تكلم مع الذكاء الاصطناعي
Deck 2: Linear Equations and Functions
ملء الشاشة (f)
سؤال
The equation in this problem leads to a linear equation. Solve for x. Because the solution to the linear equation may not be a solution to the original equation, be sure to check the solution in the original equation. 
A)x =
B)x =
C)x =
D)x = -20
E)no solution
A)x =
B)x =
C)x =
D)x = -20
E)no solution
سؤال
Solve the equation. 
A)x = 78
B)x =
C)x =
D)x =
E)x = 5
A)x = 78
B)x =
C)x =
D)x =
E)x = 5
سؤال
The equation in this problem leads to a linear equation. Solve for 
. Because the solution to the linear equation may not be a solution to the original equation, be sure to check the solution in the original equation. 
A)x = 4
B)x = 8
C)x =
D)x =
E)no solution
. Because the solution to the linear equation may not be a solution to the original equation, be sure to check the solution in the original equation. A)x = 4
B)x = 8
C)x =
D)x =
E)no solution
سؤال
Solve the equation. 
A)7
B)2
C)5
D)1
E)0
A)7
B)2
C)5
D)1
E)0
سؤال
Use a calculator to solve the equation. Round your answer to three decimal places. 
A)x = 3.759
B)x = 0.266
C)x = -0.516
D)x = -1.938
E)x = -0.877
A)x = 3.759
B)x = 0.266
C)x = -0.516
D)x = -1.938
E)x = -0.877
سؤال
Solve the equation. 
A)
B)
C)14
D)0
E)4
A)
B)
C)14
D)0
E)4
سؤال
The equation in this problem leads to a linear equation. Solve for x. Because the solution to the linear equation may not be a solution to the original equation, be sure to check the solution in the original equation. 
A)x =
B)x =
C)x =
D)x =
E)no solution
A)x =
B)x =
C)x =
D)x =
E)no solution
سؤال
Solve the equation. 
A)
B)41
C)
D)
E)10
A)
B)41
C)
D)
E)10
سؤال
Solve for 
in terms of 
. 
A)
B)
C)
D)
E)
in terms of . A)
B)
C)
D)
E)
سؤال
Solve the inequality. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Solve the equation. 
A)-2
B)36
C)-12
D)12
E)-6
A)-2
B)36
C)-12
D)12
E)-6
سؤال
Solve 
for t.
A)
B)
C)
D)
E)
for t. A)
B)
C)
D)
E)
سؤال
Solve the inequality. 
A)x < 18
B)x > 18
C)x > -18
D)x < -18
E)x > 13
A)x < 18
B)x > 18
C)x > -18
D)x < -18
E)x > 13
سؤال
Solve the equation. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Solve for y in terms of x. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Solve 
for 
.
A)
B)
C)
D)
E)
for . A)
B)
C)
D)
E)
سؤال
Use a calculator to solve the equation. Round your answer to three decimal places. 
A)x = 7.407
B)x = 1.463
C)x = 2.69
D)x = 4.529
E)x = 44.745
A)x = 7.407
B)x = 1.463
C)x = 2.69
D)x = 4.529
E)x = 44.745
سؤال
Solve the equation. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Solve the inequality. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
The equation in this problem leads to a linear equation. Solve for x. Because the solution to the linear equation may not be a solution to the original equation, be sure to check the solution in the original equation. 
A)x = 4
B)x = -4
C)x = 16
D)x = 12
E)x =
A)x = 4
B)x = -4
C)x = 16
D)x = 12
E)x =
سؤال
Solve the inequality and choose the graph of the solution. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
In Sweetwater, Arizona, water bills are taxed on the basis of the amount of the monthly bill in order to encourage conservation. If the bill is more than $0 but less than $45, the tax is 2% of the bill; if the bill is $45 or more but less than $65, the tax is 4% of the bill; and if the bill is $65 or more, the tax is 6% of the bill. Choose the inequalities that represent the amounts of tax owed in these three cases, where T is the tax to be paid and B is the monthly bill.
A)If
, then
If
, then
If
, then
B)If
, then
If
, then
If
, then
C)If
, then
If
, then
If
, then
D)If
, then
If
, then
If
, then
E)If
, then
If
, then
If
, then
A)If
, then
If
, then
If
, then
B)If
, then
If
, then
If
, then
C)If
, then
If
, then
If
, then
D)If
, then
If
, then
If
, then
E)If
, then
If
, then
If
, then
سؤال
Burnem, Inc. manufactures blank CDs and sells them to a distributor in packs of 500 CDs. Assume Burnem's total cost and total revenue (in dollars) for x packs of 500 CDs are given by
Total cost =
Total revenue = 
How many packs of 500 CDs must Burnem sell to break even?
A)540 packs
B)396 packs
C)500 packs
D)313 packs
E)1584 packs
Total cost =
Total revenue = How many packs of 500 CDs must Burnem sell to break even?
A)540 packs
B)396 packs
C)500 packs
D)313 packs
E)1584 packs
سؤال
سؤال
سؤال
A $680,000 property is depreciated for tax purposes by its owner with the straight-line depreciation method. The value of the building y, after x months of use is given by 
dollars. After how many months will the value of the building be $377,000? Round your answer to the nearest whole number of months.
