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Math Problems
Algebra 1
Interpret parts of quadratic expressions: word problems
F
=
1.35
P
+
1.50
A
F=1.35 P+1.50 A
F
=
1.35
P
+
1.50
A
\newline
Milo wishes to purchase a bouquet consisting of
P
P
P
peonies and
A
A
A
alstroemeria. If
F
F
F
is the total cost, in dollars, of a bouquet of these two types of flowers, what is the meaning of
1
1
1
.
50
50
50
in the equation?
\newline
Choose
1
1
1
answer:
\newline
(A)
$
1.50
\$ 1.50
$1.50
is the cost of one peony.
\newline
(B)
$
1.50
\$ 1.50
$1.50
divided by
A
A
A
is the cost of one alstroemeria.
\newline
(C)
$
1.50
\$ 1.50
$1.50
is the cost of one alstroemeria.
\newline
(D)
$
1.50
\$ 1.50
$1.50
times
A
A
A
is the cost of one alstroemeria.
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w
=
500
−
6.2
t
w=500-6.2 t
w
=
500
−
6.2
t
\newline
A rain barrel is being used during the dry season to water a garden with previously collected rainwater. With a hose connected to its outlet, the equation approximates amount of rainwater in the barrel,
w
w
w
, in liters, after
t
t
t
minutes of watering. What is the meaning of
6.2
t
6.2 t
6.2
t
in this equation?
\newline
Choose
1
1
1
answer:
\newline
(A) It takes
6.2
t
6.2 t
6.2
t
minutes to empty the barrel.
\newline
(B)
6.2
t
6.2 t
6.2
t
minutes are needed to fill the barrel.
\newline
(C)
6.2
t
6.2 t
6.2
t
liters of rainwater is emptied after
t
t
t
minutes.
\newline
(D) There are
6.2
t
6.2 t
6.2
t
liters in the barrel when filled for
t
t
t
minutes.
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P
=
47.4
(
G
−
174.5
)
P=47.4(G-174.5)
P
=
47.4
(
G
−
174.5
)
\newline
The profit,
P
P
P
, in dollars, to an amusement park serving
G
G
G
guests over one day is given by the equation. What is the minimum number of guests that need to be served in order to make a positive profit?
\newline
Choose
1
1
1
answer:
\newline
(A)
48
48
48
\newline
(B)
174
\mathbf{1 7 4}
174
\newline
(C)
175
\mathbf{1 7 5}
175
\newline
(D)
8
8
8
,
272
272
272
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h
=
11.2
−
0.125
d
h=11.2-0.125 d
h
=
11.2
−
0.125
d
\newline
The ceiling height,
h
h
h
, in feet, for a particular room in a house a distance of
d
d
d
feet from the west wall is given by the equation. In order for the ceiling height to decrease by
1
1
1
foot, how much does the distance from the west wall change in feet?
\newline
Choose
1
1
1
answer:
\newline
(A)
0
0
0
.
125
125
125
\newline
(B)
8
8
8
\newline
(C)
11.2
\mathbf{1 1 . 2}
11.2
\newline
(D)
89
89
89
.
6
6
6
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v
=
14.2
(
12.5
−
s
)
v=14.2(12.5-s)
v
=
14.2
(
12.5
−
s
)
\newline
The velocity,
v
v
v
, in meters per second, of an airplane
s
s
s
seconds after landing is given by the equation. What is the best interpretation of
14.2
14.2
14.2
as shown in the equation?
\newline
Choose
1
1
1
answer:
\newline
(A) The plane takes
14.2
14.2
14.2
seconds to stop.
\newline
(B) The position of the plane changes
14.2
14.2
14.2
meters every second.
\newline
(C) The velocity changes by
14.2
14.2
14.2
meters per second every second.
\newline
(D) The velocity of the plane just as it lands is
14.2
14.2
14.2
meters per second.
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Katlin wants to make
64
64
64
ounces of chocolate milk that is
12
%
12 \%
12%
chocolate. She has light chocolate milk that is
5
%
5 \%
5%
chocolate and heavy chocolate milk that is
21
%
21 \%
21%
chocolate. How many ounces of light chocolate milk and heavy chocolate milk does Katlin need to combine?
