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Math Problems
Precalculus
Partial sums of geometric series
Anna baked
3
3
3
batches of cookies with c cookies in each batch. She then ate
8
8
8
cookies!
\newline
How many cookies does Anna have left?
\newline
Write your answer as an expression.
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\newline
Our surface
S
S
S
is part of the plane containing the three points
(
1
,
0
,
0
)
,
(
0
,
9
,
0
)
(1,0,0),(0,9,0)
(
1
,
0
,
0
)
,
(
0
,
9
,
0
)
, and
(
0
,
0
,
9
)
(0,0,9)
(
0
,
0
,
9
)
. The equation of this plane is
\newline
z
=
z=
z
=
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What is the total number of different
9
9
9
-letter arrangements that can be formed using the letters in the word PERIMETER?
\newline
Answer:
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What is the total number of different
9
9
9
-letter arrangements that can be formed using the letters in the word AMENDMENT?
\newline
Answer:
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What is the total number of different
11
11
11
-letter arrangements that can be formed using the letters in the word RESPIRATION?
\newline
Answer:
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What is the total number of different
10
10
10
-letter arrangements that can be formed using the letters in the word HYPOTENUSE?
\newline
Answer:
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What is the total number of different
13
13
13
-letter arrangements that can be formed using the letters in the word POSSIBILITIES?
\newline
Answer:
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What is the total number of different
12
12
12
-letter arrangements that can be formed using the letters in the word CIVILIZATION?
\newline
Answer:
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What is the total number of different
8
8
8
-letter arrangements that can be formed using the letters in the word VEHEMENT?
\newline
Answer:
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What is the total number of different
10
10
10
-letter arrangements that can be formed using the letters in the word CHEESECAKE?
\newline
Answer:
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What is the total number of different
11
11
11
-letter arrangements that can be formed using the letters in the word PRECIPITOUS?
\newline
Answer:
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What is the total number of different
13
13
13
-letter arrangements that can be formed using the letters in the word SCARIFICATION?
\newline
Answer:
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What is the total number of different
13
13
13
-letter arrangements that can be formed using the letters in the word MATHEMATICIAN?
\newline
Answer:
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What is the total number of different
11
11
11
-letter arrangements that can be formed using the letters in the word FUNDAMENTAL?
\newline
Answer:
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Find the
2
2
2
nd term in the expansion of
(
4
x
+
7
y
)
5
(4 x+7 y)^{5}
(
4
x
+
7
y
)
5
in simplest form.
\newline
Answer:
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Find the
2
2
2
nd term in the expansion of
(
x
+
8
y
)
4
(x+8 y)^{4}
(
x
+
8
y
)
4
in simplest form.
\newline
Answer:
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Find the
3
3
3
rd term in the expansion of
(
3
x
−
2
)
4
(3 x-2)^{4}
(
3
x
−
2
)
4
in simplest form.
\newline
Answer:
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Find the
2
2
2
nd term in the expansion of
(
2
x
−
5
y
)
5
(2 x-5 y)^{5}
(
2
x
−
5
y
)
5
in simplest form.
\newline
Answer:
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Find the
6
6
6
th term in the expansion of
(
5
x
+
3
)
6
(5 x+3)^{6}
(
5
x
+
3
)
6
in simplest form.
\newline
Answer:
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Find the
2
2
2
nd term in the expansion of
(
3
x
+
2
)
4
(3 x+2)^{4}
(
3
x
+
2
)
4
in simplest form.
\newline
Answer:
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Find the
2
2
2
nd term in the expansion of
(
2
x
+
3
)
6
(2 x+3)^{6}
(
2
x
+
3
)
6
in simplest form.
\newline
Answer:
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Find the
2
2
2
nd term in the expansion of
(
4
x
−
1
)
6
(4 x-1)^{6}
(
4
x
−
1
)
6
in simplest form.
\newline
Answer:
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Find the
2
2
2
nd term in the expansion of
(
x
+
2
)
4
(x+2)^{4}
(
x
+
2
)
4
in simplest form.
\newline
Answer:
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Find the
3
3
3
rd term in the expansion of
(
x
+
5
)
7
(x+5)^{7}
(
x
+
5
)
7
in simplest form.
\newline
Answer:
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Find the
4
4
4
th term in the expansion of
(
2
x
−
3
)
6
(2 x-3)^{6}
(
2
x
−
3
)
6
in simplest form.
\newline
Answer:
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Find the
2
2
2
nd term in the expansion of
(
3
x
−
4
y
)
4
(3 x-4 y)^{4}
(
3
x
−
4
y
)
4
in simplest form.
\newline
Answer:
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Find the
3
3
3
rd term in the expansion of
(
3
x
+
y
)
6
(3 x+y)^{6}
(
3
x
+
y
)
6
in simplest form.
