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Math Problems
Algebra 1
Experimental probability
An empty pool has the capacity to hold
2700
cubic feet
(
ft
3
)
2700 \text{ cubic feet } (\text{ft}^{3})
2700
cubic feet
(
ft
3
)
of water. A particular hose fills this pool with water at a rate of
25
ft
3
per minute
25\text{ft}^{3} \text{ per minute}
25
ft
3
per minute
. If the hose is placed into the empty pool and turned on, approximately what percent of the pool will be filled with water after
1
1
1
hour?
\newline
Choose
1
1
1
answer:
\newline
(A)
10
%
10\%
10%
\newline
(B)
44
%
44\%
44%
\newline
(C)
56
%
56\%
56%
\newline
(D)
93
%
93\%
93%
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A fruit stand has to decide what to charge for their produce. They decide to charge
$
5.30
\$5.30
$5.30
for
1
1
1
apple and
1
1
1
orange. They also plan to charge
$
14
\$14
$14
for
2
2
2
apples and
2
2
2
oranges. We put this information into a system of linear equations.
\newline
Can we find a unique price for an apple and an orange?
\newline
Choose
1
1
1
answer:
\newline
(A) Yes; they should charge
$
3.00
\$3.00
$3.00
for an apple and
$
2.30
\$2.30
$2.30
for an orange.
\newline
(B) Yes; they should charge
$
3.00
\$3.00
$3.00
for an apple and
$
4.00
\$4.00
$4.00
for an orange.
\newline
(C) No; the system has many solutions.
\newline
(D) No; the system has no solution.
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A fruit stand has to decide what to charge for their produce. They need
$
5
\$5
$5
for
1
1
1
apple and
1
1
1
orange. They also need
$
15
\$15
$15
for
3
3
3
apples and
3
3
3
oranges. Put this information into a system of linear equations.
\newline
Can we find a unique price for an apple and an orange?
\newline
Choose
1
1
1
answer:
\newline
(A) Yes; they should charge
$
2.00
\$2.00
$2.00
for an apple and
$
3.00
\$3.00
$3.00
for an orange.
\newline
(B) Yes; they should charge
$
1.00
\$1.00
$1.00
for an apple and
$
4.00
\$4.00
$4.00
for an orange.
\newline
(C) No; the system has many solutions.
\newline
(D) No; the system has no solution.
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The Soup Shack usually makes tomato soup with
9
9
9
tomatoes for every
12
12
12
bowls of soup. Today, they used
6
6
6
tomatoes to make
8
8
8
bowls of soup.
\newline
How does the tomato taste in today's soup compared to the usual recipe?
\newline
Choose
1
1
1
answer:
\newline
(A) Today's soup has a weaker tomato taste.
\newline
(B) Today's soup has a stronger tomato taste.
\newline
(C) Today's soup will taste the same.
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The rate of change
d
P
d
t
\frac{d P}{d t}
d
t
d
P
of the number of students who heard a rumor is modeled by a logistic differential equation. The maximum capacity of the school is
861
861
861
students. At
2
A
M
2 \mathrm{AM}
2
AM
, the number of students who heard the rumor is
213
213
213
and is increasing at a rate of
34
34
34
students per hour. Write a differential equation to describe the situation.
\newline
d
P
d
t
=
□
\frac{d P}{d t}=\square
d
t
d
P
=
□
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A hawk sees two mice on the ground in front of it, but
20
ft
20\text{ft}
20
ft
apart. The angle of depression to mouse A is
25
25
25
degrees and the angle of depression to mouse B is
35
35
35
degrees. What is the horizontal distance from mouse A to the hawk?
\newline
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Nayeli lights a
4
m
2
4m^{2}
4
m
2
space with
12
12
12
candles. Citlali lights a
10
m
2
10m^{2}
10
m
2
space with
30
30
30
of the same type of candles.
\newline
Whose space is lit brighter?
\newline
Choose
1
1
1
answer:
\newline
(A) Nayeli's area
\newline
(B) Citlali's area
\newline
(C) The spaces are equally bright.
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A fruit stand has to decide what to charge for their produce. They decide to charge
$
5.30
\$5.30
$5.30
for
1
1
1
apple and
1
1
1
orange. They also plan to charge
$
14
\$14
$14
for
2
2
2
apples and
2
2
2
oranges. We put this information into a system of linear equations.
\newline
Can we find a unique price for an apple and an orange?
\newline
Choose
1
1
1
answer:
\newline
(A) Yes; they should charge
$
3.00
\$3.00
$3.00
for an apple and
$
2.30
\$2.30
$2.30
for an orange.
\newline
(B) Yes; they should charge
$
3.00
\$3.00
$3.00
for an apple and
$
4.00
\$4.00
$4.00
for an orange.
