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Math Problems
Algebra 1
Experimental probability
Nate is birdwatching at the coast. He has seen
2
2
2
vultures out of
12
12
12
total birds. What is the experimental probability that the next bird Nate sees will be a vulture? Simplify your answer and write it as a fraction or whole number.
\newline
P
(
vulture
)
=
_
_
P(\text{vulture}) = \_\_
P
(
vulture
)
=
__
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Celine surveyed
14
14
14
students at her school about their favorite professional sports. Of the students surveyed,
6
6
6
said tennis was their favorite sport. What is the experimental probability that the next student Celine talks to will pick tennis? Simplify your answer and write it as a fraction or whole number.
\newline
P
(
tennis
)
=
_
_
P(\text{tennis}) = \_\_
P
(
tennis
)
=
__
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Boats from all along the Atlantic coast dock at a busy marina. Of the first
13
13
13
boats to dock at the marina one day,
5
5
5
were from North Carolina. What is the experimental probability that the next boat to dock will be from North Carolina? Simplify your answer and write it as a fraction or whole number.
\newline
P
(
N
o
r
t
h
C
a
r
o
l
i
n
a
)
=
P(North Carolina) =
P
(
N
or
t
h
C
a
ro
l
ina
)
=
____
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From a sample tray,
3
3
3
of the last
9
9
9
cake samples chosen were chocolate. What is the experimental probability that the next piece of cake taken will be chocolate? Simplify your answer and write it as a fraction or whole number.
\newline
P
(
chocolate
)
=
_
_
_
P(\text{chocolate}) = \_\_\_
P
(
chocolate
)
=
___
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A white-and-green spinner landed on white on
10
10
10
out of
14
14
14
spins. What is the experimental probability that the next spin will land on white? Simplify your answer and write it as a fraction or whole number.
\newline
P
(
white
)
=
_
_
_
P(\text{white}) = \_\_\_
P
(
white
)
=
___
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There are
8
8
8
children in Sophie's preschool class. During free time yesterday,
1
1
1
of them chose to read books. What is the experimental probability that a randomly selected preschooler would choose to read books today? Simplify your answer and write it as a fraction or whole number.
\newline
P
(
read books
)
=
_
_
_
P(\text{read books}) = \_\_\_
P
(
read books
)
=
___
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Of the last
20
20
20
trains to arrive at Danville Station,
15
15
15
were on time. What is the experimental probability that the next train to arrive will be on time? Simplify your answer and write it as a fraction or whole number.
\newline
P
(
on time
)
=
_
_
P(\text{on time}) = \_\_
P
(
on time
)
=
__
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Jeanette's Pie Shop recently sold
14
14
14
pies, of which
4
4
4
were blackberry pies. What is the experimental probability that the next pie sold will be a blackberry pie? Simplify your answer and write it as a fraction or whole number.
\newline
P
(
blackberry pie
)
=
_
_
_
P(\text{blackberry pie}) = \_\_\_
P
(
blackberry pie
)
=
___
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Restaurants often slip takeout menus under Troy's apartment door. So far, Troy has collected
20
20
20
menus, including
6
6
6
for Mediterranean food. What is the experimental probability that the next menu slipped under Troy's door will be from a Mediterranean restaurant? Simplify your answer and write it as a fraction or whole number.
\newline
P
(
Mediterranean
)
=
_
_
P(\text{Mediterranean}) = \_\_
P
(
Mediterranean
)
=
__
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Restaurants often slip takeout menus under Tim's apartment door. So far, Tim has collected
5
5
5
menus for Italian food and
10
10
10
other menus. What is the experimental probability that the next menu slipped under Tim's door will be from an Italian restaurant? Simplify your answer and write it as a fraction or whole number.
\newline
P
(
Italian
)
=
_
_
P(\text{Italian}) = \_\_
P
(
Italian
)
=
__
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At Downtown Pizza,
4
4
4
of the last
6
6
6
pizzas sold had pepperoni. What is the experimental probability that the next pizza sold will have pepperoni? Simplify your answer and write it as a fraction or whole number.
\newline
P
(
pepperoni
)
=
_
_
_
P(\text{pepperoni}) = \_\_\_
P
(
pepperoni
)
=
___
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A university class has had
9
9
9
undergraduate students enroll so far, as well as
9
9
9
other students. What is the experimental probability that the next student to enroll will be an undergraduate student? Simplify your answer and write it as a fraction or whole number.
