c957 Applied Algebra
Which choice is a variable?
The cost of your daily newspaper The amount a teenager makes babysit-
The number of states in the United ting
States of America Correct! A teenager probably charges
The amount a teenager makes babysit- the same amount per hour but makes
ting more if the job lasts longer, like all day
Your shoe size
Which choice is a variable?
The name of the largest mountain range
in the United States The colors and styles of your shoes
The amount a babysitter charges per Correct! Size may always be the same,
hour but color and style certainly vary.
The colors and styles of your shoes
The operating system on your phone
Which choice is a quantitative variable?
M, representing the federal minimum
wage
P, representing the monthly profit based P, representing the monthly profit based
on the number of customers who needed on the number of customers who needed
plumbing services plumbing services
R, representing the monthly rent for your Correct! Profit can change from month to
company's office building month, and profit is a number, or quantity.
S, representing the number of regular
weekly shipping deliveries your compa-
ny's trucks make
In a lawn-mowing business, the amount
of time an employee spends mowing a
lawn depends on the size of the lawn.
It might also depend on some other fac-
tors. H, representing the hilliness of the lawn
Which choice represents a qualitative Correct! The hilliness of a lawn could af-
variable in this lawn-mowing business? fect the time needed to mow it, and this is
G, representing the amount of gas need- a quality that can vary from lawn to lawn.
ed to mow a given lawn
H, representing the hilliness of the lawn
M, representing the maximum amount of
lawn that a given mower can complete
, c957 Applied Algebra
per hour
W, representing the number of hours the
employee spends working each day
Which variable is related to the variable
temperature? Hot chocolate sales
Book sales Correct! When temperatures fall, more
Pen sales people want to buy hot chocolate to stay
Hot chocolate sales warm.
Computer sales
The amount of food prepared for a
catered event depends on the number of The number of people attending
people attending. Correct! Since the number of people pre-
Which variable is the independent vari- sent and eating influences the amount of
able? food that needs to be prepared, the num-
The number of people attending ber of people is the independent variable.
The amount of food prepared
You own a car wash that charges $10
for each car that goes through. If you
wash 50 cars a day, your revenue is
$10×50=$500
The number of cars washed
. If you only wash 20 cars a day, your
Correct! Since the number of cars
revenue is $10×20=$200
washed affects your revenue, the num-
.
ber of cars is the independent variable.
Which variable is the independent vari-
able?
Your company's revenue
The number of cars washed
The amount of money you spend on
apps depends on the number of apps
The amount of money spent
you buy.
Correct! Since the amount you spend de-
Which variable is the dependent vari-
pends on the number of apps purchased,
able?
this is the dependent variable.
The amount of money spent
The number of apps you buy
When you first started at your job, you
earned two weeks of vacation time a
year. After five years of employment,
, c957 Applied Algebra
you earn three weeks of vacation. After
ten years of employment, you earn four
weeks of vacation. The number of weeks of vacation
What is the dependent variable—the Correct! Since the number of weeks of
number of weeks of vacation or the num- vacation is influenced by the years of em-
ber of years employed? ployment, this is the dependent variable.
The number of years employed
The number of weeks of vacation
Which event allows you to predict the
output based on an input?
The color gumball you get from a gum-
ball machine based on which quarter you
What comes out of a vending machine
put into the machine
based on your selection
What comes out of a vending machine
Correct! Each button corresponds to a
based on your selection
different item—your selection predicts
Whether or not someone will opt into
what comes out of the vending machine.
a retirement savings program based on
eye color
The sex of a baby based on what the
mother eats during pregnancy
A cow eats grass, which is turned into
milk by its body, and a farmer then milks
the cow.
What is the input? The grass
The grass Correct! The grass is the input.
The milk
The cow
The farmer
Which of these represents a function?
Input: The cost of an item; Output: The
Input: The cost of an item; Output: The
sales tax owed on the item
sales tax owed on the item
Input: A teacher's gender; Output: Sub-
Correct! Since one input, the cost of the
ject he or she teaches
item, is matched with exactly one output,
Input: A student's age; Output: The num-
the amount of sales tax owed, this is a
ber of siblings a student has
function.
Input: The amount of coffee consumed;
Output: Level of intelligence
, c957 Applied Algebra
A company uses the function B to predict The inverse function could be used to fig-
the cost of benefits given the number of ure out how many employees the compa-
employees, n. ny could employ if the budget for benefits
What might the inverse function be use- was limited.
ful for? Correct! The inverse function would be
The inverse function could be used to n(B)
predict the cost of benefits for new hires. , which would give you the number of
The inverse function could be used to fig- employees given the cost of benefits. The
ure out how many employees the compa- original function would have been written
ny could employ if the budget for benefits as B(n)
was limited. .
A function doubles each input. What
does the inverse function do?
Halves each input
Doubles each input
Correct! The inverse does the reverse or
Subtracts 2 from each input
"undoes" the original operation.
Adds 2 to each input
Halves each input
Sales tax in your state is 7%.
Which function models the amount of
sales tax, T, when you spend x dollars? T(x)=0.07(x)
T(x)=7x Correct! 7% of total spent is written as
T(x)=0.07(x) 0.07x.
T(x)=0.07+x
T(x)=7+x
Your daughter babysits and charges $8
per hour.
Select the function that models the
B(h)=8h
amount of money she earns when
Correct! Since she earns $8 for each
babysitting for h hours.
hour she babysits, multiply 8 times the
B(h)=8h
number of hours.
B(h)=8+h
B(h)=8h
B(h)=h+8
Your business currently has 12 employ-
ees. You plan to add three new employ-
N(y)=12+3y
ees each year for the life of your busi-
Correct! 3y is the correct interpretation of
ness. Which function below models your
plan? Note that N represents the number
Which choice is a variable?
