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Math Problems
Algebra 1
Experimental probability
Lillian is sitting on a bench in the mall. She noticed that
3
3
3
out of the last
15
15
15
men who walked by had a beard. What is the experimental probability that the next man to walk by will have a beard?
\newline
Simplify your answer and write it as a fraction or whole number.
\newline
P
(
beard
)
=
_
_
_
_
P(\text{beard}) = \_\_\_\_
P
(
beard
)
=
____
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At a glass vase factory,
2
2
2
out of the last
10
10
10
vases produced were chipped. What is the experimental probability that the next vase will be chipped? Simplify your answer and write it as a fraction or whole number.
\newline
P
(
chipped
)
=
_
_
_
_
P(\text{chipped}) = \_\_\_\_
P
(
chipped
)
=
____
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Irma supplies costumes to a number of theater companies. She recently provided
18
18
18
different hats, including
4
4
4
fedoras. What is the experimental probability that the next hat requested from Irma's inventory will be a fedora? Simplify your answer and write it as a fraction or whole number.
\newline
P
(
fedora
)
=
_
_
_
_
P(\text{fedora}) = \_\_\_\_
P
(
fedora
)
=
____
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A miniature golf course recently provided its customers with
12
12
12
golf balls, of which
4
4
4
were pink. What is the experimental probability that the next customer will receive a pink golf ball? Simplify your answer and write it as a fraction or whole number.
\newline
P
(
pink
)
=
_
_
_
_
P(\text{pink}) = \_\_\_\_
P
(
pink
)
=
____
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Of the last
12
12
12
contestants on a game show,
3
3
3
qualified for the bonus round. What is the experimental probability that the next contestant will qualify for the bonus round? Simplify your answer and write it as a fraction or whole number.
\newline
P
(
bonus round
)
=
_
_
_
P(\text{bonus round}) = \_\_\_
P
(
bonus round
)
=
___
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A grocery store recently sold
10
10
10
cans of soup,
5
5
5
of which were lentil soup. What is the experimental probability that the next can sold will be lentil soup? Simplify your answer and write it as a fraction or whole number.
\newline
P
(
lentil
)
=
_
_
_
P(\text{lentil}) = \_\_\_
P
(
lentil
)
=
___
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Of the last
20
20
20
balloons sold at a party store,
2
2
2
were red. What is the experimental probability that the next balloon sold will be red? Simplify your answer and write it as a fraction or whole number.
\newline
P
(
red
)
=
_
_
_
P(\text{red}) = \_\_\_
P
(
red
)
=
___
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Of the trains that recently pulled into Westford Station,
16
16
16
were full and
4
4
4
had room for more passengers. What is the experimental probability that the next train to pull in will be full? Simplify your answer and write it as a fraction or whole number.
\newline
P
(
full
)
=
_
_
_
P(\text{full}) = \_\_\_
P
(
full
)
=
___
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Luca works at an appliance store. He recently sold
12
12
12
appliances,
6
6
6
of which were dishwashers. What is the experimental probability that the next appliance Luca sells will be a dishwasher? Simplify your answer and write it as a fraction or whole number.
\newline
P
(
dishwasher
)
=
_
_
P(\text{dishwasher}) = \_\_
P
(
dishwasher
)
=
__
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Dean has worn a white shirt on
6
6
6
of the last
18
18
18
days. What is the experimental probability that Dean will wear a white shirt tomorrow? Simplify your answer and write it as a fraction or whole number.
\newline
P
(
white
)
=
_
_
_
P(\text{white}) = \_\_\_
P
(
white
)
=
___
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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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Situation: Sales have been tracked by the sales department. each year beginning in
2000
2000
2000
.