A)587 months
B)378 months
C)168 months
D)209 months
E)419 months
dollars. After how many months will the value of the building be $377,000? Round your answer to the nearest whole number of months. A)587 months
B)378 months
C)168 months
D)209 months
E)419 months
سؤال
For a certain product, the revenue function is 
and the cost function is 
. To obtain a profit, the revenue must be greater than the cost. Find the graph of x which shows when there is a profit.
A)
B)
C)
D)
E)
and the cost function is . To obtain a profit, the revenue must be greater than the cost. Find the graph of x which shows when there is a profit. A)
B)
C)
D)
E)
سؤال
In wildlife management, the capture-mark-recapture technique is used to estimate the populations of fish or birds in an area or to measure the infestation of insects such as Japanese beetles. Suppose 100 individuals of the species being studied are caught, marked, and released, and one week later 100 more are caught. To estimate the total number of individuals, the following relationship is used: 
Suppose that 1000 beetles are captured, marked, and released. Suppose further that in the second capture of 1000 it is found that 59 are marked. What is the population estimate?
A)59,000
B)287
C)59
D)16,949
E)3,481
Suppose that 1000 beetles are captured, marked, and released. Suppose further that in the second capture of 1000 it is found that 59 are marked. What is the population estimate?
A)59,000
B)287
C)59
D)16,949
E)3,481
سؤال
When a $801,000 building is depreciated for tax purposes (by the straight-line method), its value y after x months of use is given by 
. How many months will it be before the building is fully depreciated (that is, its value is $0)?
A)36 months
B)356 months
C)4 months
D)28 months
E)280 months
. How many months will it be before the building is fully depreciated (that is, its value is $0)? A)36 months
B)356 months
C)4 months
D)28 months
E)280 months
سؤال
Dish Systems manufactures satellite systems and has its monthly profit P in dollars related to the number of satellite systems x by 
. Find the number of systems that Dish Systems needs to produce and sell in order to break even.
A)248 systems
B)1,890 systems
C)297 systems
D)39 systems
E)270 systems
. Find the number of systems that Dish Systems needs to produce and sell in order to break even. A)248 systems
B)1,890 systems
C)297 systems
D)39 systems
E)270 systems
سؤال
Thrifty rents a compact car for $35 per day, and Budget rents a similar car for $20 per day plus an initial fee of $120. Which of the following graphs depicts the number of days for which it would be cheaper to rent from Budget?
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
In seawater, the pressure p is related to the depth d according to 
, where d is in feet and p is in pounds per square inch. The Titanic was discovered at a depth of 12,400 ft. Find the pressure at this depth. Round your answer to the nearest whole number.
A)6,749 lb/sq in
B)22,760 lb/sq in
C)22,707 lb/sq in
D)6,778 lb/sq in
E)6764 lb/sq in
, where d is in feet and p is in pounds per square inch. The Titanic was discovered at a depth of 12,400 ft. Find the pressure at this depth. Round your answer to the nearest whole number. A)6,749 lb/sq in
B)22,760 lb/sq in
C)22,707 lb/sq in
D)6,778 lb/sq in
E)6764 lb/sq in
سؤال
Solve the inequality. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
سؤال
The percent p of high school seniors who smoke cigarettes can be modeled by the equation 
, where t is the number of years past 1975. Find the year in which p first becomes negative. Round your answer to the nearest year.
A)2981
B)2035
C)2005
D)3763
E)2034
, where t is the number of years past 1975. Find the year in which p first becomes negative. Round your answer to the nearest year. A)2981
B)2035
C)2005
D)3763
E)2034
سؤال
سؤال
Solve the inequality. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Solve the inequality and choose the graph of the solution. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
The combination of cold temperatures and wind speed determine what is called wind chill. The wind chill is a temperature that is the still-air equivalent of the combination of cold and wind. When the wind speed is 25 mph, the wind chill WC depends on the temperature t (in degrees Fahrenheit) according to 
. For what temperatures does it feel at least 25°F colder than the air temperature? That is, find t such that 
. Round your answer to two decimal places.
A)
B)
C)
D)
E)
. For what temperatures does it feel at least 25°F colder than the air temperature? That is, find t such that . Round your answer to two decimal places. A)
B)
C)
D)
E)
سؤال
Solve the inequality and choose the graph of the solution. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
If 
and 
, find 
and simplify.
A)
B)
C)
D)
E)
and , find and simplify. A)
B)
C)
D)
E)
سؤال
Is the relation defined by the table a function of x? 
A)Yes
B)No
A)Yes
B)No
سؤال
Let 
and 
. Does 
for all values of x and h?
A)Yes
B)No
and . Does for all values of x and h? A)Yes
B)No
سؤال
Let 
and 
. Does 
?
A)Yes
B)No
and . Does ? A)Yes
B)No
سؤال
If 
, find 
.
A)3
B)15
C)27
D)-3
E)45
, find . A)3
B)15
C)27
D)-3
E)45
سؤال
The relation defined by the table is a function. Choose the correct domain and range. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
If 
, find 
.
