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Math Problems
Grade 8
Identify independent and dependent variables
Reagan is taking a standardized test. Her final test score will depend on the number of questions she answers correctly.
\newline
s
=
s =
s
=
Reagan's final test score
\newline
q
=
q =
q
=
the number of questions Reagan answers correctly
\newline
Which of the variables is independent and which is dependent?
\newline
Choices:
\newline
(A)
s
s
s
is the independent variable and
q
q
q
is the dependent variable
\newline
(B)
q
q
q
is the independent variable and
s
s
s
is the dependent variable
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On a game show, contestants win money for each question they answer correctly. The number of correct answers dictates the amount of prize money.
\newline
c
=
c =
c
=
the number of correct answers
\newline
m
=
m =
m
=
the amount of prize money
\newline
Which of the variables is independent and which is dependent?
\newline
Choices:
\newline
(A)
m
m
m
is the independent variable and
c
c
c
is the dependent variable
\newline
(B)
c
c
c
is the independent variable and
m
m
m
is the dependent variable
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Gabrielle works as a consultant at a software company. The amount of her annual bonus is based upon the number of hours she works.
\newline
b
b
b
= the amount of Gabrielle's bonus
\newline
h
h
h
= the number of hours Gabrielle works
\newline
Which of the variables is independent and which is dependent?
\newline
Choices:
\newline
(A)
h
h
h
is the independent variable and
b
b
b
is the dependent variable
\newline
(B)
b
b
b
is the independent variable and
h
h
h
is the dependent variable
Get tutor help
While on vacation, Caleb plans to write some postcards to his friends. The number of stamps Caleb has will determine how many postcards Caleb can send.
\newline
s
=
s =
s
=
the number of stamps Caleb has
\newline
p
=
p =
p
=
the number of postcards Caleb can send
\newline
Which of the variables is independent and which is dependent?
\newline
Choices:
\newline
(A)
s
s
s
is the independent variable and
p
p
p
is the dependent variable
\newline
(B)
p
p
p
is the independent variable and
s
s
s
is the dependent variable
Get tutor help
Aubrey is planning a picnic for her coworkers and plans to serve veggie burgers. The more of her coworkers who attend the picnic, the more veggie burgers she will prepare.
\newline
c
c
c
= the number of Aubrey's coworkers who attend the picnic
\newline
v
v
v
= the number of veggie burgers Aubrey prepares
\newline
Which of the variables is independent and which is dependent?
\newline
Choices:
\newline
(A)
c
c
c
is the independent variable and
v
v
v
is the dependent variable
\newline
(B)
v
v
v
is the independent variable and
c
c
c
is the dependent variable
Get tutor help
Brenna, a pastry chef, is designing a cake for a retirement party. The number of guests expected will determine how many tiers the cake will have.
\newline
g
g
g
= the number of guests expected
\newline
t
t
t
= the number of tiers the cake will have
\newline
Which of the variables is independent and which is dependent?
\newline
Choices:
\newline
(A)
g
g
g
is the independent variable and
t
t
t
is the dependent variable
\newline
(B)
t
t
t
is the independent variable and
g
g
g
is the dependent variable
Get tutor help
The Harrison dairy farm produces milk and other dairy products. The number of cows on the farm changes from month to month. The more cows there are on the farm, the more milk the farm is able to produce in a month.
\newline
c
=
c =
c
=
the number of cows on the farm
\newline
m
=
m =
m
=
the amount of milk produced by the farm in a month
\newline
Which of the variables is independent and which is dependent?
\newline
Choices:
\newline
(A)
m
m
m
is the independent variable and
c
c
c
is the dependent variable
\newline
(B)
c
c
c
is the independent variable and
m
m
m
is the dependent variable
Get tutor help
Percy has a summer job mowing lawns. The amount of money he earns is determined by how many lawns he mows.
\newline
m
=
m =
m
=
the amount of money Percy makes
\newline
l
=
l =
l
=
the number of lawns Percy mows
\newline
Which of the variables is independent and which is dependent?
