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Oxana [17]
2 years ago
5

Determine whether the geometric series 27 + 18 + 12 + 8 + ... converges or diverges, and identify the sum if it exists.

Mathematics
1 answer:
Ne4ueva [31]2 years ago
6 0

The given geometric series as shown in the question is seen to; Be converging with its' sum as 81

<h3>How to identify a converging or diverging series?</h3>

We are given the geometric series;

27 + 18 + 12 + 8 + ...

Now, we see that;

First term; a₀ = 27

Second Term; a₁ = 2(27/3)

Third term; a₂ = 2²(27/3²)

Fourth term; a₃ = 2³(27/3³)

Thus, the formula is;

2ⁿ(27/3ⁿ)

Applying limits at infinity gives;

2^(∞) * (27/3^(∞)) = 0

Since the  terms of the series tend to zero, we can affirm that the series converges.

The sum of an infinite converging series is:

S_n = a/(1 - r)

S_n = 27/(1 - (2/3)

S_n = 81

Read more about converging or diverging series at; brainly.com/question/15415793

#SPJ1

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If men's heights are normally distributed with mean 68 and standard deviation 3.1 inches, and women's heights are normally distr
stira [4]

Answer:

the probability that the woman is taller than the man is  0.1423

Step-by-step explanation:

Given that :

the men's heights are normally distributed with mean \mu  68

standard deviation \sigma   = 3.1

And

the women's heights are normally distributed with mean \mu  65

standard deviation \sigma   = 2.8

We are to find the probability that the woman is taller than the man.

For woman now:

mean  \mu = 65

standard deviation \sigma = 2.8

P(x > 68 ) = 1 - p( x< 68)

\\ 1 -p  \ P[(x - \mu ) / \sigma < (68-25)/ 2.8]

= 1-P (z , 1.07)

Using z table,

= 1 - 0.8577

= 0.1423

Thus, the probability that the woman is taller than the man is  0.1423

6 0
3 years ago
Pleas help me !!! It’s due today
kolezko [41]
KE=0.5xmxv2
=0.5x 1.2x10^3x (3.4x10^3)^2=6936000000
6 0
3 years ago
Find the volume of a square pyramid with a base area of 18inch squared and the height of 4 inches
den301095 [7]
Vpyramid=1/3 times area of base times height
volume=1/3 times 18 square inches times 4in
volume=6 square inches times 4in
volume=24 cubic inches


the volume is 24 cubic inches
5 0
3 years ago
What is the value of x in the expression, x 2 = 9? Type the NUMBER in the box below.
alekssr [168]
The value of x in the expression, x 2 = 9 is 4.5

9 divided by 2 = 4.5
7 0
3 years ago
Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.
AlekseyPX

Answer:

No Solution

Step-by-step explanation:

If you grouped like terms, you would get n+(-n)+5-10=1

Both <em>n's</em> would cancel each other out.

I hope this helps! (If it's wrong, then tell me, I'll try to find the correct answer...)

6 0
2 years ago
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