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3 years ago

Find the common difference of the arithmetic sequence 5, 14, 23, ...

Mathematics

2 answers:

vodka [1.7K]3 years ago

7 0

It’s plus 9 so the next number should be 32

stepladder [879]3 years ago

6 0

Answer: 9

Step-by-step explanation: The common difference is the difference between each of the terms in an arithmetic sequence.

Let's work backwards.

First, we take the last term we are given and

subtract the second to last term.

So here, we subtract 23 - 14 to get 9.

Now, we take 14 - 5 to get 9.

Notice that 9 is our answer in both problems above.

That means it's our common difference.

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It is known that the population variance equals 484. With a .95 probability, the sample size that needs to be taken to estimate

Hitman42 [59]

Answer:

The minimum sample size is n = 75 so that the desired margin of error is 5 or less.

Step-by-step explanation:

We are given the following in the question:

Population variance = 484

Standard deviation =

$\sigma^2 = 484\\\sigma =\sqrt{484} = 22$

Confidence level = 0.95

Significance level = 0.05

Margin of error = 5

Formula:

Margin of error =

$E = z\times \dfrac{\sigma}{\sqrt{n}}\\\\n = (\dfrac{z\times \sigma}{E})^2$

$z_{critical}\text{ at}~\alpha_{0.05} = 1.96$

Putting values, we get

$E\leq 5\\\\1.96\times \dfrac{22}{\sqrt{n}} \leq 5\\\\\sqrt{n} \geq 1.96\times \dfrac{22}{5}\\\\n \geq (1.96\times \dfrac{22}{5})^2\\\\n \geq 74.373$

Thus, the minimum sample size is n = 75 so that the desired margin of error is 5 or less.

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Step-by-step explanation:

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