\newline
Choices:
\newline
(A)
m
m
m
is the independent variable and
l
l
l
is the dependent variable
\newline
(B)
l
l
l
is the independent variable and
m
m
m
is the dependent variable
Get tutor help
Kayla is making goodie bags for her child's birthday party, and she is buying bottles of bubbles for the bags. The number of party guests determines how many bottles of bubbles she will need to purchase.
\newline
g
=
g =
g
=
the number of guests
\newline
b
=
b =
b
=
the number of bottles of bubbles Kayla purchases
\newline
Which of the variables is independent and which is dependent?
\newline
Choices:
\newline
(A)
g
g
g
is the independent variable and
b
b
b
is the dependent variable
\newline
(B)
b
b
b
is the independent variable and
g
g
g
is the dependent variable
Get tutor help
At a local school, students who skip classes receive detention. They spend more time in detention if they cut more classes.
\newline
t
=
t =
t
=
the amount of time spent in detention
\newline
c
=
c =
c
=
the number of classes cut
\newline
Which of the variables is independent and which is dependent?
\newline
Choices:
\newline
(A)
t
t
t
is the independent variable and
c
c
c
is the dependent variable
\newline
(B)
c
c
c
is the independent variable and
t
t
t
is the dependent variable
Get tutor help
The Clinton Coffee House brews fresh-roasted coffee beans to serve to their patrons. The amount of coffee they will need to brew in a day depends on the number of patrons they have.
\newline
c
c
c
= the amount of coffee they will need to brew
\newline
p
p
p
= the number of patrons
\newline
Which of the variables is independent and which is dependent?
\newline
Choices:
\newline
(A)
p
p
p
is the independent variable and
c
c
c
is the dependent variable
\newline
(B)
c
c
c
is the independent variable and
p
p
p
is the dependent variable
Get tutor help
The circle has center
O
O
O
, and the measure of angle
R
O
S
ROS
ROS
is
150
150
150
degrees. The length of minor arc
R
S
RS
RS
is what fraction of the circumference of the circle? (The number of degrees of arc in a circle is
360
360
360
.)
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Nate is filling water bottles for a bicycle race. The number of water bottles he prepares is calculated based on how many hours he expects to be on the course.
\newline
w
=
w =
w
=
the number of water bottles Nate prepares
\newline
h
=
h =
h
=
the number of hours Nate expects to be on the course
\newline
Which of the variables is independent and which is dependent?
\newline
Choices:
\newline
(A)
h
h
h
is the independent variable and
w
w
w
is the dependent variable
\newline
(B)
w
w
w
is the independent variable and
h
h
h
is the dependent variable
Get tutor help
Keenan and Sam are going hiking and are trying to figure out how much water they should bring with them on the hike. The longer they plan to hike, the more water they should bring.
\newline
t
=
t =
t
=
the length of the hike
\newline
w
=
w =
w
=
the amount of water they should bring on the hike
\newline
Which of the variables is independent and which is dependent?
\newline
Choices:
\newline
(A)
w
w
w
is the independent variable and
t
t
t
is the dependent variable
\newline
(B)
t
t
t
is the independent variable and
w
w
w
is the dependent variable
Get tutor help
Nicole is planning her wedding. The number of guests she wants to invite determines the number of announcements she orders.
\newline
g
=
g =
g
=
the number of guests
\newline
a
=
a =
a
=
the number of announcements
\newline
Which of the variables is independent and which is dependent?
\newline
Choices:
\newline
(A)
g
g
g
is the independent variable and
a
a
a
is the dependent variable
\newline
(B)
a
a
a
is the independent variable and
g
g
g
is the dependent variable
Get tutor help
Shelby is selling lemonade. The amount of money she earns depends on how many cups of lemonade she sells.
\newline
m
=
m =
m
=
the amount of money Shelby earns
\newline
c
=
c =
c
=
the number of cups of lemonade Shelby sells
\newline
Which of the variables is independent and which is dependent?
