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Math Problems
Grade 7
Identify independent and dependent variables
In one hour, the distance,
d
(
s
)
d(s)
d
(
s
)
, in kilometers that a ferry can travel up and down a river flowing with a constant speed,
s
s
s
, in meters per second is:
d
(
s
)
=
10.7
−
1.2
s
2
d(s) = 10.7 - 1.2s^2
d
(
s
)
=
10.7
−
1.2
s
2
where
s
s
s
and
d
(
s
)
d(s)
d
(
s
)
are positive.
\newline
Which of the following equivalent expressions for
d
(
s
)
d(s)
d
(
s
)
contains the speed of the river in meters per second, as a constant or coefficient, for which the ferry can travel a distance of
8
8
8
kilometers in one hour?
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How does
h
(
x
)
=
5
x
h(x) = 5^x
h
(
x
)
=
5
x
change over the interval from
x
=
2
x = 2
x
=
2
to
x
=
3
x = 3
x
=
3
?
\newline
Choices:
\newline
h
(
x
)
h(x)
h
(
x
)
increases by 200%
\newline
h
(
x
)
h(x)
h
(
x
)
increases by a factor of 25
\newline
h
(
x
)
h(x)
h
(
x
)
decreases by 60%
\newline
h
(
x
)
h(x)
h
(
x
)
increases by a factor of 5
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Janet 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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Avery is bringing treats to her elementary school class on her birthday. The number of students in Avery's class determines the number of treats she brings in.
\newline
s
=
s =
s
=
the number of students
\newline
t
=
t =
t
=
the number of treats
\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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Jenny manages the Lincoln Orchard, which produces many different types of fruit, including pears. The more pear trees that have been planted in the orchard, the more barrels of pears the orchard will produce.
\newline
p
p
p
= the number of pear trees that have been planted in the orchard
\newline
b
b
b
= the number of barrels of pears the orchard will produce
\newline
Which of the variables is independent and which is dependent?
\newline
Choices:
\newline
(A)
b
b
b
is the independent variable and
p
p
p
is the dependent variable
\newline
(B)
p
p
p
is the independent variable and
b
b
b
is the dependent variable
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Sebastian, 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
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Michael runs the Randolph Farm, which produces many different crops, including wheat. The more plots of land that are devoted to growing wheat, the more bushels of wheat the farm will produce.
\newline
p
p
p
= the number of plots of land devoted to growing wheat
\newline
w
w
w
= the number of bushels of wheat produced each year
\newline
Which of the variables is independent and which is dependent?
\newline
Choices:
\newline
(A)
p
p
p
is the independent variable and
w
w
w
is the dependent variable
\newline
(B)
w
w
w
is the independent variable and
p
p
p
is the dependent variable
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Ellie is making a scrapbook. The scrapbook grows thicker as she adds more photos.
\newline
t
=
t =
t
=
the thickness of the scrapbook
\newline
p
=
p =
p
=
the number of photos added
\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
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Austen and Tanvi are raising money to purchase books for their school's library. The more money they raise, the more books they will be able to purchase for the library.
\newline
m
=
m =
m
=
the amount of money Austen and Tanvi raise
\newline
b
=
b =
b
=
the number of books Austen and Tanvi will be able to purchase
\newline
Which of the variables is independent and which is dependent?
\newline
Choices:
\newline
(A)
m
m
m
is the independent variable and
b
b
b
is the dependent variable
\newline
(B)
b
b
b
is the independent variable and
m
m
m
is the dependent variable
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For a party, Jen 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 Jen 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
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Molly, 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 Molly 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
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Darnel and Isaiah are going on a road trip together. They have a limited budget, so they consider several different routes and calculate the cost of gas for each route. The cost of gas for each route depends on the length of the route.
\newline
g
g
g
= the cost of gas
\newline
r
r
r
= the length of the route
\newline
Which of the variables is independent and which is dependent?
\newline
Choices:
\newline
(A)
r
r
r
is the independent variable and
g
g
g
is the dependent variable
\newline
(B)
g
g
g
is the independent variable and
r
r
r
is the dependent variable
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Patrick is making apple turnovers for his friends. The number of turnovers he can make is determined by how many apples he has at home.