A)-7
B)0
C)-7000
D)-700
E)25
, find . A)-7
B)0
C)-7000
D)-700
E)25
سؤال
If 
, is y a function of x?
A)Yes
B)No
, is y a function of x?A)Yes
B)No
سؤال
Let 
. Is 
?
A)Yes
B)No
. Is ? A)Yes
B)No
سؤال
Let 
and 
. Find 
and simplify.
A)
B)
C)
D)
E)
and . Find and simplify. A)
B)
C)
D)
E)
سؤال
If 
is y a function of x?
A)Yes
B)No
is y a function of x?A)Yes
B)No
سؤال
If 
, is y a function of x?
A)Yes
B)No
, is y a function of x? A)Yes
B)No
سؤال
If 
, find 
.
A)45
B)-27
C)39
D)3
E)-21
, find . A)45
B)-27
C)39
D)3
E)-21
سؤال
Which of the graphs below represent y as a function of x?
(a)
(b)
A)only (a)
B)only (b)
C)both (a) and (b)
D)neither (a) nor (b)
(a)
(b)
A)only (a)
B)only (b)
C)both (a) and (b)
D)neither (a) nor (b)
سؤال
Let 
. Find 
.
A)
B)
C)
D)
E)
. Find . A)
B)
C)
D)
E)
سؤال
If 
, find 
.
A)
B)
C)
D)
E)
, find . A)
B)
C)
D)
E)
سؤال
Which of the graphs below represent y as a function of x?
(a)
(b)
A)only (a)
B)neither (a) nor (b)
C)only (b)
D)both (a) and (b)
(a)
(b)
A)only (a)
B)neither (a) nor (b)
C)only (b)
D)both (a) and (b)
سؤال
If 
and 
, find 
and simplify.
A)
B)
C)
D)
E)
and , find and simplify. A)
B)
C)
D)
E)
سؤال
Determine whether the values in the table describe x as a function of y. 
A)True
B)False
A)True
B)False
سؤال
Is the relation defined by the table a function of x? 
A)Yes
B)No
A)Yes
B)No
سؤال
A couple seeking to buy a home decides that a monthly payment of $800 fits their budget. Their bank's interest rate is 7.5%. The amount they can borrow A is a function of the time t in years that it will take to repay the debt. If we denote this function by 
, then the following table defines the function. 
Source: Comprehensive Mortgage Payment Tables, Publication No. 492, Financial Publishing Co., Boston
Choose the expression in the form
which describes how long they will have to make payments if they need to borrow $69,000.
A)
B)
C)
D)
E)
, then the following table defines the function. Source: Comprehensive Mortgage Payment Tables, Publication No. 492, Financial Publishing Co., BostonChoose the expression in the form
which describes how long they will have to make payments if they need to borrow $69,000.
A)
B)
C)
D)
E)
سؤال
The graph of 
is shown in the figure below.
Does the point (0,1) lie on the graph? In other words, do the coordinates satisfy the equation?
A)Yes
B)No
is shown in the figure below.
Does the point (0,1) lie on the graph? In other words, do the coordinates satisfy the equation?
A)Yes
B)No
سؤال
For 
and 
, find 
.
A)
B)
C)
D)
E)
and , find . A)
B)
C)
D)
E)
سؤال
Suppose 
in the figure below. Find 
.
A)1
B)1.44225
C)-1.414214
D)0
E)1.414214
in the figure below. Find .
A)1
B)1.44225
C)-1.414214
D)0
E)1.414214
سؤال
When a debt is refinanced, sometimes the term of the loan (that is, the time it takes to repay the debt) is shortened. Suppose the current interest rate is 7%, and the current debt is $100,000. The monthly payment R of the refinanced debt is a function of the term of the loan t in years. If we represent this function by 
, then the following table defines the function. 
Source: Comprehensive Mortgage Payment Tables, Publication No. 492, Financial Publishing Co., Boston
Choose the correct verbal description of
.
A)From the table,
The value of
Is the yearly payment to repay a $100,000 loan in 10 years when the interest rate is 7%.
B)From the table,
The value of
Is the monthly payment to repay half of a $100,000 loan in 10 years when the interest rate is 7%.
C)From the table,
The value of
Is the weekly payment to repay a $100,000 loan in 10 years when the interest rate is 7%.
D)From the table,
The value of
Is the monthly payment to repay a $100,000 loan in 10 years when the interest rate is 7%.
E)From the table,
The value of
Is the monthly payment to repay a $100,000 loan in 10 years when the interest rate is 7%.
, then the following table defines the function. Source: Comprehensive Mortgage Payment Tables, Publication No. 492, Financial Publishing Co., Boston
Choose the correct verbal description of
.
A)From the table,
The value of
Is the yearly payment to repay a $100,000 loan in 10 years when the interest rate is 7%.
B)From the table,
The value of
Is the monthly payment to repay half of a $100,000 loan in 10 years when the interest rate is 7%.
C)From the table,
The value of
Is the weekly payment to repay a $100,000 loan in 10 years when the interest rate is 7%.
D)From the table,
The value of
Is the monthly payment to repay a $100,000 loan in 10 years when the interest rate is 7%.
E)From the table,
The value of
Is the monthly payment to repay a $100,000 loan in 10 years when the interest rate is 7%.