\newline
Choices:
\newline
(A)
m
m
m
is the independent variable and
c
c
c
is the dependent variable
\newline
(B)
c
c
c
is the independent variable and
m
m
m
is the dependent variable
Get tutor help
Roy is having the carpets in his house cleaned. The area of the carpets is used to calculate the cost of the cleaning.
\newline
a
=
a=
a
=
the area of the carpets
\newline
c
=
\mathrm{c}=
c
=
the cost of the cleaning
\newline
Which of the variables is independent and which is dependent?
\newline
(A)
a
a
a
is the independent variable and
c
c
c
is the dependent variable
\newline
(B)
c
c
c
is the independent variable and
a
a
a
is the dependent variable
Get tutor help
During the winter, a trucking company ships produce from California to New York. The number of truckers the company hires will depend on the amount of produce it needs to ship.
\newline
t
=
t =
t
=
the number of truckers the company will hire
\newline
p
=
p =
p
=
the amount of produce the company needs to ship
\newline
Which of the variables is independent and which is dependent?
\newline
Choices:
\newline
(A)
t
t
t
is the independent variable and
p
p
p
is the dependent variable
\newline
(B)
p
p
p
is the independent variable and
t
t
t
is the dependent variable
Get tutor help
A school in Newport is having a choir concert. The duration of the concert is determined by the number of songs performed.
\newline
d
=
d =
d
=
the duration of the concert
\newline
s
=
s =
s
=
the number of songs performed
\newline
Which of the variables is independent and which is dependent?
\newline
Choices:
\newline
(A)
s
s
s
is the independent variable and
d
d
d
is the dependent variable
\newline
(B)
d
d
d
is the independent variable and
s
s
s
is the dependent variable
Get tutor help
Diane is making fancy headbands to sell at a craft fair. The number of headbands she can make is limited by the amount of ribbon she has on hand.
\newline
h
=
h =
h
=
the number of headbands Diane can make
\newline
r
=
r =
r
=
the amount of ribbon Diane has on hand
\newline
Which of the variables is independent and which is dependent?
\newline
Choices:
\newline
(A)
h
h
h
is the independent variable and
r
r
r
is the dependent variable
\newline
(B)
r
r
r
is the independent variable and
h
h
h
is the dependent variable
Get tutor help
Britney's daughter will be participating in an upcoming dance recital. She will require a different costume for each dance she plans to performs.
\newline
c
c
c
= the number of costumes Britney's daughter will require
\newline
d
d
d
= the number of dances Britney's daughter plans to perform
\newline
Which of the variables is independent and which is dependent?
\newline
Choices:
\newline
(A)
c
c
c
is the independent variable and
d
d
d
is the dependent variable
\newline
(B)
d
d
d
is the independent variable and
c
c
c
is the dependent variable
Get tutor help
For a party, Leon made a pan pizza from scratch. The number of squares he cuts the pizza into will depend on the number of people attending the potluck.
\newline
s
=
s =
s
=
the number of squares Leon cuts the pizza into
\newline
p
=
p =
p
=
the number of people attending the potluck
\newline
Which of the variables is independent and which is dependent?
\newline
Choices:
\newline
(A)
s
s
s
is the independent variable and
p
p
p
is the dependent variable
\newline
(B)
p
p
p
is the independent variable and
s
s
s
is the dependent variable
Get tutor help
Barry is participating in a walkathon to raise money for local literacy programs. The farther Barry walks, the more money he will raise.
\newline
d
d
d
= the distance Barry walks
\newline
m
m
m
= the amount of money Barry will raise
\newline
Which of the variables is independent and which is dependent?
\newline
Choices:
\newline
(A)
m
m
m
is the independent variable and
d
d
d
is the dependent variable
\newline
(B)
d
d
d
is the independent variable and
m
m
m
is the dependent variable
Get tutor help
Leslie's daughter will be participating in an upcoming dance recital. She will require a different costume for each dance she plans to performs.
\newline
c
c
c
= the number of costumes Leslie's daughter will require
\newline
d
d
d
= the number of dances Leslie's daughter plans to perform
\newline
Which of the variables is independent and which is dependent?
