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Math Problems
Precalculus
Partial sums of geometric series
\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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Find the area in the right tail more extreme than
z
=
3.01
z=3.01
z
=
3.01
in a standard normal distribution.
\newline
Round your answer to three decimal places.
\newline
Area
=
=
=
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If the sum of three consecutive even integers is
78
78
78
, what is the first of the three even integers? (Hint: If
x
x
x
and
x
+
2
x+2
x
+
2
represent the first two consecutive even integers, then how would the third consecutive even integer be represented?)
\newline
The first of the three even integers is
□
\square
□
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Q
3
3
3
. Find the value of
x
x
x
in the following
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(
2
2
2
points) Find the perimeter and the area of the shaded figure. Round your answers to the nearest tenth.
\newline
Perimeter:
\newline
Area:
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(
2
2
2
points) Estimate the perimeter and the area of the shaded figure.
\newline
Perimeter:
\newline
Area:
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Round this number to a single digit times a power of
10
10
10
. Write your answer in scientific notation.
\newline
0.00099163
0.00099163
0.00099163
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What is
25
%
25 \%
25%
of
520
520
520
?
\newline
Hint: We can think of
25
%
25 \%
25%
as a common fraction.
\newline
□
\square
□
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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
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
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 HYPOTENUSE?
\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
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
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
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
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
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
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 FUNDAMENTAL?
\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
+
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
(
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
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
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
(
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
(
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
)
3
(x+4)^{3}
(
x
+
4
)
3
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
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
(
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
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
−
3
)
8
(x-3)^{8}
(
x
−
3
)
8
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
(
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
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
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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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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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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Question
2
2
2
\newline
Give the first three terms of
(
1
+
x
)
15
(1+x)^{15}
(
1
+
x
)
15
in descending order
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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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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
5
7
÷
3
\frac{5}{7} \div 3
7
5
÷
3
\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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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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2
3
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