\newline
Choose
1
1
1
answer:
\newline
(A)
24
24
24
light and
40
40
40
heavy
\newline
(B)
28
28
28
light and
36
36
36
heavy
\newline
(C)
36
36
36
light and
28
28
28
heavy
\newline
(D)
40
40
40
light and
24
24
24
heavy
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Anthropologists can predict the height of a human based on the length of their femur. The relationship between the human's height in centimeters,
H
H
H
, and length of the femur in centimeters,
f
f
f
, can be modeled by the given equation.
\newline
H
=
2.72
f
+
42.12
H=2.72 f+42.12
H
=
2.72
f
+
42.12
\newline
One anthropologist found the femurs of two different people. One femur measured
22
22
22
centimeters and the other femur measured
23
23
23
centimeters. What is the difference in their heights?
\newline
Choose
1
1
1
answer:
\newline
(A)
1
1
1
centimeter
\newline
(B)
2
2
2
.
72
72
72
centimeters
\newline
(C)
27
27
27
.
2
2
2
centimeters
\newline
(D)
42
42
42
.
12
12
12
centimeters
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C
=
40
(
5
−
s
)
C=40(5-s)
C
=
40
(
5
−
s
)
\newline
After Hiro's family photoshoot, the photographer sells the printed photos by the sheet. Hiro has a
$
200
\$ 200
$200
credit from a prior session, and the equation gives the total credit left,
C
C
C
, in dollars, if he buys
s
s
s
sheets. How many sheets can Hiro purchase with his credit?
\newline
Choose
1
1
1
answer:
\newline
(A)
5
5
5
sheets
\newline
(B)
8
8
8
sheets
\newline
(C)
40
40
40
sheets
\newline
(D)
200
200
200
sheets
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m
=
14
(
11
−
t
)
m=14(11-t)
m
=
14
(
11
−
t
)
\newline
The mass,
m
m
m
, in grams, of a piece of marble after being in a rock tumbler for
t
t
t
minutes is given by the equation. After how many minutes in the rock tumbler does the piece of marble disintegrate by reaching a mass of
0
0
0
grams?
\newline
Choose
1
1
1
answer:
\newline
(A)
3
3
3
\newline
(B)
11
11
11
\newline
(C)
14
14
14
\newline
(D)
154
\mathbf{1 5 4}
154
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B
=
11.5
(
132
−
n
)
B=11.5(132-n)
B
=
11.5
(
132
−
n
)
\newline
The monthly electricity bill,
B
B
B
, in dollars, for a museum using
n
n
n
solar panels is given by the equation. What is the best interpretation of
132
132
132
in the equation?
\newline
Choose
1
1
1
answer:
\newline
(A) The museum is currently using
132
132
132
solar panels.
\newline
(B) The monthly electric bill is
132
132
132
dollars without solar panels.
\newline
(C) The electric bill is
0
0
0
dollars when the museum uses
132
132
132
solar panels.
\newline
(D) The electric bill decreases by
132
132
132
dollars for each additional solar panel.
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A tennis club is organizing group lessons. The club supplies each player with
40
40
40
new balls, which costs the club
$
1
\$ 1
$1
each ball. Each player pays
$
300
\$ 300
$300
for the lessons. The club must pay each instructor
$
1
,
000
\$ 1,000
$1
,
000
for conducting the lessons, and there must be at least
1
1
1
instructor for every
6
6
6
players. Which amount of players and instructors meets these requirements and still gives the club a net profit?
\newline
Choose
1
1
1
answer:
\newline
(A)
6
6
6
players and
2
2
2
instructors
\newline
(B)
10
10
10
players and
3
3
3
instructors
\newline
(C)
13
13
13
players and
2
2
2
instructors
\newline
(D)
16
16
16
players and
3
3
3
instructors
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A memory chip is being designed to hold a number of transistors and heat sinks. The transistors hold memory while the heat sinks cool the chip. There must be at least one heat sink for every
2
2
2
,
000
000
000
transistors to prevent overheating. Also, each transistor has an area of
2.0
×
1
0
−
10
m
m
2
2.0 \times 10^{-10} \mathrm{~mm}^{2}
2.0
×
1
0
−
10
mm
2
(square millimeters), each heat sink has an area of
3.6
×
1
0
−
6
m
m
2
3.6 \times 10^{-6} \mathrm{~mm}^{2}
3.6
×
1
0
−
6
mm
2
, and the total area of transistors and heat sinks must be at most
2
m
m
2
2 \mathrm{~mm}^{2}
2
mm
2
. What is the approximate maximum number of transistors that the chip can hold according to this design?