سؤال
The number (in millions) of women in the work force, given as a function f, of the year for selected years from 1920 to 2000, is shown in the figure below. Estimate 
and explain its meaning. 
Source: 2004 World Almanac
A)
: The number of women in the work force increased by 10,000,000.
B)
: The number of women in the work force decreased by 2,000,000.
C)
: The number of women in the work force did not increase.
D)
: The number of women in the work force increased by 2,000,000.
E)
: The number of women in the work force decreased by 10,000,000
and explain its meaning. Source: 2004 World Almanac
A)
: The number of women in the work force increased by 10,000,000.
B)
: The number of women in the work force decreased by 2,000,000.
C)
: The number of women in the work force did not increase.
D)
: The number of women in the work force increased by 2,000,000.
E)
: The number of women in the work force decreased by 10,000,000
سؤال
For 
, find 
.
A)1
B)
C)
D)
E)x
, find . A)1
B)
C)
D)
E)x
سؤال
A function and its graph are given. Find the domain. 
A)domain:
B)domain:
C)domain:
D)domain:
E)domain:
A)domain:
B)domain:
C)domain:
D)domain:
E)domain:
سؤال
For 
and 
, find 
.
A)
B)
C)
D)
E)
and , find . A)
B)
C)
D)
E)
سؤال
For 
and 
, find 
.
A)
B)
C)
D)
E)
and , find . A)
B)
C)
D)
E)
سؤال
For 
and 
, find 
.
A)
B)
C)
D)
E)
and , find . A)
B)
C)
D)
E)
سؤال
A function and its graph are given. Find the domain. 
A)domain: all real numbers
B)domain: all real numbers
C)domain: all real numbers
D)domain: all real numbers
E)domain: all real numbers
A)domain: all real numbers
B)domain: all real numbers
C)domain: all real numbers
D)domain: all real numbers
E)domain: all real numbers
سؤال
If t represents the number of hours after 9:30 A.M. on Tuesday, October 5, 2004, then the graph defines the Dow Jones Industrial Average D as a function of time t. If we represent this function by 
use the graph to find f(6.5). 
Source: Bloomberg Financial Markets, The New York Times, October 6, 2004. Copyright © 2004 The New York Times Co. Reprinted by permission.
A)10,220
B)10,175
C)10,217
D)10,160
E)10,190
use the graph to find f(6.5). Source: Bloomberg Financial Markets, The New York Times, October 6, 2004. Copyright © 2004 The New York Times Co. Reprinted by permission.
A)10,220
B)10,175
C)10,217
D)10,160
E)10,190
سؤال
Find the domain and range of the function below. 
A)domain: real numbers
Range: real numbers
B)domain: real numbers
Range: real numbers
C)domain: all reals range: real numbers
D)domain: real numbers
Range: real numbers
E)domain: all reals range: real numbers
A)domain: real numbers
Range: real numbers
B)domain: real numbers
Range: real numbers
C)domain: all reals range: real numbers
D)domain: real numbers
Range: real numbers
E)domain: all reals range: real numbers
سؤال
State the domain and range of the function below. 
A)domain: real numbers
Range: real numbers
B)domain: all reals range: real numbers
C)domain: real numbers
Range: all reals
D)domain: all reals range: real numbers
E)domain: real numbers
Range: real numbers
A)domain: real numbers
Range: real numbers
B)domain: all reals range: real numbers
C)domain: real numbers
Range: all reals
D)domain: all reals range: real numbers
E)domain: real numbers
Range: real numbers
سؤال
For 
and 
, find 
.
A)
B)
C)
D)
E)
and , find . A)
B)
C)
D)
E)
سؤال
Find the domain and range of the function below. 
A)domain: all reals range: real numbers
B)domain: all reals range: real numbers
C)domain: real numbers
Range: all reals
D)domain: real numbers
Range: all reals
E)domain: all reals range: real numbers
A)domain: all reals range: real numbers
B)domain: all reals range: real numbers
C)domain: real numbers
Range: all reals
D)domain: real numbers
Range: all reals
E)domain: all reals range: real numbers
سؤال
Suppose 
in the figure below. How many values of x satisfy 
? 
A)2
B)1
C)4
D)5
E)3
in the figure below. How many values of x satisfy ? A)2
B)1
C)4
D)5
E)3
سؤال
The graph of 
is shown in the figure below. 
If the point P (with coordinates (a, b)) is on the graph, how are a and b related?
A)
B)
C)
D)
E)There is no relation.
is shown in the figure below. If the point P (with coordinates (a, b)) is on the graph, how are a and b related?
A)
B)
C)
D)
E)There is no relation.
سؤال
For 
and 
, find 
.
A)
B)
C)
D)
E)
and , find . A)
B)
C)
D)
E)
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ملء الشاشة (f)
Deck 2: Linear Equations and Functions
1
The equation in this problem leads to a linear equation. Solve for x. Because the solution to the linear equation may not be a solution to the original equation, be sure to check the solution in the original equation.
A)x =
B)x =
C)x =
D)x = -20
E)no solution
A)x =
B)x =
C)x =
D)x = -20
E)no solution
x =
2
Solve the equation.
