoe company will make a new type of shoe. The fixed cost for the production will be $24,000.
The variable cost will be $38 per pair of shoes. The shoes will sell for $106 for each pair. What is
the profit if 600 pairs are sold?
89)
A)
$40,800
B)
$16,800
C)
$62,400
D)
$64,800
B
Find an equation in slope–intercept form (where possible) for the line.
90)
y–intercept –5, x–intercept 10
90)
A)
y =1
2x – 5
B)
y = – 2x + 10
C)
y = – 1
2x – 5
D)
y =2x + 10
A
D
Solve the problem.
91)
Ten students in a graduate program were randomly selected. Their grade point averages (GPAs)
when they entered the program were between 3.5 and 4.0. The following data were obtained
regarding their GPAs on entering the program versus their current GPAs. Use the equation of the
least squares line to predict the current GPA of a student whose entering GPA is 3.2.
Entering GPA (x) Current GPA(y)
3.5 3.6
3.8 3.7
3.6 3.9
3.6 3.6
3.5 3.9
3.9 3.8
4.0 3.7
3.9 3.9
3.5 3.8
3.7 4.0
91)
A)
3.57
B)
3.28
C)
3.77
D)
3.39
Find the slope of the line passing through the given pair of points.
92)
(–3, 6) and (–5, 6)
92)
A)
– 6
B)
–3
2
C)
Not defined
D)
0
D
Evaluate the function as indicated.
93)
Find f(–17) when f(x) =13x – 9.
93)
A)
–221.9
B)
212
C)
–230
D)
–212
C
C
Solve the problem.
94)
The paired data below consist of the temperatures on randomly chosen days and the amount a
certain kind of plant grew (in millimeters). Use the equation of the least squares line to predict the
growth of a plant if the temperature is 72.
Temp (x) 62 76 50 51 71 46 51 44 79
Growth (y) 36 39 50 13 33 33 17 616
94)
A)
28.28 mm
B)
30.94 mm
C)
30.37 mm
D)
29.79 mm
95)
Let the demand and supply functions be represented by D(p) and S(p), where p is the price in
dollars. Find the equilibrium price and equilibrium quantity for the given functions.
D(p) =3328 – 50p
S(p) =210p – 832
95)
A)
$19; 2378
B)
$19; 2528
C)
$26; 2028
D)
$16; 2528
96)
Suppose the function y =1.8t – 3.3 determines the actual time that has elapsed, in minutes, for t
minutes of a person‘s estimate of the elapsed time. Find the actual time that has elapsed for an
estimate of t =60 minutes.
96)
A)
104.7 min
B)
111.3 min
C)
65.94 min
D)
54.06 min
97)
The relationship between the list price, x, in thousands of dollars, and the dealer invoice price, y,
also in thousands of dollars, for pickup trucks can be approximated by the linear equation
y = 0.715x + 2.82. Use this equation to predict the dealer invoice price for a pickup truck with a list
price of 19.5 thousand dollars.
97)
A)
23.329 thousand dollars
B)
16.763 thousand dollars
C)
20.914 thousand dollars
D)
13.943 thousand dollars
Evaluate the function as indicated.
98)
Find g(m2) when g(x) = – 8– 4x.
98)
A)
–8+ – 4m2
B)
–8– 4x2
C)
–8+ 4m2
D)
–8+m2
99)
Find f(0) when f(x) = – 3x + 19.
99)
A)
–3
B)
0
C)
19
D)
16
Solve the problem.
100)
Suppose that the demand and price for a certain model of graphing calculator are related by
p = D(q) =99 –3q, where p is the price (in dollars) and q is the demand (in hundreds). Find the
price if the demand is 300 calculators.
100)
A)
$90.00
B)
$189.00
C)
$108.00
D)
$9.00
Graph the equation.
101)
4x +3y =12
101)
32
A)
B)
C)
D)
Find an equation in slope–intercept form (where possible) for the line.
102)
Through (–2, 1) and (10, 1)
102)
A)
y =1
B)
1
5x + 10y = 0
C)
5x – 2y = 0
D)
x = – 2
Explanation:
Explanation:
Find the correlation coefficient.
103)
The following are the temperatures on randomly chosen days and the amount a certain kind of
plant grew (in millimeters):
Temp 62 76 50 51 71 46 51 44 79
Growth 36 39 50 13 33 33 17 6 16
103)
A)
0.2563
B)
–0.2105
C)
0.1955
D)
0
Find the equation of the least squares line.
104)
Managers rate employees according to job performance and attitude. The results for several
randomly selected employees are given below.
Attitude (x) 59 63 65 69 58 77 76 69 70 64
Performance (y) 72 67 78 82 75 87 92 83 87 78
104)
A)
y = 92.3 – 0.669x
B)
y = 11.7 + 1.02x
C)
y = 2.81 + 1.35x
D)
y = – 47.3 + 2.02x
Solve the problem.
105)
On a summer day, the bottom water of a lake is at a temperature of 5° Celsius. What is this
temperature in Fahrenheit?
105)
A)
37°
B)
9°
C)
5°
D)
41°
Find the equation of the least squares line.
106)
The paired data below consist of the temperatures on randomly chosen days and the amount a
certain kind of plant grew (in millimeters).
Temp (x) 62 76 50 51 71 46 51 44 79
Growth (y) 36 39 50 13 33 33 17 616
106)
A)
y = – 14.6 – 0.211x
B)
y = 14.6 + 0.211x
C)
y = 7.30 + 0.122x
D)
y = 7.30 – 0.112x
Find the slope of the line.
107)
A line parallel to 2x =5y + 9
107)
A)
5
2
B)
–2
5
C)
2
5
D)
9
2
Find an equation in slope–intercept form (where possible) for the line.