\newline
Choose
1
1
1
answer:
\newline
(A)
2.78
×
1
0
2
2.78 \times 10^{2}
2.78
×
1
0
2
\newline
(B)
5.56
×
1
0
5
5.56 \times 10^{5}
5.56
×
1
0
5
\newline
(C)
1.0
×
1
0
9
1.0 \times 10^{9}
1.0
×
1
0
9
\newline
(D)
1.0
×
1
0
10
1.0 \times 10^{10}
1.0
×
1
0
10
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A business analyst is deciding the amount of time allotted to each employee for meetings and training. He wants the sum of meeting and training time to be no more than
16
16
16
hours per month. Also, there should be at least one training hour for every two meeting hours. Finally, there should be at least
2
2
2
meeting hours per month to discuss shortterm goals. What is the difference between the maximum and minimum number of monthly training hours that could be allotted to an employee?
\newline
Choose
1
1
1
answer:
\newline
(A)
10
10
10
hours
\newline
(B)
13
13
13
hours
\newline
(C)
14
14
14
hours
\newline
(D)
16
16
16
hours
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Rodolfo wants to determine how best to benefit from his weekly workouts. His goal is to burn at least
3300
3300
3300
calories per week from jogging and playing soccer. He can burn
700
700
700
calories each hour he spends jogging and
600
600
600
calories each hour he spends playing soccer. If Rodolfo's schedule permits him to spend at most
3
3
3
hours per week playing soccer and at most
5
5
5
total hours per week exercising, which of the following exercise schedules will allow him to meet his weekly goal?
\newline
Choose
1
1
1
answer:
\newline
(A)
4
4
4
hours playing soccer and
1
1
1
hour jogging
\newline
(B)
1
1
1
hour playing soccer and
5
5
5
hours jogging
\newline
(C)
3
3
3
hours playing soccer and
2
2
2
hours jogging
\newline
(D)
2
2
2
hours playing soccer and
3
3
3
hours jogging
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17
T
+
6
C
≤
150
34
T
+
27
C
≤
330
\begin{array}{r} 17 T+6 C \leq 150 \\ 34 T+27 C \leq 330 \end{array}
17
T
+
6
C
≤
150
34
T
+
27
C
≤
330
\newline
Fleur wants to make tables and chairs. Each chair or table is made with the same number of wooden boards and nails. She has a total of
150
150
150
wooden boards and
330
330
330
nails. The system of inequalities shown represents the number of tables
(
T
)
(T)
(
T
)
and chairs
(
C
)
(C)
(
C
)
she can make in this situation. Does Fleur have enough boards and nails to make
3
3
3
tables and
9
9
9
chairs?
\newline
Choose
1
1
1
answer:
\newline
(A) Fleur has enough boards and nails.
\newline
(B) Fleur has enough boards but not enough nails.
\newline
(C) Fleur has enough nails but not enough boards.
\newline
(D) Fleur has neither enough boards nor enough nails.
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Some zoo monkeys are on a diet of fruit and nuts. Fruit has about
13
13
13
.
3
3
3
grams
(
g
)
(\mathrm{g})
(
g
)
of sugar per cup and
1.36
g
1.36 \mathrm{~g}
1.36
g
of protein per cup. Nuts have about
4.04
g
4.04 \mathrm{~g}
4.04
g
of sugar per cup and
15.56
g
15.56 \mathrm{~g}
15.56
g
of protein per cup. Each monkey must get between
70
g
70 \mathrm{~g}
70
g
and
90
g
90 \mathrm{~g}
90
g
of sugar per day and at least
85
g
85 \mathrm{~g}
85
g
of protein per day. Which of the following daily diets fits the monkeys' needs?