\newline
(C) No; the system has many solutions.
\newline
(D) No; the system has no solution.
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During one decade, the price of silver decreased at a rate that was proportional to the price of silver at that time.
\newline
The price for an ounce of silver was
$
22
\$ 22
$22
initially, and it was
$
5.50
\$ 5.50
$5.50
after
7
7
7
years.
\newline
What was the price for an ounce of silver after
5
5
5
years?
\newline
Choose
1
1
1
answer:
\newline
(A)
$
8.17
\$ 8.17
$8.17
\newline
(B)
$
10.21
\$ 10.21
$10.21
\newline
(C)
$
26.30
\$ 26.30
$26.30
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March Madness Movies served
23
23
23
lemonades out of a total of
111
111
111
fountain drinks last weekend.
\newline
Based on this data, what is a reasonable estimate of the probability that the next fountain drink ordered is a lemonade?
\newline
Choose the best answer.
\newline
Choose
1
1
1
answer:
\newline
(A)
23
111
\frac{23}{111}
111
23
\newline
(B)
23
88
\frac{23}{88}
88
23
\newline
(C)
111
111
\frac{111}{111}
111
111
\newline
(D)
88
111
\frac{88}{111}
111
88
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So far,
907
907
907
of the
1223
1223
1223
voters have agreed to the new amendment.
\newline
Based on this data, what is a reasonable estimate of the probability that the next voter does not agree to the new amendment?
\newline
Choose
1
1
1
answer:
\newline
(A)
316
1223
\frac{316}{1223}
1223
316
\newline
(B)
907
1223
\frac{907}{1223}
1223
907
\newline
(C)
1223
2130
\frac{1223}{2130}
2130
1223
\newline
(D)
316
907
\frac{316}{907}
907
316
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The Cinemania theater showed
108
108
108
different movies last year. Of those,
15
15
15
movies were action movies.
\newline
Based on this data, what is a reasonable estimate of the probability that the next movie is an action movie?
\newline
Choose
1
1
1
answer:
\newline
(A)
108
93
\frac{108}{93}
93
108
\newline
(B)
93
108
\frac{93}{108}
108
93
\newline
(C)
15
108
\frac{\mathbf{1 5}}{108}
108
15
\newline
(D)
15
93
\frac{15}{93}
93
15
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Justin, Cam, and Ben are playing a board game where exactly one player will win. Ben estimates that Justin has a
20
%
20 \%
20%
chance of winning each game and that Cam has a
50
%
50 \%
50%
chance of winning each game.
\newline
What is the probability that Ben will win the board game?
\newline
Choose
1
1
1
answer:
\newline
(A)
20
%
\mathbf{2 0 \%}
20%
\newline
(B)
30
%
30 \%
30%
\newline
(C)
50
%
50 \%
50%
\newline
(D)
70
%
\mathbf{7 0 \%}
70%
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After Cynthia microwaves her bowl of morning porridge, it is either too cold, just right, or too hot. She estimates that there is a
35
%
35 \%
35%
chance that it will be too cold and a
50
%
50 \%
50%
chance that it will be too hot.
\newline
What is the probability that Cynthia's morning porridge will be just right?
\newline
Choose
1
1
1
answer:
\newline
(A)
10
%
10 \%
10%
\newline
(B)
15
%
\mathbf{1 5 \%}
15%
\newline
(C)
25
%
25 \%
25%
\newline
(D)
85
%
85 \%
85%
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Khalil is
3
3
3
years older than his cousin Noah. Khalil wants to write an equation for his own age
(
k
)
(k)
(
k
)
in terms of Noah's age
(
n
)
(n)
(
n
)
.
\newline
How should Khalil write his equation?
\newline
Choose
1
1
1
answer:
\newline
(A)
k
−
n
=
3
k-n=3
k
−
n
=
3
\newline
(B)
k
−
3
=
n
k-3=n
k
−
3
=
n
\newline
(C)
n
+
3
=
k
n+3=k
n
+
3
=
k
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What is the least common multiple of
12
12
12
and
9
9
9
?
\newline
lcm
(
12
,
9
)
=
\operatorname{lcm}(12,9)=
lcm
(
12
,
9
)
=
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What is the least common multiple of
12
12
12
and
16
16
16
?
\newline
lcm
(
12
,
16
)
=
\operatorname{lcm}(12,16)=
lcm
(
12
,
16
)
=
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What is the least common multiple of
8
8
8
and
10
10
10
?
\newline
lcm
(
8
,
10
)
=
\operatorname{lcm}(8,10)=
lcm
(
8
,
10
)
=
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What is the least common multiple of
4
4
4
and
10
10
10
?