\newline
Choices:
\newline
(A)
c
c
c
is the independent variable and
d
d
d
is the dependent variable
\newline
(B)
d
d
d
is the independent variable and
c
c
c
is the dependent variable
Get tutor help
The members of a sewing circle are making quilts to donate to homeless shelters. The number of quilts they can produce is determined by how much fabric they have available.
\newline
q
=
q =
q
=
the number of quilts they can produce
\newline
f
=
f =
f
=
the amount of fabric they have available
\newline
Which of the variables is independent and which is dependent?
\newline
Choices:
\newline
(A)
f
f
f
is the independent variable and
q
q
q
is the dependent variable
\newline
(B)
q
q
q
is the independent variable and
f
f
f
is the dependent variable
Get tutor help
Trudy owns a jewelry shop and sells, among other things, diamond rings. She has a chart that shows how the cost of a diamond corresponds to its size. The bigger the diamond, the greater its cost.
\newline
s
=
s =
s
=
the size of a diamond
\newline
c
=
c =
c
=
the cost of a diamond
\newline
Which of the variables is independent and which is dependent?
\newline
Choices:
\newline
(A)
s
s
s
is the independent variable and
c
c
c
is the dependent variable
\newline
(B)
c
c
c
is the independent variable and
s
s
s
is the dependent variable
Get tutor help
Every day at lunch, Hakim swims laps in the pool for one hour. The faster his speed, the more laps he is able to swim in the hour.
\newline
s
=
s =
s
=
the speed at which Hakim swims
\newline
l
=
l =
l
=
the number of laps Hakim is able to swim in one hour
\newline
Which of the variables is independent and which is dependent?
\newline
Choices:
\newline
(A)
l
l
l
is the independent variable and
s
s
s
is the dependent variable
\newline
(B)
s
s
s
is the independent variable and
l
l
l
is the dependent variable
Get tutor help
Tisha is throwing a party. The number of party favors she buys is based on how many guests she wants to invite.
\newline
p
=
p =
p
=
the number of party favors
\newline
g
=
g =
g
=
the number of guests
\newline
Which of the variables is independent and which is dependent?
\newline
Choices:
\newline
(A)
g
g
g
is the independent variable and
p
p
p
is the dependent variable
\newline
(B)
p
p
p
is the independent variable and
g
g
g
is the dependent variable
Get tutor help
Hakim is buying birthday candles for his grandmother's birthday cake. The number of boxes of candles he will purchase is based on her age, in years.
\newline
b
b
b
= how many boxes of candles Hakim will purchase
\newline
y
y
y
= Hakim's grandmother's age, in years
\newline
Which of the variables is independent and which is dependent?
\newline
Choices:
\newline
(A)
y
y
y
is the independent variable and
b
b
b
is the dependent variable
\newline
(B)
b
b
b
is the independent variable and
y
y
y
is the dependent variable
Get tutor help
Kinsley is hosting a potluck dinner for her book club. The number of chairs she will need depends on the number of members who attend.
\newline
c
=
c =
c
=
the number of chairs Kinsley will need
\newline
m
=
m =
m
=
the number of members who attend the potluck
\newline
Which of the variables is independent and which is dependent?
\newline
Choices:
\newline
(A)
c
c
c
is the independent variable and
m
m
m
is the dependent variable
\newline
(B)
m
m
m
is the independent variable and
c
c
c
is the dependent variable
Get tutor help
Shawna, a florist, is assembling bouquets of roses to sell at her flower shop. The number of bouquets she can assemble depends on how many roses are in her shop.
\newline
b
b
b
= the number of bouquets Shawna can assemble
\newline
r
r
r
= the number of roses in the flower shop
\newline
Which of the variables is independent and which is dependent?
\newline
Choices:
\newline
(A)
b
b
b
is the independent variable and
r
r
r
is the dependent variable
\newline
(B)
r
r
r
is the independent variable and
b
b
b
is the dependent variable
Get tutor help
Mr. Patterson, the debate team coach, is organizing a debate tournament at his school. The number of rounds in the tournament will determine how many volunteers he will need as judges.