A)x = 78
B)x =
C)x =
D)x =
E)x = 5
A)x = 78
B)x =
C)x =
D)x =
E)x = 5
x =
3
The equation in this problem leads to a linear equation. Solve for . Because the solution to the linear equation may not be a solution to the original equation, be sure to check the solution in the original equation.
A)x = 4
B)x = 8
C)x =
D)x =
E)no solution
. Because the solution to the linear equation may not be a solution to the original equation, be sure to check the solution in the original equation. A)x = 4
B)x = 8
C)x =
D)x =
E)no solution
x = 8
4
Solve the equation.
A)7
B)2
C)5
D)1
E)0
A)7
B)2
C)5
D)1
E)0
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5
Use a calculator to solve the equation. Round your answer to three decimal places.
A)x = 3.759
B)x = 0.266
C)x = -0.516
D)x = -1.938
E)x = -0.877
A)x = 3.759
B)x = 0.266
C)x = -0.516
D)x = -1.938
E)x = -0.877
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6
Solve the equation.
A)
B)
C)14
D)0
E)4
A)
B)
C)14
D)0
E)4
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7
The equation in this problem leads to a linear equation. Solve for x. Because the solution to the linear equation may not be a solution to the original equation, be sure to check the solution in the original equation.
A)x =
B)x =
C)x =
D)x =
E)no solution
A)x =
B)x =
C)x =
D)x =
E)no solution
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8
Solve the equation.
A)
B)41
C)
D)
E)10
A)
B)41
C)
D)
E)10
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9
Solve for in terms of .
A)
B)
C)
D)
E)
in terms of . A)
B)
C)
D)
E)
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10
Solve the inequality.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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11
Solve the equation.
A)-2
B)36
C)-12
D)12
E)-6
A)-2
B)36
C)-12
D)12
E)-6
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12
Solve for t.
A)
B)
C)
D)
E)
for t. A)
B)
C)
D)
E)
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13
Solve the inequality.
A)x < 18
B)x > 18
C)x > -18
D)x < -18
E)x > 13
A)x < 18
B)x > 18
C)x > -18
D)x < -18
E)x > 13
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14
Solve the equation.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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15
Solve for y in terms of x.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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16
Solve for .
A)
B)
C)
D)
E)
for . A)
B)
C)
D)
E)
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17
Use a calculator to solve the equation. Round your answer to three decimal places.
A)x = 7.407
B)x = 1.463
C)x = 2.69
D)x = 4.529
E)x = 44.745
A)x = 7.407
B)x = 1.463
C)x = 2.69
D)x = 4.529
E)x = 44.745
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18
Solve the equation.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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19
Solve the inequality.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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20
The equation in this problem leads to a linear equation. Solve for x. Because the solution to the linear equation may not be a solution to the original equation, be sure to check the solution in the original equation.
A)x = 4
B)x = -4
C)x = 16
D)x = 12
E)x =
A)x = 4
B)x = -4
C)x = 16
D)x = 12
E)x =
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21
Solve the inequality and choose the graph of the solution.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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22
In Sweetwater, Arizona, water bills are taxed on the basis of the amount of the monthly bill in order to encourage conservation. If the bill is more than $0 but less than $45, the tax is 2% of the bill; if the bill is $45 or more but less than $65, the tax is 4% of the bill; and if the bill is $65 or more, the tax is 6% of the bill. Choose the inequalities that represent the amounts of tax owed in these three cases, where T is the tax to be paid and B is the monthly bill.
A)If
, then
If
, then
If
, then
B)If
, then
If
, then
If
, then
C)If
, then
If
, then
If
, then
D)If
, then
If
, then
If
, then
E)If
, then
If
, then
If
, then
A)If
, then
If
, then
If
, then
B)If
, then
If
, then
If
, then
C)If
, then
If
, then
If
, then
D)If
, then
If
, then
If
, then
E)If
, then
If
, then
If
, then
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23
Burnem, Inc. manufactures blank CDs and sells them to a distributor in packs of 500 CDs. Assume Burnem's total cost and total revenue (in dollars) for x packs of 500 CDs are given by
Total cost = Total revenue =
How many packs of 500 CDs must Burnem sell to break even?
A)540 packs
B)396 packs
C)500 packs
D)313 packs
E)1584 packs
Total cost =
Total revenue = How many packs of 500 CDs must Burnem sell to break even?
A)540 packs
B)396 packs
C)500 packs
D)313 packs
E)1584 packs
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24
One safe investment pays 10% per year, and a more risky investment pays 18% per year. A woman who has $146,400 to invest would like to have an income of $21,000 per year from her investments. How much should she invest at in the 18% rate fund?
A)$66,900
B)$79,500
C)$116,100
D)$92,880
E)$63,600
A)$66,900
B)$79,500
C)$116,100
D)$92,880
E)$63,600
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25
Suppose a professor counts the final exam as being equal to each of the other tests in her course, and she will also change the lowest test score to match the final exam score if the final exam score is higher. If a student's four test scores are 82, 75, 55, and 92, what is the lowest score the student can earn on the final exam and still obtain at least an 80 average for the course?