The cost of your daily newspaper The amount a teenager makes babysit-
The number of states in the United ting
States of America Correct! A teenager probably charges
The amount a teenager makes babysit- the same amount per hour but makes
ting more if the job lasts longer, like all day
Your shoe size
Which choice is a variable?
The name of the largest mountain range
in the United States The colors and styles of your shoes
The amount a babysitter charges per Correct! Size may always be the same,
hour but color and style certainly vary.
The colors and styles of your shoes
The operating system on your phone
Which choice is a quantitative variable?
M, representing the federal minimum
wage
P, representing the monthly profit based P, representing the monthly profit based
on the number of customers who needed on the number of customers who needed
plumbing services plumbing services
R, representing the monthly rent for your Correct! Profit can change from month to
company's office building month, and profit is a number, or quantity.
S, representing the number of regular
weekly shipping deliveries your compa-
ny's trucks make
In a lawn-mowing business, the amount
of time an employee spends mowing a
lawn depends on the size of the lawn.
It might also depend on some other fac-
tors. H, representing the hilliness of the lawn
Which choice represents a qualitative Correct! The hilliness of a lawn could af-
variable in this lawn-mowing business? fect the time needed to mow it, and this is
G, representing the amount of gas need- a quality that can vary from lawn to lawn.
ed to mow a given lawn
H, representing the hilliness of the lawn
M, representing the maximum amount of
lawn that a given mower can complete
, c957 Applied Algebra
per hour
W, representing the number of hours the
employee spends working each day
Which variable is related to the variable
temperature? Hot chocolate sales
Book sales Correct! When temperatures fall, more
Pen sales people want to buy hot chocolate to stay
Hot chocolate sales warm.
Computer sales
The amount of food prepared for a
catered event depends on the number of The number of people attending
people attending. Correct! Since the number of people pre-
Which variable is the independent vari- sent and eating influences the amount of
able? food that needs to be prepared, the num-
The number of people attending ber of people is the independent variable.
The amount of food prepared
You own a car wash that charges $10
for each car that goes through. If you
wash 50 cars a day, your revenue is
$10×50=$500
The number of cars washed
. If you only wash 20 cars a day, your
Correct! Since the number of cars
revenue is $10×20=$200
washed affects your revenue, the num-
.
ber of cars is the independent variable.
Which variable is the independent vari-
able?
Your company's revenue
The number of cars washed
The amount of money you spend on
apps depends on the number of apps
The amount of money spent
you buy.
Correct! Since the amount you spend de-
Which variable is the dependent vari-
pends on the number of apps purchased,
able?
this is the dependent variable.
The amount of money spent
The number of apps you buy
When you first started at your job, you
earned two weeks of vacation time a
year. After five years of employment,
, c957 Applied Algebra
you earn three weeks of vacation. After
ten years of employment, you earn four
weeks of vacation. The number of weeks of vacation
What is the dependent variable—the Correct! Since the number of weeks of
number of weeks of vacation or the num- vacation is influenced by the years of em-
ber of years employed? ployment, this is the dependent variable.
The number of years employed
The number of weeks of vacation
Which event allows you to predict the
output based on an input?
The color gumball you get from a gum-
ball machine based on which quarter you
What comes out of a vending machine
put into the machine
based on your selection
What comes out of a vending machine
Correct! Each button corresponds to a
based on your selection
different item—your selection predicts
Whether or not someone will opt into
what comes out of the vending machine.
a retirement savings program based on
eye color
The sex of a baby based on what the
mother eats during pregnancy
A cow eats grass, which is turned into
milk by its body, and a farmer then milks
the cow.
What is the input? The grass
The grass Correct! The grass is the input.
The milk
The cow
The farmer
Which of these represents a function?
Input: The cost of an item; Output: The
Input: The cost of an item; Output: The
sales tax owed on the item
sales tax owed on the item
Input: A teacher's gender; Output: Sub-
Correct! Since one input, the cost of the
ject he or she teaches
item, is matched with exactly one output,
Input: A student's age; Output: The num-
the amount of sales tax owed, this is a
ber of siblings a student has
function.
Input: The amount of coffee consumed;
Output: Level of intelligence
, c957 Applied Algebra
A company uses the function B to predict The inverse function could be used to fig-
the cost of benefits given the number of ure out how many employees the compa-
employees, n. ny could employ if the budget for benefits
What might the inverse function be use- was limited.
ful for? Correct! The inverse function would be
The inverse function could be used to n(B)
predict the cost of benefits for new hires. , which would give you the number of
The inverse function could be used to fig- employees given the cost of benefits. The
ure out how many employees the compa- original function would have been written
ny could employ if the budget for benefits as B(n)
was limited. .
A function doubles each input. What
does the inverse function do?
Halves each input
Doubles each input
Correct! The inverse does the reverse or
Subtracts 2 from each input
"undoes" the original operation.
Adds 2 to each input
Halves each input
Sales tax in your state is 7%.
Which function models the amount of
sales tax, T, when you spend x dollars? T(x)=0.07(x)
T(x)=7x Correct! 7% of total spent is written as
T(x)=0.07(x) 0.07x.
T(x)=0.07+x
T(x)=7+x
Your daughter babysits and charges $8
per hour.
Select the function that models the
B(h)=8h
amount of money she earns when
Correct! Since she earns $8 for each
babysitting for h hours.
hour she babysits, multiply 8 times the
B(h)=8h
number of hours.
B(h)=8+h
B(h)=8h
B(h)=h+8
Your business currently has 12 employ-
ees. You plan to add three new employ-
N(y)=12+3y
ees each year for the life of your busi-
Correct! 3y is the correct interpretation of
ness. Which function below models your
plan? Note that N represents the number