\newline
Let
t
t
t
be the year,
i
i
i
be the iterns sold, and
S
S
S
be the sales function
\newline
\begin{tabular}{|r|r|}
\newline
\hline Year
(
t
)
0
=
2000
(t) 0=2000
(
t
)
0
=
2000
& Items sold
(
i
)
(i)
(
i
)
in thousands \\
\newline
\hline
0
0
0
&
28
28
28
\\
\newline
\hline
1
1
1
&
40
40
40
\\
\newline
\hline
2
2
2
&
44
44
44
\\
\newline
\hline
3
3
3
&
30
30
30
\\
\newline
\hline
4
4
4
&
23
23
23
\\
\newline
\hline
5
5
5
&
21
21
21
\\
\newline
\hline
6
6
6
&
34
34
34
\\
\newline
\hline
7
7
7
&
22
22
22
\\
\newline
\hline
8
8
8
&
46
46
46
\\
\newline
\hline
\newline
\end{tabular}
\newline
A. What were sales in
2007
2007
2007
?
\newline
22
22
22
\newline
items
\newline
B. In what year were sales
40000
40000
40000
?
\newline
1
1
1
\newline
C.
S
(
3
)
=
S(3)=
S
(
3
)
=
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A group consists of four Democrats and five Republicans. Three people are selected to attend a conference.
\newline
a. In how many ways can three people be selected from this group of nine?
\newline
b. In how many ways can three Republicans be selected from the five Republicans?
\newline
c. Find the probability that the selected group will consist of all Republicans.
\newline
a. The number of ways to select three people from the group of nine is
□
\square
□
.
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Algebra
1
⩾
1 \geqslant
1
⩾
Y. Write a quadratic function from its
x
x
x
-intercepts and another point UDD
\newline
Write the equation of the parabola that passes through the points shown in the table.
\newline
\begin{tabular}{|c|c|}
\newline
\hline
x
x
x
&
y
y
y
\\
\newline
\hline
−
5
-5
−
5
&
−
24
-24
−
24
\\
\newline
\hline
−
3
-3
−
3
&
0
0
0
\\
\newline
\hline
−
2
-2
−
2
&
0
0
0
\\
\newline
\hline
\newline
\end{tabular}
\newline
Write your answer in the form
y
=
a
(
x
−
p
)
(
x
−
q
)
\mathrm{y}=\mathrm{a}(\mathrm{x}-\mathrm{p})(\mathrm{x}-\mathrm{q})
y
=
a
(
x
−
p
)
(
x
−
q
)
, where
a
,
p
\mathrm{a}, \mathrm{p}
a
,
p
, and
q
\mathrm{q}
q
are integers, decimals, or simplified fractions.
\newline
Submit
\newline
Work it out
\newline
Not feeling ready yet? These can help:
\newline
Solve one-step linear equations
\newline
Lesson: Quadratic equations
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A snack pack contains a certain number of potato chips, candy bars, and gummy bears. Each and every snack pack contains identical amounts of each of the snack types. Jack has
x
x
x
amount of snack packs, and when all of them are opened, he counted
42
42
42
potato chips,
24
24
24
candy bars, and
36
36
36
gummy bears in total. What is the highest possible value for
x
x
x
?
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Question
10
10
10
\newline
The cost
C
(
x
)
C(x)
C
(
x
)
, where
x
x
x
is the number of miles driven, of renting a car for a day is
$
32
\$ 32
$32
plus
$
1.45
\$ 1.45
$1.45
per mile.
\newline
What is the slope of the linear function and its units?
\newline
Select an answer
∨
\vee
∨
.
\newline
select the correct units
\newline
What is the
y
y
y
-intercept and its units?
\newline
Select an answer
✓
\checkmark
✓
- select the correct units
\newline
What is the linear function,
C
(
x
)
?
C
(
x
)
=
C(x) ? C(x)=
C
(
x
)?
C
(
x
)
=
\newline
Submit Question
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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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Jonah is conducting an experiment by spinning a spinner. Use the results of his experiment to answer the following questions. Be sure to write each probability as a simplified fraction.
\newline
Green
\newline
13
13
13
\newline
Blue
\newline
5
5
5
\newline
Red
\newline
17
17
17
\newline
Yellow
\newline
15
15
15
\newline
Find the probability that the spinner will land on green.
\newline
P
(
green
)
=
P(\text{green})=
P
(
green
)
=
\newline
Find the probability that the spinner will land on red.
