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UNO [17]
3 years ago
11

What is the sum of the geometric series 2^0 + 2^1 + 2^2 + 2^3 + 2^3 + 2^4 + … + 2^9?

Mathematics
2 answers:
Murljashka [212]3 years ago
8 0
Hello,

1+2+2^2+2^3+...+2^9=\frac{2^{10}-1}{2-1}=1023
Download xls
mars1129 [50]3 years ago
3 0
The nth term is
an=a1(r)^(n-1)
an=1(2)^(n-1)
a1=1
r=2

the sum of a geometric seequence is
S_{n}=\frac{a_{1}(1-r^{n})}{1-r}
a1=1
r=2
we want to find S_{10} (since we minus 1, the highest exponet is 9 so add 1 to make it correct)

S_{10}=\frac{1(1-2^{10})}{1-2}
S_{10}=\frac{(1-1024}{-1}
S_{10}=\frac{(-1023}{-1}
S_{10}=1023

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list as many combinations of three dimensions you can come up with that would give you a volume if 1536 cubic feet.
Monica [59]

Answer:

1.) Length = 8ft, width = 8ft, height = 24ft

2.) Length = 8ft, width = 16ft, height = 12ft

3.) Length = 8ft, width = 24ft, height = 8ft

4.) Length = 8ft, width = 32ft, height = 6ft

5.) Length = 6ft, width = 8ft, height = 32ft

6.) Length = 16ft, width = 4ft, height = 24ft

7) Length = 12ft, width = 8ft, height = 16ft

8.) Length = 2ft, width = 64ft, height = 12ft

9.) Length = 48ft, width = 16ft, height = 2ft

Step-by-step explanation:

To obtain a volume of 1536 cubic feet:

This means Length × width × Height equals 1536ft^3

1.) Length = 8ft, width = 8ft, height = 24ft

2.) Length = 8ft, width = 16ft, height = 12ft

3.) Length = 8ft, width = 24ft, height = 8ft

6 0
3 years ago
A triangle ABC has its vertices at A(-2, -3), B(2, 1), and C(5,-1).
maksim [4K]

~\hfill \stackrel{\textit{\large distance between 2 points}}{d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2}}~\hfill ~ \\\\[-0.35em] ~\dotfill\\\\ A(\stackrel{x_1}{-2}~,~\stackrel{y_1}{-3})\qquad B(\stackrel{x_2}{2}~,~\stackrel{y_2}{1}) ~\hfill AB=\sqrt{( 2- (-2))^2 + ( 1- (-3))^2} \\\\\\ AB=\sqrt{(2+2)^2+(1+3)^2}\implies AB=\sqrt{32}\implies \boxed{AB=4\sqrt{2}} \\\\[-0.35em] ~\dotfill

B(\stackrel{x_1}{2}~,~\stackrel{y_1}{1})\qquad C(\stackrel{x_2}{5}~,~\stackrel{y_2}{-1}) ~\hfill BC=\sqrt{( 5- 2)^2 + ( -1- 1)^2} \\\\\\ BC=\sqrt{3^2+(-2)^2}\implies BC=\sqrt{9+4}\implies \boxed{BC=\sqrt{13}} \\\\[-0.35em] ~\dotfill\\\\ C(\stackrel{x_1}{5}~,~\stackrel{y_1}{-1})\qquad A(\stackrel{x_2}{-2}~,~\stackrel{y_2}{-3}) ~\hfill CA=\sqrt{( -2- 5)^2 + ( -3- (-1))^2} \\\\\\ CA=\sqrt{(-7)^2+(-3+1)^2}\implies CA=\sqrt{49+(-2)^2}\implies \boxed{CA=\sqrt{53}}

\stackrel{\textit{\large perimeter of ABC}}{4\sqrt{2}+\sqrt{13}+\sqrt{53}~~\approx~~ 16.54}

3 0
2 years ago
This is the choices <br> 88<br> 70<br> 110<br> 120
s344n2d4d5 [400]

Answer:

110

Step-by-step explanation:

Y and X have to equal 180

70+x+180

=110

7 0
3 years ago
Read 2 more answers
What is the side length of a cube with a volume of 0.216 m3?
aksik [14]

。☆✼★ ━━━━━━━━━━━━━━━  ☾

Cube root 0.216 to get your answer

(Note: This makes sense if you know the volume of a cube is the same value multiplied together 3 times)

The answer is option A 0.6 m

Have A Nice Day ❤

Stay Brainly! ヅ

- Ally ✧

。☆✼★ ━━━━━━━━━━━━━━━━  ☾

6 0
4 years ago
According to a poll, 30% of voters support a ballot initiative. Hans randomly surveys 5 voters. What is the probability that exa
VMariaS [17]

The probability that exactly 2 voters will be in favor of the ballot initiative is 0.309.

<h2>Given</h2>

Number of voters who support ballot initiative = 30 % = 0.30

Number of voters who does not support this initiative = 1 - 0.30 = 0.70

Number of voters selected for Surveying = 5

<h3>What is probability?</h3>

The probability of success and failure remain the same throughout the trials.

The probability that exactly 2 voters will be in favor of the ballot initiative is given by;

If P denotes Success and Q denotes failure;

\rm = ^{5}C_2 \times (0.3)^2 \times (0.70)^3\\\\= 10 \times 0.09 \times 0.343\\\\= 0.309

Hence, the probability that exactly 2 voters will be in favor of the ballot initiative is 0.309.

To know more about Probability click the link given below.

brainly.com/question/20344726

3 0
2 years ago
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