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Math Problems
Algebra 2
Find trigonometric functions using a calculator
Solve for
x
x
x
, rounding to the nearest hundredth.
\newline
7
⋅
3
x
4
=
1
7 \cdot 3^{\frac{x}{4}}=1
7
⋅
3
4
x
=
1
\newline
Answer:
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Solve for
x
x
x
, rounding to the nearest hundredth.
\newline
3
x
4
=
35
3^{\frac{x}{4}}=35
3
4
x
=
35
\newline
Answer:
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Solve for
x
x
x
, rounding to the nearest hundredth.
\newline
88
e
x
=
48
88 e^{x}=48
88
e
x
=
48
\newline
Answer:
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Solve for
x
x
x
, rounding to the nearest hundredth.
\newline
48
⋅
3
4
x
=
8
48 \cdot 3^{4 x}=8
48
⋅
3
4
x
=
8
\newline
Answer:
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Find the sum of the first
10
10
10
terms of the following sequence. Round to the nearest hundredth if necessary.
\newline
4
,
−
10
,
25
,
…
4, \quad-10, \quad 25, \ldots
4
,
−
10
,
25
,
…
\newline
Sum of a finite geometric series:
\newline
S
n
=
a
1
−
a
1
r
n
1
−
r
S_{n}=\frac{a_{1}-a_{1} r^{n}}{1-r}
S
n
=
1
−
r
a
1
−
a
1
r
n
\newline
Answer:
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Find the sum of the first
7
7
7
terms of the following sequence. Round to the nearest hundredth if necessary.
\newline
5
,
6
,
36
5
,
…
5, \quad 6, \quad \frac{36}{5}, \ldots
5
,
6
,
5
36
,
…
\newline
Sum of a finite geometric series:
\newline
S
n
=
a
1
−
a
1
r
n
1
−
r
S_{n}=\frac{a_{1}-a_{1} r^{n}}{1-r}
S
n
=
1
−
r
a
1
−
a
1
r
n
\newline
Answer:
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Find the sum of the first
8
8
8
terms of the following sequence. Round to the nearest hundredth if necessary.
\newline
12
,
−
18
,
27
,
…
12, \quad-18, \quad 27, \ldots
12
,
−
18
,
27
,
…
\newline
Sum of a finite geometric series:
\newline
S
n
=
a
1
−
a
1
r
n
1
−
r
S_{n}=\frac{a_{1}-a_{1} r^{n}}{1-r}
S
n
=
1
−
r
a
1
−
a
1
r
n
\newline
Answer:
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Find the sum of the first
7
7
7
terms of the following sequence. Round to the nearest hundredth if necessary.
\newline
8
,
24
,
72
,
…
8, \quad 24, \quad 72, \ldots
8
,
24
,
72
,
…
\newline
Sum of a finite geometric series:
\newline
S
n
=
a
1
−
a
1
r
n
1
−
r
S_{n}=\frac{a_{1}-a_{1} r^{n}}{1-r}
S
n
=
1
−
r
a
1
−
a
1
r
n
\newline
Answer:
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Find the sum of the first
9
9
9
terms of the following sequence. Round to the nearest hundredth if necessary.
\newline
20
,
−
100
,
500
,
…
20, \quad-100, \quad 500, \ldots
20
,
−
100
,
500
,
…
\newline
Sum of a finite geometric series:
\newline
S
n
=
a
1
−
a
1
r
n
1
−
r
S_{n}=\frac{a_{1}-a_{1} r^{n}}{1-r}
S
n
=
1
−
r
a
1
−
a
1
r
n
\newline
Answer:
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Find the sum of the first
7
7
7
terms of the following sequence. Round to the nearest hundredth if necessary.
\newline
92
,
78.2
,
66.47
,
…
92, \quad 78.2, \quad 66.47, \ldots
92
,
78.2
,
66.47
,
…
\newline
Sum of a finite geometric series:
\newline
S
n
=
a
1
−
a
1
r
n
1
−
r
S_{n}=\frac{a_{1}-a_{1} r^{n}}{1-r}
S
n
=
1
−
r
a
1
−
a
1
r
n
\newline
Answer:
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Find the sum of the first
9
9
9
terms of the following sequence. Round to the nearest hundredth if necessary.