\newline
t
=
t =
t
=
the number of turnovers Patrick can make
\newline
a
=
a =
a
=
the number of apples Patrick has at home
\newline
Which of the variables is independent and which is dependent?
\newline
Choices:
\newline
(A)
a
a
a
is the independent variable and
t
t
t
is the dependent variable
\newline
(B)
t
t
t
is the independent variable and
a
a
a
is the dependent variable
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The Lawrence 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
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Polly and Erin are going on vacation and are trying to figure out how much money they should bring with them. The longer the vacation, the more money they should bring.
\newline
t
=
t =
t
=
the length of Polly and Erin's vacation
\newline
m
=
m =
m
=
the amount of money Polly and Erin should bring
\newline
Which of the variables is independent and which is dependent?
\newline
Choices:
\newline
(A)
m
m
m
is the independent variable and
t
t
t
is the dependent variable
\newline
(B)
t
t
t
is the independent variable and
m
m
m
is the dependent variable
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Rick is going backpacking in a couple of days and is buying trail mix for the trip. The amount of trail mix he will bring depends on how long he plans to backpack.
\newline
a
=
a =
a
=
the amount of trail mix Rick will bring
\newline
l
=
l =
l
=
the length of the backpacking trip
\newline
Which of the variables is independent and which is dependent?
\newline
Choices:
\newline
(A)
a
a
a
is the independent variable and
l
l
l
is the dependent variable
\newline
(B)
l
l
l
is the independent variable and
a
a
a
is the dependent variable
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Mary is picking apples for apple pies. The number of apple pies she will be able to bake depends on the number of apples she picks.
\newline
p
=
p =
p
=
the number of apple pies Mary will be able to bake
\newline
a
=
a =
a
=
the number of apples Mary picks
\newline
Which of the variables is independent and which is dependent?
\newline
Choices:
\newline
(A)
a
a
a
is the independent variable and
p
p
p
is the dependent variable
\newline
(B)
p
p
p
is the independent variable and
a
a
a
is the dependent variable
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In order to earn extra money over the summer, Heather is working as an English tutor. The amount of money she earns depends on the number of students she tutors.
\newline
m
m
m
= the amount of money Heather earns
\newline
s
s
s
= the number of students Heather tutors
\newline
Which of the variables is independent and which is dependent?
\newline
Choices:
\newline
(A)
s
s
s
is the independent variable and
m
m
m
is the dependent variable
\newline
(B)
m
m
m
is the independent variable and
s
s
s
is the dependent variable
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In order to earn extra spending money, Mark babysits children after school. The amount of money he earns depends on the number of hours he babysits.
\newline
m
=
m =
m
=
the amount of money Mark earns
\newline
h
=
h =
h
=
the number of hours Mark babysits
\newline
Which of the variables is independent and which is dependent?
\newline
Choices:
\newline
(A)
h
h
h
is the independent variable and
m
m
m
is the dependent variable
\newline
(B)
m
m
m
is the independent variable and
h
h
h
is the dependent variable
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A team from the Department of Public Works is painting lines on the freeway. The length of road that needs to be lined determines how many hours the project will take.
\newline
r
r
r
= the length of road
\newline
h
h
h
= the number of hours needed
\newline
Which of the variables is independent and which is dependent?
\newline
Choices:
\newline
(A)
r
r
r
is the independent variable and
h
h
h
is the dependent variable
\newline
(B)
h
h
h
is the independent variable and
r
r
r
is the dependent variable
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In hockey, the number of goals a team has scored determines that team's score.
\newline
g
=
g =
g
=
the number of goals a team has scored
\newline
s
=
s =
s
=
the team's score
\newline
Which of the variables is independent and which is dependent?
\newline
Choices:
\newline
(A)
s
s
s
is the independent variable and
g
g
g
is the dependent variable
\newline
(B)
g
g
g
is the independent variable and
s
s
s
is the dependent variable
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The number of fish a collector has determines the size of the tank that is needed to house them.