A)76
B)96
C)87
D)83
E)79
A)76
B)96
C)87
D)83
E)79
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26
A $680,000 property is depreciated for tax purposes by its owner with the straight-line depreciation method. The value of the building y, after x months of use is given by dollars. After how many months will the value of the building be $377,000? Round your answer to the nearest whole number of months.
A)587 months
B)378 months
C)168 months
D)209 months
E)419 months
dollars. After how many months will the value of the building be $377,000? Round your answer to the nearest whole number of months. A)587 months
B)378 months
C)168 months
D)209 months
E)419 months
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27
For a certain product, the revenue function is and the cost function is . To obtain a profit, the revenue must be greater than the cost. Find the graph of x which shows when there is a profit.
A)
B)
C)
D)
E)
and the cost function is . To obtain a profit, the revenue must be greater than the cost. Find the graph of x which shows when there is a profit. A)
B)
C)
D)
E)
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28
In wildlife management, the capture-mark-recapture technique is used to estimate the populations of fish or birds in an area or to measure the infestation of insects such as Japanese beetles. Suppose 100 individuals of the species being studied are caught, marked, and released, and one week later 100 more are caught. To estimate the total number of individuals, the following relationship is used:
Suppose that 1000 beetles are captured, marked, and released. Suppose further that in the second capture of 1000 it is found that 59 are marked. What is the population estimate?
A)59,000
B)287
C)59
D)16,949
E)3,481
Suppose that 1000 beetles are captured, marked, and released. Suppose further that in the second capture of 1000 it is found that 59 are marked. What is the population estimate?
A)59,000
B)287
C)59
D)16,949
E)3,481
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29
When a $801,000 building is depreciated for tax purposes (by the straight-line method), its value y after x months of use is given by . How many months will it be before the building is fully depreciated (that is, its value is $0)?
A)36 months
B)356 months
C)4 months
D)28 months
E)280 months
. How many months will it be before the building is fully depreciated (that is, its value is $0)? A)36 months
B)356 months
C)4 months
D)28 months
E)280 months
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30
Dish Systems manufactures satellite systems and has its monthly profit P in dollars related to the number of satellite systems x by . Find the number of systems that Dish Systems needs to produce and sell in order to break even.
A)248 systems
B)1,890 systems
C)297 systems
D)39 systems
E)270 systems
. Find the number of systems that Dish Systems needs to produce and sell in order to break even. A)248 systems
B)1,890 systems
C)297 systems
D)39 systems
E)270 systems
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31
Thrifty rents a compact car for $35 per day, and Budget rents a similar car for $20 per day plus an initial fee of $120. Which of the following graphs depicts the number of days for which it would be cheaper to rent from Budget?
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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32
In seawater, the pressure p is related to the depth d according to , where d is in feet and p is in pounds per square inch. The Titanic was discovered at a depth of 12,400 ft. Find the pressure at this depth. Round your answer to the nearest whole number.
A)6,749 lb/sq in
B)22,760 lb/sq in
C)22,707 lb/sq in
D)6,778 lb/sq in
E)6764 lb/sq in
, where d is in feet and p is in pounds per square inch. The Titanic was discovered at a depth of 12,400 ft. Find the pressure at this depth. Round your answer to the nearest whole number. A)6,749 lb/sq in
B)22,760 lb/sq in
C)22,707 lb/sq in
D)6,778 lb/sq in
E)6764 lb/sq in
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33
Solve the inequality.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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34
A retired woman has $130,000 to invest. She has chosen one relatively safe investment fund that has an annual yield of 9% and another, riskier one that has an annual yield of 13%. How much should she invest in the fund yielding 9% if she would like to earn $14,000 per year from her investments?
A)$11,700
B)$16,900
C)$57,500
D)$72,500
E)$113,100
A)$11,700
B)$16,900
C)$57,500
D)$72,500
E)$113,100
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35
The percent p of high school seniors who smoke cigarettes can be modeled by the equation , where t is the number of years past 1975. Find the year in which p first becomes negative. Round your answer to the nearest year.
A)2981
B)2035
C)2005
D)3763
E)2034
, where t is the number of years past 1975. Find the year in which p first becomes negative. Round your answer to the nearest year. A)2981
B)2035
C)2005
D)3763
E)2034
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36
The total price of a new car (including 5% sales tax) is $23,456. How much of this is tax? Round your answer to the nearest cent.
A)$1,114.16
B)$5,226,747.39
C)$2,345.60
D)$2,228.32
E)$1,116.95
A)$1,114.16
B)$5,226,747.39
C)$2,345.60
D)$2,228.32
E)$1,116.95
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37
Solve the inequality.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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38
Solve the inequality and choose the graph of the solution.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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39
The combination of cold temperatures and wind speed determine what is called wind chill. The wind chill is a temperature that is the still-air equivalent of the combination of cold and wind. When the wind speed is 25 mph, the wind chill WC depends on the temperature t (in degrees Fahrenheit) according to . For what temperatures does it feel at least 25°F colder than the air temperature? That is, find t such that . Round your answer to two decimal places.
A)
B)
C)
D)
E)
. For what temperatures does it feel at least 25°F colder than the air temperature? That is, find t such that . Round your answer to two decimal places. A)
B)
C)
D)
E)
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40
Solve the inequality and choose the graph of the solution.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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41
If and , find and simplify.
