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Rufina [12.5K]
3 years ago
11

He first term of a sequence is 2, and each subsequent term is the reciprocal of the square of the preceding term. what is the po

sitive square root of the fifth term?
Mathematics
1 answer:
polet [3.4K]3 years ago
4 0
The first term is a₁ = 2.
Each subsequent term is the reciprocal of the square of the preceding term.

2nd term:
a₂ = 1/2² = 1/4

3rd term:
a₃ = 1/(1/4)² = 1/(1/16) = 16

4th term:
a₄ = 1/16² = 1/256

5th term:
a₅ = 1/(1/256)² = 1/(1/65536) = 65536
The positive square root of the fifth term is
√(65536) = 256

Answer: 256
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Answer:

a. 39.55%

b. 44.02%

Step-by-step explanation:

We have the following data:

n = 5

x = 1

p = 5/20 = 0.25

to. If the sampling is done with replacement.

We apply the binomial distribution formula, which is as follows:

P = nCx * (p ^ x) * ((1-p) ^ (n-x))

Where nCx, is a combination, and is equal to:

nCx = n! / x! * (n-x)!

replacing we have:

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replacing in the main formula:

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P = 0.3955

that is, without replacing the probability is 39.55%

b. if the sampling is done without replacement.

Here it is a little different from the previous one, but what you should do is calculate three cases,

the first was the one at point a, when n = 5 and x = 1

5C1 = 5! / 1! * 4! = 5

the second is when n = 20 and x = 5, this is all possible scenarios.

20C5 = 20! / 5! * 15! = 15504

and the third is when n = 15 (20-5) and x = 4 (5-1), which corresponds to the cases when none were damaged

15C4 = 15! / 4! * 11! = 1365

In the end, it would be:

P = (5C1 * 15C4) / 20C5

Replacing:

P = 5 * 1365/15504

P = 0.4402

Which means that without replacing the probability is 44.02%

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