\newline
n
=
n =
n
=
the number of fish
\newline
s
=
s =
s
=
the size of the fish tank needed
\newline
Which of the variables is independent and which is dependent?
\newline
Choices:
\newline
(A)
s
s
s
is the independent variable and
n
n
n
is the dependent variable
\newline
(B)
n
n
n
is the independent variable and
s
s
s
is the dependent variable
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Anne is organizing a martial arts tournament and is ordering trophies for the winners. The more divisions there are in the tournament, the more trophies Anne needs to order.
\newline
d
=
d =
d
=
the number of divisions in the tournament
\newline
t
=
t =
t
=
the number of trophies Anne orders
\newline
Which of the variables is independent and which is dependent?
\newline
Choices:
\newline
(A)
d
d
d
is the independent variable and
t
t
t
is the dependent variable
\newline
(B)
t
t
t
is the independent variable and
d
d
d
is the dependent variable
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Tiana is going backpacking in a couple of days and is buying trail mix for the trip. The amount of trail mix she will bring depends on how long she plans to backpack.
\newline
a
=
a =
a
=
the amount of trail mix Tiana will bring
\newline
l
=
l =
l
=
the length of the backpacking trip
\newline
Which of the variables is independent and which is dependent?
\newline
Choices:
\newline
(A)
l
l
l
is the independent variable and
a
a
a
is the dependent variable
\newline
(B)
a
a
a
is the independent variable and
l
l
l
is the dependent variable
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Jamie, an artist, is painting portraits to use up the canvases he has in the garage. The number of blank canvases he has available determines how many portraits he can produce.
\newline
c
=
c =
c
=
the number of canvases Jamie has
\newline
p
=
p =
p
=
the number of portraits Jamie can produce
\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
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Rosa works for a small company that sells books online and is responsible for mailing out the books to customers. Every morning she gets in line at the local post office and estimates the length of her wait. The length of her wait depends on the number of people in line ahead of her.
\newline
w
w
w
= the length of time Rosa will need to wait
\newline
p
p
p
= the number of people in line ahead of Rosa
\newline
Which of the variables is independent and which is dependent?
\newline
Choices:
\newline
(A)
p
p
p
is the independent variable and
w
w
w
is the dependent variable
\newline
(B)
w
w
w
is the independent variable and
p
p
p
is the dependent variable
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The Harrison farm sells eggs to local restaurants. The number of hens on the farm varies from month to month. The number of eggs that the farm is able to produce in a month depends on the number of hens on the farm.
\newline
g
g
g
= the number of eggs produced by the farm in a month
\newline
h
h
h
= the number of hens on the farm
\newline
Which of the variables is independent and which is dependent?
\newline
Choices:
\newline
(A)
g
g
g
is the independent variable and
h
h
h
is the dependent variable
\newline
(B)
h
h
h
is the independent variable and
g
g
g
is the dependent variable
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For Valentine's Day, Gabrielle is bringing cards to class. The number of students in Gabrielle's class dictates the number of cards she brings in.
\newline
s
=
s =
s
=
the number of students
\newline
c
=
c =
c
=
the number of cards
\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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The Clark Math Club is hosting a puzzle hunt. The number of teams depends on how many participants there are.
\newline
t
=
t =
t
=
the number of teams
\newline
p
=
p =
p
=
the number of participants
\newline
Which of the variables is independent and which is dependent?
\newline
Choices:
\newline
(
A
)
(A)
(
A
)
p
p
p
is the independent variable and
t
t
t
is the dependent variable
\newline
(
B
)
(B)
(
B
)
t
t
t
is the independent variable and
p
p
p
is the dependent variable
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Rachel is organizing a martial arts tournament and is ordering trophies for the winners. The number of trophies she orders is based on how many divisions there are in the tournament.
\newline
t
=
t =
t
=
the number of trophies Rachel orders
\newline
d
=
d =
d
=
the number of divisions in the tournament
\newline
Which of the variables is independent and which is dependent?