A)
B)
C)
D)
E)
and , find and simplify. A)
B)
C)
D)
E)
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42
Is the relation defined by the table a function of x?
A)Yes
B)No
A)Yes
B)No
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43
Let and . Does for all values of x and h?
A)Yes
B)No
and . Does for all values of x and h? A)Yes
B)No
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44
Let and . Does ?
A)Yes
B)No
and . Does ? A)Yes
B)No
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45
If , find .
A)3
B)15
C)27
D)-3
E)45
, find . A)3
B)15
C)27
D)-3
E)45
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46
The relation defined by the table is a function. Choose the correct domain and range.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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47
If , find .
A)-7
B)0
C)-7000
D)-700
E)25
, find . A)-7
B)0
C)-7000
D)-700
E)25
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48
If , is y a function of x?
A)Yes
B)No
, is y a function of x?A)Yes
B)No
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49
Let . Is ?
A)Yes
B)No
. Is ? A)Yes
B)No
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50
Let and . Find and simplify.
A)
B)
C)
D)
E)
and . Find and simplify. A)
B)
C)
D)
E)
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51
If is y a function of x?
A)Yes
B)No
is y a function of x?A)Yes
B)No
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52
If , is y a function of x?
A)Yes
B)No
, is y a function of x? A)Yes
B)No
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53
If , find .
A)45
B)-27
C)39
D)3
E)-21
, find . A)45
B)-27
C)39
D)3
E)-21
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54
Which of the graphs below represent y as a function of x?
(a)
(b)
A)only (a)
B)only (b)
C)both (a) and (b)
D)neither (a) nor (b)
(a)
(b)
A)only (a)
B)only (b)
C)both (a) and (b)
D)neither (a) nor (b)
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55
Let . Find .
A)
B)
C)
D)
E)
. Find . A)
B)
C)
D)
E)
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56
If , find .
A)
B)
C)
D)
E)
, find . A)
B)
C)
D)
E)
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57
Which of the graphs below represent y as a function of x?
(a)
(b)
A)only (a)
B)neither (a) nor (b)
C)only (b)
D)both (a) and (b)
(a)
(b)
A)only (a)
B)neither (a) nor (b)
C)only (b)
D)both (a) and (b)
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58
If and , find and simplify.
A)
B)
C)
D)
E)
and , find and simplify. A)
B)
C)
D)
E)
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59
Determine whether the values in the table describe x as a function of y.
A)True
B)False
A)True
B)False
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60
Is the relation defined by the table a function of x?
A)Yes
B)No
A)Yes
B)No
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61
A couple seeking to buy a home decides that a monthly payment of $800 fits their budget. Their bank's interest rate is 7.5%. The amount they can borrow A is a function of the time t in years that it will take to repay the debt. If we denote this function by , then the following table defines the function. Source: Comprehensive Mortgage Payment Tables, Publication No. 492, Financial Publishing Co., Boston
Choose the expression in the form which describes how long they will have to make payments if they need to borrow $69,000.
A)
B)
C)
D)
E)
, then the following table defines the function. Source: Comprehensive Mortgage Payment Tables, Publication No. 492, Financial Publishing Co., BostonChoose the expression in the form
which describes how long they will have to make payments if they need to borrow $69,000.
A)
B)
C)
D)
E)
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62
The graph of is shown in the figure below.
Does the point (0,1) lie on the graph? In other words, do the coordinates satisfy the equation?
A)Yes
B)No
is shown in the figure below.
Does the point (0,1) lie on the graph? In other words, do the coordinates satisfy the equation?
A)Yes
B)No
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63
For and , find .
A)
B)
C)
D)
E)
and , find . A)
B)
C)
D)
E)
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64
Suppose in the figure below. Find .
A)1
B)1.44225
C)-1.414214
D)0
E)1.414214
in the figure below. Find .
A)1
B)1.44225
C)-1.414214
D)0
E)1.414214
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65
When a debt is refinanced, sometimes the term of the loan (that is, the time it takes to repay the debt) is shortened. Suppose the current interest rate is 7%, and the current debt is $100,000. The monthly payment R of the refinanced debt is a function of the term of the loan t in years. If we represent this function by , then the following table defines the function.
Source: Comprehensive Mortgage Payment Tables, Publication No. 492, Financial Publishing Co., Boston
Choose the correct verbal description of .
A)From the table,
The value of
Is the yearly payment to repay a $100,000 loan in 10 years when the interest rate is 7%.
B)From the table,
The value of
Is the monthly payment to repay half of a $100,000 loan in 10 years when the interest rate is 7%.
C)From the table,
The value of
Is the weekly payment to repay a $100,000 loan in 10 years when the interest rate is 7%.
D)From the table,
The value of
Is the monthly payment to repay a $100,000 loan in 10 years when the interest rate is 7%.
E)From the table,
The value of
Is the monthly payment to repay a $100,000 loan in 10 years when the interest rate is 7%.
, then the following table defines the function. Source: Comprehensive Mortgage Payment Tables, Publication No. 492, Financial Publishing Co., Boston
Choose the correct verbal description of
.