\newline
P
(
undergraduate
)
=
_
_
_
P(\text{undergraduate}) = \_\_\_
P
(
undergraduate
)
=
___
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Trevor gets
10
10
10
heads when flipping a weighted coin
18
18
18
times. What is the experimental probability that the next flip will come up heads? Simplify your answer and write it as a fraction or whole number.
\newline
P
(
heads
)
=
_
_
_
P(\text{heads}) = \_\_\_
P
(
heads
)
=
___
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Carl is planning out his route for an upcoming race. He uses negative numbers to represent points before the finish line and positive numbers to represent points past the finish line.
\newline
On Carl's map, the last water station is at
−
27
-27
−
27
meters, and his family is watching him at
9
9
9
meters.
\newline
What does
0
0
0
meters represent?
\newline
Choose
1
1
1
answer:
\newline
(A) The finish line
\newline
(B) Carl's family
\newline
(C) The last water station
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Gabe is mapping out important family events. He uses negative numbers to represent time before he was born and positive numbers to represent time after he was born. For example, Gabe's mom was given a special coin in year
−
20
-20
−
20
, and Gabe's sister was born in year
7
7
7
.
\newline
What does year
0
0
0
represent?
\newline
Choose
1
1
1
answer:
\newline
(A) The year Gabe's sister was born
\newline
(B) The year Gabe's mom was given a special coin
\newline
(C) The year Gabe was born
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There is a
2
%
2 \%
2%
probability that a selected life insurance application contains an error. An auditor randomly selects
50
50
50
applications. Using the Poisson approximation to the Binomial, calculate the probability that
90
%
90 \%
90%
or less of the applications are error-free.
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Solve the following equation for
a
a
a
. Be sure to take into account whether a letter is capitalized or not.
\newline
D
a
+
g
a
=
4
b
3
D a+g a=4 b^{3}
D
a
+
g
a
=
4
b
3
\newline
Answer:
a
=
a=
a
=
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Solve the following equation for
A
A
A
. Be sure to take into account whether a letter is capitalized or not.
\newline
b
=
d
A
+
f
A
b=d A+f A
b
=
d
A
+
f
A
\newline
Answer:
A
=
A=
A
=
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Solve the following equation for
A
A
A
. Be sure to take into account whether a letter is capitalized or not.
\newline
2
b
=
5
A
+
h
2
A
2 b=5 A+h^{2} A
2
b
=
5
A
+
h
2
A
\newline
Answer:
A
=
A=
A
=
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Solve the following equation for
a
a
a
. Be sure to take into account whether a letter is capitalized or not.
\newline
D
=
a
5
m
+
N
D=\frac{a}{5 m}+N
D
=
5
m
a
+
N
\newline
Answer:
a
=
a=
a
=
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Solve the following equation for
a
a
a
. Be sure to take into account whether a letter is capitalized or not.
\newline
N
=
f
a
−
m
N=f a-m
N
=
f
a
−
m
\newline
Answer:
a
=
a=
a
=
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Solve the following equation for
a
a
a
. Be sure to take into account whether a letter is capitalized or not.
\newline
B
a
=
M
n
\frac{B}{a}=\frac{M}{n}
a
B
=
n
M
\newline
Answer:
a
=
a=
a
=
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Solve the following equation for
D
D
D
. Be sure to take into account whether a letter is capitalized or not.
\newline
n
=
D
g
n=\frac{D}{g}
n
=
g
D
\newline
Answer:
D
=
D=
D
=
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Solve the following equation for
A
A
A
. Be sure to take into account whether a letter is capitalized or not.
\newline
(
d
−
g
)
A
=
m
(d-g) A=m
(
d
−
g
)
A
=
m
\newline
Answer:
A
=
A=
A
=
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Solve the following equation for
a
a
a
. Be sure to take into account whether a letter is capitalized or not.
\newline
5
r
a
=
F
2
5 r a=F^{2}
5
r
a
=
F
2
\newline
Answer:
a
=
a=
a
=
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Solve the following equation for
A
A
A
. Be sure to take into account whether a letter is capitalized or not.
\newline
M
=
A
(
f
+
5
2
)
M=A\left(f+5^{2}\right)
M
=
A
(
f
+
5
2
)
\newline
Answer:
A
=
A=
A
=
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Solve the following equation for
a
a
a
. Be sure to take into account whether a letter is capitalized or not.
\newline
a
(
b
3
−
f
)
=
H
a\left(b^{3}-f\right)=H
a
(
b
3
−
f
)
=
H
\newline
Answer:
a
=
a=
a
=
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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
)
=
Get tutor help
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
)
=
Get tutor help
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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