\newline
Choose
1
1
1
answer:
\newline
(A)
0
0
0
cups of fruit and
16
16
16
cups of nuts
\newline
(B)
4
4
4
cups of fruit and
8
8
8
cups of nuts
\newline
(C)
8
8
8
cups of fruit and
4
4
4
cups of nuts
\newline
(D)
16
16
16
cups of fruit and
0
0
0
cups of nuts
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At the beginning of January
2002
2002
2002
, the price of ground beef was
$
1.70
\$ 1.70
$1.70
per pound and the price of tuna fish was
$
2.20
\$ 2.20
$2.20
per pound. For the following
15
15
15
months, the price of ground beef increased at the rate of
$
0.03
\$ 0.03
$0.03
per month and the price of tuna fish decreased at
$
0.02
\$ 0.02
$0.02
per month. In approximately how many months after the beginning of January
2002
2002
2002
was the price of ground beef and tuna fish the same, and what was the price?
\newline
Choose
1
1
1
answer:
\newline
(A)
7
7
7
.
5
5
5
months and
$
1.90
\$ 1.90
$1.90
\newline
(B)
7
7
7
.
5
5
5
months and
$
2.00
\$ 2.00
$2.00
\newline
(C)
10
\mathbf{1 0}
10
months and
$
1.90
\$ 1.90
$1.90
\newline
(D)
10
10
10
months and
$
2.00
\$ 2.00
$2.00
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The equations
x
+
y
=
3
x+y=3
x
+
y
=
3
and
−
5
x
−
5
y
=
−
15
-5 x-5 y=-15
−
5
x
−
5
y
=
−
15
are graphed in the
x
y
x y
x
y
-plane. Which of the following must be true of the graphs of the two equations?
\newline
Choose
1
1
1
answer:
\newline
(A) The slope of the graph of
x
+
y
=
3
x+y=3
x
+
y
=
3
is
1
1
1
and the slope of the graph of
−
5
x
−
5
y
=
−
15
-5 x-5 y=-15
−
5
x
−
5
y
=
−
15
is
−
1
-1
−
1
.
\newline
(B) The graphs of the two equations are perpendicular lines.
\newline
(C) The
y
y
y
-intercept of the graph of
−
5
x
−
5
y
=
−
15
-5 x-5 y=-15
−
5
x
−
5
y
=
−
15
is
−
15
-15
−
15
.
\newline
(D) The graphs of the two equations are the same line.
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Anouk is an engineer planning sound and lighting for a free concert in the park. The concert was advertised with a promise to use no more than
108
108
108
kilowatts
(
k
W
)
(\mathrm{kW})
(
kW
)
of power. It was determined that the main contributors to power usage, speakers and floodlights, use
1.8
k
W
1.8 \mathrm{~kW}
1.8
kW
and
2.2
k
W
2.2 \mathrm{~kW}
2.2
kW
, respectively. Anouk also must keep within her budget of
$
3
,
300
\$ 3,300
$3
,
300
. The rental company is charging
$
75
\$ 75
$75
for each speaker and
$
42
\$ 42
$42
for each floodlight. Which of the following combinations meets Anouk's requirements?
\newline
Choose
1
1
1
answer:
\newline
(A)
40
40
40
speakers and
30
30
30
floodlights
\newline
(B)
12
12
12
speakers and
54
54
54
floodlights
\newline
(C)
26
26
26
speakers and
13
13
13
floodlights
\newline
(D)
38
38
38
speakers and
22
22
22
floodlights
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Alek went for a walk.
\newline
D
(
t
)
D(t)
D
(
t
)
models the distance Alek walked (in kilometers) after
t
t
t
hours.
\newline
What does the statement
D
(
0.5
)
<
D
(
1
)
−
D
(
0.5
)
D(0.5) < D(1) - D(0.5)
D
(
0.5
)
<
D
(
1
)
−
D
(
0.5
)
mean?
\newline
Choose
1
1
1
answer:
\newline
(A) The distance Alek has walked after walking for an hour is greater than the distance he has walked after half an hour.
\newline
(B) The time it took Alek to walk the first half kilometer is shorter than the time it took him to walk the following half kilometer.
\newline
(C) The distance Alek walked during the first half hour is shorter than the distance he walked during the following half hour.
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Copacabana beach in Rio de Janeiro is one of the most popular beaches in the world.