A)From the table,
The value of
Is the yearly payment to repay a $100,000 loan in 10 years when the interest rate is 7%.
B)From the table,
The value of
Is the monthly payment to repay half of a $100,000 loan in 10 years when the interest rate is 7%.
C)From the table,
The value of
Is the weekly payment to repay a $100,000 loan in 10 years when the interest rate is 7%.
D)From the table,
The value of
Is the monthly payment to repay a $100,000 loan in 10 years when the interest rate is 7%.
E)From the table,
The value of
Is the monthly payment to repay a $100,000 loan in 10 years when the interest rate is 7%.
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66
The number (in millions) of women in the work force, given as a function f, of the year for selected years from 1920 to 2000, is shown in the figure below. Estimate and explain its meaning.
Source: 2004 World Almanac
A)
: The number of women in the work force increased by 10,000,000.
B)
: The number of women in the work force decreased by 2,000,000.
C)
: The number of women in the work force did not increase.
D)
: The number of women in the work force increased by 2,000,000.
E)
: The number of women in the work force decreased by 10,000,000
and explain its meaning. Source: 2004 World Almanac
A)
: The number of women in the work force increased by 10,000,000.
B)
: The number of women in the work force decreased by 2,000,000.
C)
: The number of women in the work force did not increase.
D)
: The number of women in the work force increased by 2,000,000.
E)
: The number of women in the work force decreased by 10,000,000
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67
For , find .
A)1
B)
C)
D)
E)x
, find . A)1
B)
C)
D)
E)x
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68
A function and its graph are given. Find the domain.
A)domain:
B)domain:
C)domain:
D)domain:
E)domain:
A)domain:
B)domain:
C)domain:
D)domain:
E)domain:
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69
For and , find .
A)
B)
C)
D)
E)
and , find . A)
B)
C)
D)
E)
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70
For and , find .
A)
B)
C)
D)
E)
and , find . A)
B)
C)
D)
E)
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71
For and , find .
A)
B)
C)
D)
E)
and , find . A)
B)
C)
D)
E)
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72
A function and its graph are given. Find the domain.
A)domain: all real numbers
B)domain: all real numbers
C)domain: all real numbers
D)domain: all real numbers
E)domain: all real numbers
A)domain: all real numbers
B)domain: all real numbers
C)domain: all real numbers
D)domain: all real numbers
E)domain: all real numbers
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73
If t represents the number of hours after 9:30 A.M. on Tuesday, October 5, 2004, then the graph defines the Dow Jones Industrial Average D as a function of time t. If we represent this function by use the graph to find f(6.5).
Source: Bloomberg Financial Markets, The New York Times, October 6, 2004. Copyright © 2004 The New York Times Co. Reprinted by permission.
A)10,220
B)10,175
C)10,217
D)10,160
E)10,190
use the graph to find f(6.5). Source: Bloomberg Financial Markets, The New York Times, October 6, 2004. Copyright © 2004 The New York Times Co. Reprinted by permission.
A)10,220
B)10,175
C)10,217
D)10,160
E)10,190
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74
Find the domain and range of the function below.
A)domain: real numbers
Range: real numbers
B)domain: real numbers
Range: real numbers
C)domain: all reals range: real numbers
D)domain: real numbers
Range: real numbers
E)domain: all reals range: real numbers
A)domain: real numbers
Range: real numbers
B)domain: real numbers
Range: real numbers
C)domain: all reals range: real numbers
D)domain: real numbers
Range: real numbers
E)domain: all reals range: real numbers
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75
State the domain and range of the function below.
A)domain: real numbers
Range: real numbers
B)domain: all reals range: real numbers
C)domain: real numbers
Range: all reals
D)domain: all reals range: real numbers
E)domain: real numbers
Range: real numbers
A)domain: real numbers
Range: real numbers
B)domain: all reals range: real numbers
C)domain: real numbers
Range: all reals
D)domain: all reals range: real numbers
E)domain: real numbers
Range: real numbers
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76
For and , find .
A)
B)
C)
D)
E)
and , find . A)
B)
C)
D)
E)
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77
Find the domain and range of the function below.
A)domain: all reals range: real numbers
B)domain: all reals range: real numbers
C)domain: real numbers
Range: all reals
D)domain: real numbers
Range: all reals
E)domain: all reals range: real numbers
A)domain: all reals range: real numbers
B)domain: all reals range: real numbers
C)domain: real numbers
Range: all reals
D)domain: real numbers
Range: all reals
E)domain: all reals range: real numbers
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78
Suppose in the figure below. How many values of x satisfy ?
A)2
B)1
C)4
D)5
E)3
in the figure below. How many values of x satisfy ? A)2
B)1
C)4
D)5
E)3
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79
The graph of is shown in the figure below.
If the point P (with coordinates (a, b)) is on the graph, how are a and b related?
A)
B)
C)
D)
E)There is no relation.
is shown in the figure below. If the point P (with coordinates (a, b)) is on the graph, how are a and b related?
A)
B)
C)
D)
E)There is no relation.
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80
For and , find .
A)
B)
C)
D)
E)
and , find . A)
B)
C)
D)
E)
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