\newline
P
(
red
)
=
P(\text{red})=
P
(
red
)
=
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When
7.57
7.57
7.57
mole of propane gas
(
C
3
H
8
)
(C_3H_8)
(
C
3
H
8
)
is burned in oxygen, how many mole of oxygen is consumed? Assume all reactant is converted into products.
\newline
C
3
H
8
+
5
O
2
⟶
3
C
O
2
+
4
H
2
O
C_3H_8 + 5O_2 \longrightarrow 3CO_2 + 4H_2O
C
3
H
8
+
5
O
2
⟶
3
C
O
2
+
4
H
2
O
\newline
Please do NOT include unit in your answer!
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You look over the songs in a jukebox and determine that you like
16
16
16
of the
59
59
59
songs.
\newline
(a) What is the probability that you like the next four songs that are played? (Assume a song cannot be repeated.)
\newline
(b) What is the probability that you do not like the any of the next four songs that are played? (Assume a song cannot be repeated.)
\newline
(a) The probability that you like the next four songs that are played is
\newline
oxed{ ext{ ule{0pt}{1.5ex} ule{1.5ex}{0pt}}}.
\newline
(Round to three decimal places as needed.)
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You look over the songs in a jukebox and determine that you like
14
14
14
of the
57
57
57
songs.
\newline
(a) What is the probability that you like the next four songs that are played? (Assume a song cannot be repeated.)
\newline
(b) What is the probability that you do not like the any of the next four songs that are played? (Assume a song cannot be repeated.)
\newline
(a) The probability that you like the next four songs that are played is
\newline
□
\square
□
.
\newline
(Round to three decimal places as needed.)
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Your answer is incorrect.
\newline
(a): Your answer is incorrect.
\newline
(b): Your answer is incorrect.
\newline
Suppose that a certain college class contains
47
47
47
students. Of these,
21
21
21
are sophomores,
30
30
30
are business majors, andom from the class.
\newline
(a) What is the probability that the student is both a sophomore and a business major?
\newline
(b) Given that the student selected is a sophomore, what is the probability that she is also a business major? Write your responses as fractions. (If necessary, consult a list of formulas.)
\newline
(a)
\newline
44
47
\frac{44}{47}
47
44
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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.
1
1
1
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A small town has two local high schools. High School A currently has
650
650
650
students and is projected to grow by
90
90
90
students each year. High School B currently has
750
750
750
students and is projected to grow by
70
70
70
students each year. Let
\newline
A
A
A
represent the number of students in 'High School A in
\newline
t
t
t
years, and let
\newline
B
B
B
represent the number of students in High School B after
\newline
t
t
t
years. Write an equation for each situation, in terms of
\newline
t
t
t
, and determine how many students would be in each high school in the year they are projected to have the same number of students.
\newline
Answer Attempt
1
1
1
out of
2
2
2
\newline
A
=
□
A=\square
A
=
□
\newline
90
90
90
0
0
0
\newline
Answer:
\newline
Submit Answer
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A small town has two local high schools. High School A currently has
650
650
650
students and is projected to grow by
90
90
90
students each year. High School B currently has
750
750
750
students and is projected to grow by
70
70
70
students each year. Let
A
A
A
represent the number of students in 'High School A in
t
t
t
years, and let
B
B
B
represent the number of students in High School B after
t
t
t
years. Write an equation for each situation, in terms of
t
t
t
, and determine how many students would be in each high school in the year they are projected to have the same number of students.
\newline
Answer Attempt
1
1
1
out of
2
2
2
\newline
A
=
□
B
=
A=\square \quad B=
A
=
□
B
=
\newline
Answer:
\newline
Submit Answer
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A sundae requires
3
3
3
ice-cream scoops and
4
4
4
strawberries, and a milkshake requires
2
2
2
ice-cream scoops and
6
6
6
strawberries. Ramses wants to make sundaes and milkshakes with at most
25
25
25
ice-cream scoops and
37
37
37
strawberries. Let's form a system of inequalities to represent Ramses's conditions. Let
S
S
S
denote the number of sundaes he makes and
M
M
M
the number of milkshakes he makes. Which system of inequalities best describes this situation?
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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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