\newline
P
(
t
)
P(t)
P
(
t
)
models the number of people at the beach,
t
t
t
hours past midnight on a specific day.
\newline
What does the statement
P
(
10
)
=
N
P(10)=N
P
(
10
)
=
N
mean?
\newline
Choose
1
1
1
answer:
\newline
(A) There were
10
10
10
people at the beach at
N
N
N
hours past midnight.
\newline
(B) There were
N
N
N
people at the beach at
10
:
00
10:00
10
:
00
a.m.
\newline
(C) There was an equal number of people at the beach at
10
:
00
10:00
10
:
00
a.m. and at
N
N
N
hours past midnight.
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Jayce is a taxi driver.
\newline
M
(
n
)
M(n)
M
(
n
)
models Jayce's fee (in dollars) for his
n
th
n^{\text{th}}
n
th
drive on a certain day.
\newline
What does the statement
M
(
10
)
=
K
M(10)=K
M
(
10
)
=
K
mean?
\newline
Choose
1
1
1
answer:
\newline
(A) Jayce's fees for his
K
th
K^{\text{th}}
K
th
drive and his
1
0
th
10^{\text{th}}
1
0
th
drive are equal.
\newline
(B) Jayce's fee for his
1
0
th
10^{\text{th}}
1
0
th
drive is equal to
K
K
K
dollars.
\newline
(C) Jayce's fee for his
K
th
K^{\text{th}}
K
th
drive is equal to
$
10
\$10
$10
.
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Kaori is taking a free-throw.
\newline
H
(
d
)
H(d)
H
(
d
)
models the basketball's height (in meters) at a horizontal distance of
d
d
d
meters from Kaori.
\newline
What does the statement
H
(
R
)
=
4
H(R) = 4
H
(
R
)
=
4
mean?
\newline
Choose
1
1
1
answer:
\newline
(A) At a horizontal distance of
R
R
R
meters from Kaori, the ball's height was equal to
4
4
4
meters.
\newline
(B) At a horizontal distance of
4
4
4
meters from Kaori, the ball's height was equal to
R
R
R
meters.
\newline
(C) The ball was at the same height at the horizontal distances of
4
4
4
meters and
R
R
R
meters.
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Copacabana beach in Rio de Janeiro is one of the most popular beaches in the world.
\newline
P
(
t
)
P(t)
P
(
t
)
models the number of people at the beach,
t
t
t
hours past midnight on a specific day.
\newline
What does the statement
P
(
10
)
=
N
P(10)=N
P
(
10
)
=
N
mean?
\newline
Choose
1
1
1
answer:
\newline
(A) There were
N
N
N
people at the beach at
10
10
10
:
00
00
00
a.m.
\newline
(B) There were
10
10
10
people at the beach at
N
N
N
hours past midnight.
\newline
(C) There was an equal number of people at the beach at
10
10
10
:
00
00
00
a.m. and at
N
N
N
hours past midnight.
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Baby Amelia's parents measure her height every month.
\newline
H
(
t
)
H(t)
H
(
t
)
models Amelia's height (in centimeters) when she was
t
t
t
months old.
\newline
What does the statement
H
(
30
)
=
H
(
25
)
+
5
H(30) = H(25) + 5
H
(
30
)
=
H
(
25
)
+
5
mean?
\newline
Choose
1
1
1
answer:
\newline
(A) It took Amelia
5
5
5
months to grow from a height of
25
25
25
centimeters to a height of
30
30
30
centimeters.
\newline
(B) When Amelia was
30
30
30
months old, she was
5
5
5
centimeters taller than when she was
25
25
25
months old.
\newline
(C) The sum of Amelia's heights at
5
5
5
months and
25
25
25
months old is equal to her height at
30
30
30
months old.
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Baby Kana's parents measure her height every month.
\newline
H
(
t
)
H(t)
H
(
t
)
models Kana's height (in centimeters) when she was
t
t
t
months old.
\newline
What does the statement
H
(
160
)
=
150
H(160)=150
H
(
160
)
=
150
mean?
\newline
Choose
1
1
1
answer:
\newline
(A) When Kana was
150
150
150
months old, her height was equal to
160
160
160
centimeters.