\newline
lcm
(
4
,
10
)
=
\operatorname{lcm}(4,10)=
lcm
(
4
,
10
)
=
Get tutor help
What is the least common multiple of
4
4
4
and
8
8
8
?
\newline
lcm
(
4
,
8
)
=
\operatorname{lcm}(4,8)=
lcm
(
4
,
8
)
=
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A box of fruit candy contains
50
50
50
candy pieces in five different colors: red, orange, yellow, green, and purple. Willy opened the box and found that
22
%
22 \%
22%
of the candy pieces are purple. If the box Willy opened is representative of that particular brand of fruit candy, which of the following best estimates the total number of non-purple candy pieces in
36
36
36
boxes of the same candy?
\newline
Choose
1
1
1
answer:
\newline
(A)
400
400
400
\newline
(B)
1
1
1
,
100
100
100
\newline
(C)
1
1
1
,
400
400
400
\newline
(D)
1
1
1
,
800
800
800
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In a random sample of attendees at a pop culture convention,
1
3
\frac{1}{3}
3
1
of the attendees are in costume. At this rate, approximately how many of the
6
6
6
,
000
000
000
convention attendees are in costume?
\newline
Choose
1
1
1
answer:
\newline
(A)
1
1
1
,
000
000
000
\newline
(B)
2
2
2
,
000
000
000
\newline
(C)
3
3
3
,
000
000
000
\newline
(D)
6
6
6
,
000
000
000
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According to market research, approximately
2
%
2 \%
2%
of concertgoers buy merchandise at concerts. At this rate, approximately how many concertgoers at a
7
7
7
,
000
000
000
-people concert are expected to buy merchandise there?
\newline
Choose
1
1
1
answer:
\newline
(A)
140
\mathbf{1 4 0}
140
\newline
(B)
200
200
200
\newline
(C)
350
350
350
\newline
(D)
1
1
1
,
400
400
400
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In a random sample of a particular model of drone,
2.5
%
2.5 \%
2.5%
of the drones have a manufacturing defect. At this rate, how many of
4
4
4
,
000
000
000
drones of the same model will have a manufacturing defect?
\newline
Choose
1
1
1
answer:
\newline
(A)
2
2
2
.
5
5
5
\newline
(B)
25
25
25
\newline
(C)
100
100
100
\newline
(D)
1
1
1
,
000
000
000
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Timpony School District surveyed a random sample of
60
60
60
middle school students about the amount of time they watch TV. Of the students surveyed,
14
14
14
average watching more than
4
4
4
hours of TV each day. There are
1143
1143
1143
middle school students in the Timpony School District. Based on the data, what is the most reasonable estimate for the number of Timpony School District middle school students who average watching more than
4
4
4
hours of TV each day?
\newline
Choose
1
1
1
answer:
\newline
(A)
14
14
14
\newline
(B)
76
76
76
\newline
(C)
267
\mathbf{2 6 7}
267
\newline
(D)
876
876
876
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Bernard randomly selected
10
%
10 \%
10%
of St. Francis citizens and asked them about their favorite coffee shop. Of the citizens surveyed,
7
7
7
said that Energize was their favorite coffee shop. Based on the data, what is the most reasonable estimate of the number of St. Francis citizens whose favorite coffee shop is Energize?
\newline
Choose
1
1
1
answer:
\newline
(A)
7
7
7
\newline
(B)
10
10
10
\newline
(C)
63
63
63
\newline
(D)
70
70
70
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Timpony School District surveyed a random sample of
60
60
60
middle school students about the amount of time they watch TV. Of the students surveyed,
14
14
14
average watching more than
4
4
4
hours of TV each day. There are
1143
1143
1143
middle school students in the Timpony School District. Based on the data, what is the most reasonable estimate for the number of Timpony School District middle school students who average watching more than
4
4
4
hours of TV each day?
\newline
Choose
1
1
1
answer:
\newline
(A)
14
14
14
\newline
(B)
76
76
76
\newline
(C)
267
\mathbf{2 6 7}
267
\newline
(D)
876
876
876
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Two airplanes, which start
3
3
3
,
300
300
300
miles apart, fly toward each other. The two planes fly at a constant speed, but their speeds differ by
80
80
80
miles per hour (mph). After
5
5
5
hours, the planes pass each other. What is the speed of the faster plane?
\newline
Choose
1
1
1
answer:
\newline
(A)
290
m
p
h
290 \mathrm{mph}
290
mph
\newline
(B)
338
m
p
h
338 \mathrm{mph}
338
mph
\newline
(C)
370
m
p
h
370 \mathrm{mph}
370
mph
\newline
(D)
450
m
p
h
450 \mathrm{mph}
450
mph
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