\newline
Answer:
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Find the
4
4
4
th term in the expansion of
(
x
+
2
y
)
6
(x+2 y)^{6}
(
x
+
2
y
)
6
in simplest form.
\newline
Answer:
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Find the
2
2
2
nd term in the expansion of
(
x
−
6
y
)
5
(x-6 y)^{5}
(
x
−
6
y
)
5
in simplest form.
\newline
Answer:
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Find the
2
2
2
nd term in the expansion of
(
x
+
4
)
3
(x+4)^{3}
(
x
+
4
)
3
in simplest form.
\newline
Answer:
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Find the
6
6
6
th term in the expansion of
(
4
x
−
1
)
7
(4 x-1)^{7}
(
4
x
−
1
)
7
in simplest form.
\newline
Answer:
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Find the
2
2
2
nd term in the expansion of
(
x
+
4
)
4
(x+4)^{4}
(
x
+
4
)
4
in simplest form.
\newline
Answer:
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Find the
6
6
6
th term in the expansion of
(
x
+
2
y
)
8
(x+2 y)^{8}
(
x
+
2
y
)
8
in simplest form.
\newline
Answer:
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Find the
4
4
4
th term in the expansion of
(
x
−
3
)
8
(x-3)^{8}
(
x
−
3
)
8
in simplest form.
\newline
Answer:
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Evaluate the expression shown below and write your answer as a fraction in simplest form.
\newline
9
10
+
12
7
\frac{9}{10}+\frac{12}{7}
10
9
+
7
12
\newline
Answer:
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Evaluate the expression shown below and write your answer as a fraction in simplest form.
\newline
4
3
+
11
12
\frac{4}{3}+\frac{11}{12}
3
4
+
12
11
\newline
Answer:
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Perform the operation and reduce the answer fully. Make sure to express your answer as a simplified fraction.
\newline
1
4
×
2
5
\frac{1}{4} \times \frac{2}{5}
4
1
×
5
2
\newline
Answer:
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What is the value of the expression below when
z
=
4
z=4
z
=
4
?
\newline
7
z
−
4
7 z-4
7
z
−
4
\newline
Answer:
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Perform the operation and reduce the answer fully. Make sure to express your answer as a simplified fraction.
\newline
1
5
×
5
6
\frac{1}{5} \times \frac{5}{6}
5
1
×
6
5
\newline
Answer:
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Perform the operation and reduce the answer fully. Make sure to express your answer as a simplified fraction.
\newline
5
7
÷
3
\frac{5}{7} \div 3
7
5
÷
3
\newline
Answer:
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Evaluate the expression shown below and write your answer as a fraction in simplest form.
\newline
5
6
−
3
4
\frac{5}{6}-\frac{3}{4}
6
5
−
4
3
\newline
Answer:
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Evaluate the expression shown below and write your answer as a fraction in simplest form.
\newline
1
6
+
1
4
\frac{1}{6}+\frac{1}{4}
6
1
+
4
1
\newline
Answer:
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Evaluate the expression shown below and write your answer as a fraction in simplest form.
\newline
5
7
−
3
7
\frac{5}{7}-\frac{3}{7}
7
5
−
7
3
\newline
Answer:
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Evaluate the expression shown below and write your answer as a fraction in simplest form.
\newline
6
11
−
3
8
\frac{6}{11}-\frac{3}{8}
11
6
−
8
3
\newline
Answer:
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Evaluate the expression shown below and write your answer as a fraction in simplest form.
\newline
2
3
−
1
5
\frac{2}{3}-\frac{1}{5}
3
2
−
5
1
\newline
Answer:
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Select the equivalent expression
6
×
6
×
6
×
6
×
6
6\times 6\times 6\times 6\times 6
6
×
6
×
6
×
6
×
6
\newline
find
2
2
2
answers
\newline
(A)
(
6
2
)
3
(6^2)^3
(
6
2
)
3
\newline
(B)
2
5
⋅
3
5
2^5 \cdot 3^5
2
5
⋅
3
5
\newline
(C)
6
6
6
1
\frac{6^6}{6^1}
6
1
6
6
\newline
(D)
3
2
⋅
2
3
3^2 \cdot 2^3
3
2
⋅
2
3
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Find each of the numbers below.
\newline
Simplify your answers as much as possible.
\newline
The opposite of
2
2
2
:
□
\square
□
\newline
The opposite of the opposite of
5
5
5
:
□
\square
□
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Express the given expression as an integer or as a fraction in simplest form.
\newline
ln
(
e
1
4
)
\ln \left(e^{\frac{1}{4}}\right)
ln
(
e
4
1
)
\newline
Answer:
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Write the following expression without negative exponents and without parentheses.
\newline
(
10
x
)
−
2
(10 x)^{-2}
(
10
x
)
−
2
\newline
Answer:
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Write the following expression without negative exponents and without parentheses.
\newline
3
x
−
2
3 x^{-2}
3
x
−
2
\newline
Answer:
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2
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