\newline
(B) When Kana was
160
160
160
months old, her height was equal to
150
150
150
centimeters.
\newline
(C) Kana had the same height at
150
150
150
months old and at
160
160
160
months old.
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Alek went for a walk.
\newline
D
(
t
)
D(t)
D
(
t
)
models the distance Alek walked (in kilometers) after
t
t
t
hours.
\newline
What does the statement
D
(
0.5
)
<
D
(
1
)
−
D
(
0.5
)
D(0.5) < D(1)-D(0.5)
D
(
0.5
)
<
D
(
1
)
−
D
(
0.5
)
mean?
\newline
Choose
1
1
1
answer:
\newline
(A) The time it took Alek to walk the first half kilometer is shorter than the time it took him to walk the following half kilometer.
\newline
(B) The distance Alek has walked after walking for an hour is greater than the distance he has walked after half an hour.
\newline
(C) The distance Alek walked during the first half hour is shorter than the distance he walked during the following half hour.
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Baby Amelia's parents measure her height every month.
\newline
H
(
t
)
H(t)
H
(
t
)
models Amelia's height (in centimeters) when she was
t
t
t
months old.
\newline
What does the statement
H
(
30
)
=
H
(
25
)
+
5
H(30) = H(25) + 5
H
(
30
)
=
H
(
25
)
+
5
mean?
\newline
Choose
1
1
1
answer:
\newline
(A) It took Amelia
5
5
5
months to grow from a height of
25
25
25
centimeters to a height of
30
30
30
centimeters.
\newline
(B) The sum of Amelia's heights at
5
5
5
months and
25
25
25
months old is equal to her height at
30
30
30
months old.
\newline
(C) When Amelia was
30
30
30
months old, she was
5
5
5
centimeters taller than when she was
25
25
25
months old.
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Kaori is taking a free-throw.
\newline
H
(
d
)
H(d)
H
(
d
)
models the basketball's height (in meters) at a horizontal distance of
d
d
d
meters from Kaori.
\newline
What does the statement
H
(
R
)
=
4
H(R) = 4
H
(
R
)
=
4
mean?
\newline
Choose
1
1
1
answer:
\newline
A
A
A
The ball was at the same height at the horizontal distances of
4
4
4
meters and
R
R
R
meters.
\newline
B
B
B
At a horizontal distance of
R
R
R
meters from Kaori, the ball's height was equal to
4
4
4
meters.
\newline
C
C
C
At a horizontal distance of
4
4
4
meters from Kaori, the ball's height was equal to
R
R
R
meters.
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Jayce is a taxi driver.
\newline
M
(
n
)
M(n)
M
(
n
)
models Jayce's fee (in dollars) for his
n
th
n^{\text{th}}
n
th
drive on a certain day.
\newline
What does the statement
M
(
10
)
=
K
M(10)=K
M
(
10
)
=
K
mean?
\newline
Choose
1
1
1
answer:
\newline
(A) Jayce's fee for his
K
th
K^{\text{th}}
K
th
drive is equal to
$
10
\$10
$10
.
\newline
(B) Jayce's fees for his
K
th
K^{\text{th}}
K
th
drive and his
1
0
th
10^{\text{th}}
1
0
th
drive are equal.
\newline
(C) Jayce's fee for his
1
0
th
10^{\text{th}}
1
0
th
drive is equal to
K
K
K
dollars.
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Tessa's class had a math exam where the grades were between
0
0
0
and
10
10
10
.
\newline
N
(
g
)
N(g)
N
(
g
)
models the number of students whose grade on the exam was
g
g
g
.
\newline
What does the statement
\newline
N
(
8
)
>
2
⋅
N
(
5
)
N(8) > 2 \cdot N(5)
N
(
8
)
>
2
⋅
N
(
5
)
mean?
\newline
Choose
1
1
1
answer:
\newline
(A) The number of students whose grade was higher than
5
5
5
is greater than the number of students whose grade was
5
5
5
or lower.
\newline
(B) The number of students whose grade was
8
8
8
is more than twice the number of students whose grade was
5
5
5
.
\newline
(C) There are
8
8
8
students whose grade was higher than twice the grade of another group of
5
5
5
students.
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