\newline
8
,
−
4
,
2
,
…
8, \quad-4, \quad 2, \ldots
8
,
−
4
,
2
,
…
\newline
Sum of a finite geometric series:
\newline
S
n
=
a
1
−
a
1
r
n
1
−
r
S_{n}=\frac{a_{1}-a_{1} r^{n}}{1-r}
S
n
=
1
−
r
a
1
−
a
1
r
n
\newline
Answer:
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Find the sum of the first
10
10
10
terms of the following sequence. Round to the nearest hundredth if necessary.
\newline
12
,
2
,
1
3
,
…
12, \quad 2, \quad \frac{1}{3}, \ldots
12
,
2
,
3
1
,
…
\newline
Sum of a finite geometric series:
\newline
S
n
=
a
1
−
a
1
r
n
1
−
r
S_{n}=\frac{a_{1}-a_{1} r^{n}}{1-r}
S
n
=
1
−
r
a
1
−
a
1
r
n
\newline
Answer:
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Find the sum of the first
8
8
8
terms of the following sequence. Round to the nearest hundredth if necessary.
\newline
16
,
−
8
,
4
,
…
16, \quad-8, \quad 4, \ldots
16
,
−
8
,
4
,
…
\newline
Sum of a finite geometric series:
\newline
S
n
=
a
1
−
a
1
r
n
1
−
r
S_{n}=\frac{a_{1}-a_{1} r^{n}}{1-r}
S
n
=
1
−
r
a
1
−
a
1
r
n
\newline
Answer:
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Find the sum of the first
9
9
9
terms of the following sequence. Round to the nearest hundredth if necessary.
\newline
36
,
9
,
9
4
,
…
36, \quad 9, \quad \frac{9}{4}, \ldots
36
,
9
,
4
9
,
…
\newline
Sum of a finite geometric series:
\newline
S
n
=
a
1
−
a
1
r
n
1
−
r
S_{n}=\frac{a_{1}-a_{1} r^{n}}{1-r}
S
n
=
1
−
r
a
1
−
a
1
r
n
\newline
Answer:
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Find the sum of the first
7
7
7
terms of the following sequence. Round to the nearest hundredth if necessary.
\newline
21
,
−
7
,
7
3
,
…
21, \quad-7, \quad \frac{7}{3}, \ldots
21
,
−
7
,
3
7
,
…
\newline
Sum of a finite geometric series:
\newline
S
n
=
a
1
−
a
1
r
n
1
−
r
S_{n}=\frac{a_{1}-a_{1} r^{n}}{1-r}
S
n
=
1
−
r
a
1
−
a
1
r
n
\newline
Answer:
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Find the sum of the first
8
8
8
terms of the following series, to the nearest integer.
\newline
3
,
4
,
16
3
,
…
3,4, \frac{16}{3}, \ldots
3
,
4
,
3
16
,
…
\newline
Answer:
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Find the sum of the first
7
7
7
terms of the following series, to the nearest integer.
\newline
8
,
6
,
9
2
,
…
8,6, \frac{9}{2}, \ldots
8
,
6
,
2
9
,
…
\newline
Answer:
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Find the value of the following expression and round to the nearest integer:
\newline
∑
n
=
0
93
400
(
0.94
)
n
+
1
\sum_{n=0}^{93} 400(0.94)^{n+1}
n
=
0
∑
93
400
(
0.94
)
n
+
1
\newline
Answer:
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Find the
11
11
11
th term of the arithmetic sequence
x
+
1
,
−
5
x
+
7
,
−
11
x
+
13
,
…
x+1,-5 x+7,-11 x+13, \ldots
x
+
1
,
−
5
x
+
7
,
−
11
x
+
13
,
…
\newline
Answer:
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Find the
5
th
5^{\text {th }}
5
th
term of the arithmetic sequence
−
3
x
+
3
,
4
x
−
1
,
11
x
−
5
,
…
-3 x+3,4 x-1,11 x-5, \ldots
−
3
x
+
3
,
4
x
−
1
,
11
x
−
5
,
…
\newline
Answer:
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Find the
1
3
th
13^{\text {th }}
1
3
th
term of the arithmetic sequence
5
x
−
6
,
−
2
x
−
11
,
−
9
x
−
16
,
…
5 x-6,-2 x-11,-9 x-16, \ldots
5
x
−
6
,
−
2
x
−
11
,
−
9
x
−
16
,
…
\newline
Answer:
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Find the
5
th
5^{\text {th }}
5
th
term of the arithmetic sequence
−
3
x
+
7
,
−
7
x
+
3
,
−
11
x
−
1
,
…