\newline
Choices:
\newline
(A)
t
t
t
is the independent variable and
d
d
d
is the dependent variable
\newline
(B)
d
d
d
is the independent variable and
t
t
t
is the dependent variable
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Xavier is renting buses for a school field trip. The number of buses needed depends on how many students are going on the trip.
\newline
b
=
b =
b
=
the number of buses needed
\newline
s
=
s =
s
=
the number of students going 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
b
b
b
is the dependent variable
\newline
(B)
b
b
b
is the independent variable and
s
s
s
is the dependent variable
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Diana harvests mushrooms in the forests of Oregon and then sells them to local restaurant chefs. The greater the weight of the mushrooms, the greater their value.
\newline
w
=
w =
w
=
the weight of the mushrooms
\newline
v
=
v =
v
=
the value of the mushrooms
\newline
Which of the variables is independent and which is dependent?
\newline
Choices:
\newline
(A)
v
v
v
is the independent variable and
w
w
w
is the dependent variable
\newline
(B)
w
w
w
is the independent variable and
v
v
v
is the dependent variable
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Patrick is getting ready for a hike. The number of hours he expects to be gone will affect how many snacks Patrick packs.
\newline
h
=
h =
h
=
the number of hours Patrick expects to be gone
\newline
s
=
s =
s
=
the number of snacks Patrick packs
\newline
Which of the variables is independent and which is dependent?
\newline
Choices:
\newline
(A)
s
s
s
is the independent variable and
h
h
h
is the dependent variable
\newline
(B)
h
h
h
is the independent variable and
s
s
s
is the dependent variable
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Charlotte-Mecklenburg Schools (CMS) is going to host a Superhero ＂Dinner and a Movie＂ fundraiser at a local theater. Tickets will be for dinner and a screening of Wakanda Forever. They hire you as a consultant to help set the selling price of the tickets. You analyze the costs and consumer demands and arrive at a function for the profit,
P
(
x
)
=
−
x
2
+
90
x
−
100
P(x)=-x^{2}+90x-100
P
(
x
)
=
−
x
2
+
90
x
−
100
, where
x
x
x
represents the price of a ticket for dinner and watching Wakanda Forever.
\newline
What are the break-even points (the selling prices for which the profit is
\newline
$
0
\$0
$0
)? Give answers to the nearest cent.
\newline
x
=
x=
x
=
$
\$
$
◻(left-most break-even point)
\newline
x
=
x=
x
=
$
\$
$
◻(right-most break-even point)
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The number of hours Mark works and the amount of money he makes are related. He earns
$
24
\$24
$24
for every
2
2
2
hours he works. Which statements about the relationship are true?
\newline
A. The amount of money Mark earns is the dependent variable.
\newline
B. The amount of money Mark earns is the independent variable.
\newline
C. The number of hours Mark works is the dependent variable.
\newline
D. The number of hours Mark works is the independent variable.
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Mark is earning money by mowing lawns over the summer. The function
y
=
40
x
y = 40x
y
=
40
x
represents the total number of dollars Mark earns,
y
y
y
, depending on the number of lawns he mows,
x
x
x
.
\newline
What is true about the function?
\newline
Choices:
\newline
(A)It is nonlinear because the rate of change is always zero.
\newline
(B)It is nonlinear because it increases at a constant rate.
\newline
(C)It is linear because the rate of change is always zero.
\newline
(D)It is linear because it increases at a constant rate.
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Evaluate. Write your answer as a whole number or as a simplified fraction.
\newline
2
−
2
2^{-2}
2
−
2
⋅
\cdot
⋅
6
−
3
6^{-3}
6
−
3
⋅
\cdot
⋅
10
10
10
=
=
=
\newline
◻
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Twenty two people purchase raffle tickets. Three winning tickets are selected at random if the first prize is
$
1000
\$1000
$1000
, the second prize is
$
500
\$500
$500
, and the third prize is
$
100
\$100
$100
, in how many different ways can the prizes be awarded?
\newline
There are
□
\square
□
different ways in which the prizes can be awarded (Simplify your answer).
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Every day at lunch, Carly swims laps in the pool for one hour. The faster her speed, the more laps she is able to swim in the hour.