108)
Through (–6, 4.5) and (–4, 8.5)
108)
A)
y = – 0.5x + 1.5
B)
y = – 2x – 7.5
C)
y =2x + 16.5
D)
y =0.5x + 7.5
C
Explanation:
Find the slope of the line passing through the given pair of points.
109)
(5, 4) and (3, 8)
109)
A)
3
2
B)
– 2
C)
2
D)
–1
2
B
Explanation:
Solve the problem.
110)
The cost of owning a home includes both fixed costs and variable utility costs. Assume that it costs
$5619 per month for mortgage and insurance payments and it costs an average of $2.96 per unit for
natural gas, electricity, and water usage. Determine a linear equation that computes the annual cost
of owning this home if x utility units are used.
110)
A)
y =2.96x +5619
B)
y = – 2.96x +67,428
C)
y = – 2.96x +5619
D)
y =2.96x +67,428
D
Explanation:
111)
Northwest Molded molds plastic handles which cost $1.00 per handle to mold. The fixed cost to run
the molding machine is $4244 per week. If the company sells the handles for $3.00 each, how many
handles must be molded weekly to break even?
111)
A)
2122 handles
B)
1414 handles
C)
1061 handles
D)
4244 handles
A
Explanation:
C
Explanation:
Find an equation in slope–intercept form (where possible) for the line.
112)
Through (–13, –1), m =2
112)
A)
y =2x – 1
B)
y = – 2x – 11
C)
y = – 2x – 25
D)
y =2x + 25
Find the correlation coefficient.
113)
The test scores of 6 randomly picked students and the number of hours they prepared are as
follows:
Hours 410 5 5 3 3
Score 54 99 56 99 70 72
113)
A)
0.2015
B)
–0.6781
C)
0.6039
D)
–0.2241
Explanation:
Solve the problem.
114)
A shoe company will make a new type of shoe. The fixed cost for the production will be $24,000.
The variable cost will be $31 per pair of shoes. The shoes will sell for $100 for each pair. How
many pairs of shoes will have to be sold for the company to break even on this new line of shoes?
114)
A)
348 pairs
B)
775 pairs
C)
69 pairs
D)
241 pairs
Explanation:
Find an equation in slope–intercept form (where possible) for the line.
115)
Through (–1, –7), perpendicular to x =5
115)
A)
y =5
B)
y =7
C)
x =5
D)
y = – 7
Explanation:
Write a cost function for the problem. Assume that the relationship is linear.
116)
Fixed cost, $30; 5 items cost $4460 to produce
116)
A)
C(x) =886x + 4460
B)
C(x) =1772x + 30
C)
C(x) =1772x + 4460
D)
C(x) =886x + 30
Explanation:
Explanation:
Find an equation in slope–intercept form (where possible) for the line.
117)
Through (3, 0), m = – 1
117)
A)
y =3x
B)
y = x –3
C)
y = – 3x
D)
y = – x +3
Solve the problem.
118)
The information in the chart gives the salary of a person for the stated years. Model the data with a
linear function using the points (1, 24,800) and (3, 26,500).
Year, x Salary, y
1990, 0 $23,500
1991, 1 $24,800
1992, 2 $25,200
1993, 3 $26,500
1994, 4 $27,200
118)
A)
y = – 1098x + 23,950
B)
y =850x
C)
y =28.2x + 23,950
D)
y =850x + 23,950
Explanation:
Find the slope of the line.
119)
The x–axis
119)
A)
0
B)
1
C)
–1
D)
Not defined
Explanation:
Graph the equation.
120)
x = – 2
120)
37
Explanation:
A)
B)
C)
D)
Solve the problem.
121)
Let the supply and demand functions for a certain model of electric pencil sharpener be given by
p = S(q) =2
3qand p = D(q) =15 –2
3q ,
where p is the price in dollars and q is the quantity of pencil sharpeners (in hundreds). Graph these
functions on the same axes (graph the supply function as a dashed line and the demand function
as a solid line). Also, find the equilibrium quantity and the equilibrium price.
121)
38
A)
Equilibrium quantity: 900
Equilibrium price: $6.00
B)
Equilibrium quantity: 600
Equilibrium price: $9.00
C)
Equilibrium quantity: 1125
Equilibrium price: $7.5
D)
Equilibrium quantity: 950
Equilibrium price: $7
Find an equation in slope–intercept form (where possible) for the line.
122)
Through (0, –1), m =3
4
122)
A)
y =3
4x – 1
B)
y = – 3
4x – 1
C)
y = – 3
4x + 1
D)
y =3
4x + 1
Solve the problem.
123)
A book publisher found that the cost to produce 1000 calculus textbooks is $25,100, while the cost
to produce 2000 calculus textbooks is $50,700. Assume that the cost C(x) is a linear function of x, the
number of textbooks produced. What is the marginal cost of a calculus textbook?
123)
A)
$2.56
B)
$25.60
C)
$25,600.00
D)
$0.03
124)
Find an equation for the least squares line representing weight, in pounds, as a function of height,
in inches, of men. Then, predict the height of a man who is 145 pounds to the nearest tenth of an
inch. The following data are the (height, weight) pairs for 8 men: (66, 150), (68, 160), (69, 166), (70,
175), (71, 181), (72, 191), (73, 198), (74, 206).
124)
A)
65.7 inches
B)
64.6 inches
C)
63.2 inches
D)
68.2 inches
Find the equation of the least squares line.
125)
In the table below, x represents the number of years since 2000 and y represents the population (in
thousands) of the town Boomville.
Year x 1 2 3 4 5
Sales y 30 40 60 90 130
125)
A)
y = 18x + 8
B)
y = 28x – 10
C)
y = 25x – 5
D)
y = 12x + 20