-3 x+7,-7 x+3,-11 x-1, \ldots
−
3
x
+
7
,
−
7
x
+
3
,
−
11
x
−
1
,
…
\newline
Answer:
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Find the
14
14
14
th term of the arithmetic sequence
x
+
8
,
8
x
+
2
,
15
x
−
4
,
…
x+8,8 x+2,15 x-4, \ldots
x
+
8
,
8
x
+
2
,
15
x
−
4
,
…
\newline
Answer:
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Find the
7
7
7
th term of the arithmetic sequence
5
x
−
4
,
−
2
x
−
9
,
−
9
x
−
14
,
…
5 x-4,-2 x-9,-9 x-14, \ldots
5
x
−
4
,
−
2
x
−
9
,
−
9
x
−
14
,
…
\newline
Answer:
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Find the
14
14
14
th term of the arithmetic sequence
x
+
3
,
7
x
−
4
,
13
x
−
11
,
…
x+3,7 x-4,13 x-11, \ldots
x
+
3
,
7
x
−
4
,
13
x
−
11
,
…
\newline
Answer:
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Find the
1
5
th
15^{\text {th }}
1
5
th
term of the arithmetic sequence
5
x
+
1
,
9
x
+
7
,
13
x
+
13
,
…
5 x+1,9 x+7,13 x+13, \ldots
5
x
+
1
,
9
x
+
7
,
13
x
+
13
,
…
\newline
Answer:
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Find the
11
11
11
th term of the arithmetic sequence
−
5
x
+
9
,
−
7
x
+
2
,
−
9
x
−
5
,
…
-5 x+9,-7 x+2,-9 x-5, \ldots
−
5
x
+
9
,
−
7
x
+
2
,
−
9
x
−
5
,
…
\newline
Answer:
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Find the
5
th
5^{\text {th }}
5
th
term of the arithmetic sequence
x
+
3
,
5
x
+
5
,
9
x
+
7
,
…
x+3,5 x+5,9 x+7, \ldots
x
+
3
,
5
x
+
5
,
9
x
+
7
,
…
\newline
Answer:
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Find the
14
14
14
th term of the arithmetic sequence
−
2
x
+
5
,
x
+
3
,
4
x
+
1
,
…
-2 x+5, x+3,4 x+1, \ldots
−
2
x
+
5
,
x
+
3
,
4
x
+
1
,
…
\newline
Answer:
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Find the
1
3
th
13^{\text {th }}
1
3
th
term of the arithmetic sequence
x
+
1
,
−
2
x
−
3
,
−
5
x
−
7
,
…
x+1,-2 x-3,-5 x-7, \ldots
x
+
1
,
−
2
x
−
3
,
−
5
x
−
7
,
…
\newline
Answer:
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Find the
12
12
12
th term of the geometric sequence shown below.
\newline
−
x
8
,
−
2
x
9
,
−
4
x
10
,
…
-x^{8},-2 x^{9},-4 x^{10}, \ldots
−
x
8
,
−
2
x
9
,
−
4
x
10
,
…
\newline
Answer:
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Find the
8
8
8
th term of the geometric sequence shown below.
\newline
−
8
x
6
,
−
8
x
7
,
−
8
x
8
,
…
-8 x^{6},-8 x^{7},-8 x^{8}, \ldots
−
8
x
6
,
−
8
x
7
,
−
8
x
8
,
…
\newline
Answer:
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Find the
12
12
12
th term of the geometric sequence shown below.
\newline
4
x
,
−
8
x
3
,
16
x
5
,
…
4 x,-8 x^{3}, 16 x^{5}, \ldots
4
x
,
−
8
x
3
,
16
x
5
,
…
\newline
Answer:
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Find the
9
9
9
th term of the geometric sequence shown below.
\newline
−
x
5
,
−
x
9
,
−
x
13
,
…
-x^{5},-x^{9},-x^{13}, \ldots
−
x
5
,
−
x
9
,
−
x
13
,
…
\newline
Answer:
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Find the
7
7
7
th term of the geometric sequence shown below.
\newline
−
6
x
7
,
30
x
8
,
−
150
x
9
,
…
-6 x^{7}, 30 x^{8},-150 x^{9}, \ldots
−
6
x
7
,
30
x
8
,
−
150
x
9
,
…
\newline
Answer:
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Find the
7
7
7
th term of the geometric sequence shown below.
\newline
−
10
x
6
,
10
x
11
,
−
10
x
16
,
…
-10 x^{6}, 10 x^{11},-10 x^{16}, \ldots
−
10
x
6
,
10
x
11
,
−
10
x
16
,
…
\newline
Answer:
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Find the
10
10
10
th term of the geometric sequence shown below.