\newline
s
=
s =
s
=
the speed at which Carly swims
\newline
l
=
l =
l
=
the number of laps Carly 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
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Anne 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)
a
a
a
is the independent variable and
g
g
g
is the dependent variable
\newline
(B)
g
g
g
is the independent variable and
a
a
a
is the dependent variable
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Mr. Hogan is getting history textbooks for his class from a school storeroom. The number of students in the class determines how many books he gets.
\newline
s
=
s =
s
=
the number of students in Mr. Hogan's class
\newline
t
=
t =
t
=
the number of history textbooks Mr. Hogan gets from the storeroom
\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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Lillian, 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 Lillian 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)
r
r
r
is the independent variable and
b
b
b
is the dependent variable
\newline
(B)
b
b
b
is the independent variable and
r
r
r
is the dependent variable
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The number of seats in a performing arts theater determines how many tickets can be sold for the local high school musical.
\newline
s
=
s =
s
=
the number of seats in the theater
\newline
t
=
t =
t
=
the number of tickets that can be sold for the performance
\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
Get tutor help
A small publishing house is taking pre-orders for a novel to be released next month. The number of copies of the novel they will print depends on the number of pre-orders they receive.
\newline
c
c
c
= the number of copies of the novel they will print
\newline
p
p
p
= the number of pre-orders
\newline
Which of the variables is independent and which is dependent?
\newline
Choices:
\newline
(A)
c
c
c
is the independent variable and
p
p
p
is the dependent variable
\newline
(B)
p
p
p
is the independent variable and
c
c
c
is the dependent variable
Get tutor help
A small publishing house is taking pre-orders for a novel to be released next month. The number of copies of the novel they will print depends on the number of pre-orders they receive.
\newline
c
c
c
= the number of copies of the novel they will print
\newline
p
p
p
= the number of pre-orders
\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
Janice is a consultant for a software company. The number of hours she works determines the amount of her annual bonus.
\newline
h
=
h =
h
=
the number of hours Janice works
\newline
b
=
b =
b
=
the amount of Janice's bonus
\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
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At a deli counter, the weight of a customer's order determines the price.
\newline
w
=
w =
w
=
the weight
\newline
p
=
p =
p
=
the price
\newline
Which of the variables is independent and which is dependent?
\newline
Choices:
\newline
(A)
w
w
w
is the independent variable and
p
p
p
is the dependent variable
\newline
(B)
p
p
p
is the independent variable and
w
w
w
is the dependent variable
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A wind farm in California produces much of its output during the summer, when the winds are fastest. The amount of power produced depends on the average wind speed.
\newline
p
=
p =
p
=
the amount of power produced
\newline
w
=
w =
w
=
the average wind speed
\newline
Which of the variables is independent and which is dependent?
\newline
Choices:
\newline
(A)
p
p
p
is the independent variable and
w
w
w
is the dependent variable
\newline
(B)
w
w
w
is the independent variable and
p
p
p
is the dependent variable
Get tutor help
Wayne, a food blogger, receives payment from an advertiser each month. The amount of money he earns depends on how many site visitors he receives each month.
\newline
m
m
m
= the amount of money Wayne earns
\newline
v
v
v
= the number of visitors Wayne receives
\newline
Which of the variables is independent and which is dependent?
\newline
Choices:
\newline
(A)
m
m
m
is the independent variable and
v
v
v
is the dependent variable
\newline
(B)
v
v
v
is the independent variable and
m
m
m
is the dependent variable
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The students in Charlie's Spanish class are planning a trip to Guatemala, during which they will stay with local host families. The more students who go on the trip, the more host families they will need.
\newline
s
=
s =
s
=
the number of students who go on the trip
\newline
f
=
f =
f
=
the number of host families they will need
\newline
Which of the variables is independent and which is dependent?
\newline
Choices:
\newline
(A)
f
f
f
is the independent variable and
s
s
s
is the dependent variable
\newline
(B)
s
s
s
is the independent variable and
f
f
f
is the dependent variable
Get tutor help
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