\newline
r
r
r
= the number of rounds in the tournament
\newline
v
v
v
= the number of volunteers needed for judging
\newline
Which of the variables is independent and which is dependent?
\newline
Choices:
\newline
(A)
v
v
v
is the independent variable and
r
r
r
is the dependent variable
\newline
(B)
r
r
r
is the independent variable and
v
v
v
is the dependent variable
Get tutor help
At a fancy dinner party, the number of courses that will be served determines how many forks will be set out by the hostess.
\newline
c
=
c =
c
=
the number of courses served during dinner
\newline
f
=
f =
f
=
the number of forks set out by the hostess
\newline
Which of the variables is independent and which is dependent?
\newline
Choices:
\newline
(A)
c
c
c
is the independent variable and
f
f
f
is the dependent variable
\newline
(B)
f
f
f
is the independent variable and
c
c
c
is the dependent variable
Get tutor help
A soccer team's score depends on how many goals the team has made.
\newline
s
s
s
= the team's score
\newline
g
g
g
= the number of goals a team has made
\newline
Which of the variables is independent and which is dependent?
\newline
Choices:
\newline
(A)
g
g
g
is the independent variable and
s
s
s
is the dependent variable
\newline
(B)
s
s
s
is the independent variable and
g
g
g
is the dependent variable
Get tutor help
The Sullivan farm sells eggs to local restaurants. The number of hens on the farm varies from month to month. The greater the number of hens on the farm, the more eggs the farm is able to produce in a month.
\newline
h
h
h
= the number of hens on the farm
\newline
g
g
g
= the number of eggs produced by the farm in a month
\newline
Which of the variables is independent and which is dependent?
\newline
Choices:
\newline
(A)
h
h
h
is the independent variable and
g
g
g
is the dependent variable
\newline
(B)
g
g
g
is the independent variable and
h
h
h
is the dependent variable
Get tutor help
The entire high school marching band is going on a field trip. According to school district policy, the number of students on the trip determines how many parent chaperones are required to go along.
\newline
s
s
s
= the number of band students on the trip
\newline
p
p
p
= the number of parent chaperones required on the trip
\newline
Which of the variables is independent and which is dependent?
\newline
Choices:
\newline
(A)
s
s
s
is the independent variable and
p
p
p
is the dependent variable
\newline
(B)
p
p
p
is the independent variable and
s
s
s
is the dependent variable
Get tutor help
For a party, Martina made a pan pizza from scratch. The number of people in attendance will determine how many squares she cuts the pizza into.
\newline
p
=
p =
p
=
the number of people attending the potluck
\newline
s
=
s =
s
=
the number of squares Martina cuts the pizza into
\newline
Which of the variables is independent and which is dependent?
\newline
Choices:
\newline
(A)
p
p
p
is the independent variable and
s
s
s
is the dependent variable
\newline
(B)
s
s
s
is the independent variable and
p
p
p
is the dependent variable
Get tutor help
Brittany and Kinsley are baking cookies to sell at their school's bake sale. The amount of money they will be able to raise for their school depends on the number of cookies they bake.
\newline
m
m
m
= the amount of money they will be able to raise
\newline
c
c
c
= the number of cookies they bake
\newline
Which of the variables is independent and which is dependent?
\newline
Choices:
\newline
(A)
c
c
c
is the independent variable and
m
m
m
is the dependent variable
\newline
(B)
m
m
m
is the independent variable and
c
c
c
is the dependent variable
Get tutor help
While on vacation, Vincent plans to write some postcards to his friends. The number of stamps Vincent has will determine how many postcards Vincent can send.
\newline
s
=
s =
s
=
the number of stamps Vincent has
\newline
p
=
p =
p
=
the number of postcards Vincent can send
\newline
Which of the variables is independent and which is dependent?
\newline
Choices:
\newline
(A)
s
s
s
is the independent variable and
p
p
p
is the dependent variable
\newline
(B)
p
p
p
is the independent variable and
s
s
s
is the dependent variable
Get tutor help
At a coffee shop, the amount of tax due is calculated based on the cost of the customer's order.