\newline
−
3
x
6
,
6
x
10
,
−
12
x
14
,
…
-3 x^{6}, 6 x^{10},-12 x^{14}, \ldots
−
3
x
6
,
6
x
10
,
−
12
x
14
,
…
\newline
Answer:
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Find the
7
7
7
th term of the geometric sequence shown below.
\newline
x
4
,
−
3
x
7
,
9
x
10
,
…
x^{4},-3 x^{7}, 9 x^{10}, \ldots
x
4
,
−
3
x
7
,
9
x
10
,
…
\newline
Answer:
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Find the
8
8
8
th term of the geometric sequence shown below.
\newline
−
2
x
8
,
−
4
x
10
,
−
8
x
12
,
…
-2 x^{8},-4 x^{10},-8 x^{12}, \ldots
−
2
x
8
,
−
4
x
10
,
−
8
x
12
,
…
\newline
Answer:
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Find the
8
8
8
th term of the geometric sequence shown below.
\newline
−
2
x
3
,
4
x
6
,
−
8
x
9
,
…
-2 x^{3}, 4 x^{6},-8 x^{9}, \ldots
−
2
x
3
,
4
x
6
,
−
8
x
9
,
…
\newline
Answer:
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Find the
9
9
9
th term of the geometric sequence shown below.
\newline
−
4
x
6
,
4
x
11
,
−
4
x
16
,
…
-4 x^{6}, 4 x^{11},-4 x^{16}, \ldots
−
4
x
6
,
4
x
11
,
−
4
x
16
,
…
\newline
Answer:
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Find the
8
8
8
th term of the geometric sequence shown below.
\newline
−
4
x
6
,
−
20
x
8
,
−
100
x
10
,
…
-4 x^{6},-20 x^{8},-100 x^{10}, \ldots
−
4
x
6
,
−
20
x
8
,
−
100
x
10
,
…
\newline
Answer:
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Find the
12
12
12
th term of the geometric sequence shown below.
\newline
−
8
x
2
,
16
x
5
,
−
32
x
8
,
…
-8 x^{2}, 16 x^{5},-32 x^{8}, \ldots
−
8
x
2
,
16
x
5
,
−
32
x
8
,
…
\newline
Answer:
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Rotate the yellow dot to a location of
π
\pi
π
radians. After you rotate the angle, determine the value of
sin
π
\sin \pi
sin
π
, to the nearest hundredth.
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Rotate the yellow dot to a location of
1
1
1
radian. After you rotate the angle, determine the value of
sin
1
\sin 1
sin
1
, to the nearest hundredth.
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Rotate the yellow dot to a location of
4
4
4
radians. After you rotate the angle, determine the value of
sec
4
\sec 4
sec
4
, to the nearest hundredth.
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Rotate the yellow dot to a location of
5
5
5
radians. After you rotate the angle, determine the value of
sin
5
\sin 5
sin
5
, to the nearest hundredth.
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Given
P
(
A
)
=
0.74
,
P
(
B
)
=
0.6
P(A)=0.74, P(B)=0.6
P
(
A
)
=
0.74
,
P
(
B
)
=
0.6
and
P
(
A
∣
B
)
=
0.9
P(A \mid B)=0.9
P
(
A
∣
B
)
=
0.9
, find the value of
P
(
A
P(A
P
(
A
and
B
)
B)
B
)
, rounding to the nearest thousandth, if necessary.
\newline
Answer:
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Given
P
(
A
)
=
0.66
,
P
(
B
)
=
0.3
P(A)=0.66, P(B)=0.3
P
(
A
)
=
0.66
,
P
(
B
)
=
0.3
and
P
(
A
P(A
P
(
A
and
B
)
=
0.248
B)=0.248
B
)
=
0.248
, find the value of
P
(
A
∣
B
)
P(A \mid B)
P
(
A
∣
B
)
, rounding to the nearest thousandth, if necessary.
\newline
Answer:
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Given
P
(
A
)
=
0.72
,
P
(
B
)
=
0.3
P(A)=0.72, P(B)=0.3
P
(
A
)
=
0.72
,
P
(
B
)
=
0.3
and
P
(
A
P(A
P
(
A
or
B
)
=
0.754
B)=0.754
B
)
=
0.754
, find the value of
P
(
A
P(A
P
(
A
and
B
)
B)
B
)
, rounding to the nearest thousandth, if necessary.
\newline
Answer:
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