\newline
t
=
t =
t
=
the amount of tax due
\newline
c
=
c =
c
=
the cost of the order
\newline
Which of the variables is independent and which is dependent?
\newline
Choices:
\newline
(A)
c
c
c
is the independent variable and
t
t
t
is the dependent variable
\newline
(B)
t
t
t
is the independent variable and
c
c
c
is the dependent variable
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In a bowling class, the students are organized into teams. The number of students in the class is used to calculate how many teams will be formed.
\newline
s
s
s
= the number of students in the class
\newline
t
t
t
= the number of teams to be formed
\newline
Which of the variables is independent and which is dependent?
\newline
Choices:
\newline
(A)
s
s
s
is the independent variable and
t
t
t
is the dependent variable
\newline
(B)
t
t
t
is the independent variable and
s
s
s
is the dependent variable
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In a bowling class, the students are organized into teams. The number of students in the class is used to calculate how many teams will be formed.
\newline
s
=
s =
s
=
the number of students in the class
\newline
t
=
t =
t
=
the number of teams to be formed
\newline
Which of the variables is independent and which is dependent?
\newline
Choices:
\newline
(A)
t
t
t
is the independent variable and
s
s
s
is the dependent variable
\newline
(B)
s
s
s
is the independent variable and
t
t
t
is the dependent variable
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Pam is throwing a party. The number of guests she wants to invite determines the number of party favors she buys.
\newline
g
=
g =
g
=
the number of guests
\newline
p
=
p =
p
=
the number of party favors
\newline
Which of the variables is independent and which is dependent?
\newline
Choices:
\newline
(A)
p
p
p
is the independent variable and
g
g
g
is the dependent variable
\newline
(B)
g
g
g
is the independent variable and
p
p
p
is the dependent variable
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The students at Springfield High School are collecting food for a local food bank. The amount of food collected will determine the number of trucks needed to deliver the food to the food bank.
\newline
f
=
f =
f
=
the amount of food collected
\newline
t
=
t =
t
=
the number of trucks needed to deliver the food
\newline
Which of the variables is independent and which is dependent?
\newline
Choices:
\newline
(A)
t
t
t
is the independent variable and
f
f
f
is the dependent variable
\newline
(B)
f
f
f
is the independent variable and
t
t
t
is the dependent variable
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Jonah is ordering sandwiches for a team meeting at work. The number of coworkers attending will determine how many sandwiches he will order.
\newline
c
c
c
= the number of Jonah's coworkers attending the meeting
\newline
s
s
s
= the number of sandwiches Jonah will order
\newline
Which of the variables is independent and which is dependent?
\newline
Choices:
\newline
(A)
c
c
c
is the independent variable and
s
s
s
is the dependent variable
\newline
(B)
s
s
s
is the independent variable and
c
c
c
is the dependent variable
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Clarence's daughter will be participating in an upcoming dance recital. She will require a different costume for each dance she plans to performs.
\newline
c
c
c
= the number of costumes Clarence's daughter will require
\newline
d
d
d
= the number of dances Clarence's daughter plans to perform
\newline
Which of the variables is independent and which is dependent?
\newline
Choices:
\newline
(A)
d
d
d
is the independent variable and
c
c
c
is the dependent variable
\newline
(B)
c
c
c
is the independent variable and
d
d
d
is the dependent variable
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Clarence is making goodie bags for his child's birthday party, and he is buying bottles of bubbles for the bags. The quantity of bubbles Clarence purchases will be determined by how many guests attend the party.
\newline
b
=
b =
b
=
the number of bottles of bubbles Clarence purchases
\newline
g
=
g =
g
=
the number of guests
\newline
Which of the variables is independent and which is dependent?
\newline
Choices:
\newline
(A)
g
g
g
is the independent variable and
b
b
b
is the dependent variable
\newline
(B)
b
b
b
is the independent variable and
g
g
g
is the dependent variable
Get tutor help
