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2 years ago

What is the explicit formula for this sequence? -7,-3,1,5

Mathematics

1 answer:

uranmaximum [27]2 years ago

6 0

Answer:

$a_{n}$ = 4n - 11

Step-by-step explanation:

These are the terms of an arithmetic sequence with n th term

$a_{n}$ = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

d = - 3 - (- 7) = 1 - (- 3) = 5 - 1 = 4

and a₁ = - 7, hence

$a_{n}$ = - 7 + 4(n - 1) = - 7 + 4n - 4 = 4n - 11

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Using the z-distribution, as we are working with a proportion, the 95% confidence interval for the proportion of consumers who would buy the product at it's proposed price is (0.3016, 0.3830).

<h3>What is a confidence interval of proportions?</h3>

A confidence interval of proportions is given by:

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

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$\pi$ is the sample proportion.

z is the critical value.

n is the sample size.

In this problem, we have a 95% confidence level, hence $\alpha = 0.95$ , z is the value of Z that has a p-value of $\frac{1+0.95}{2} = 0.975$ , so the critical value is z = 1.96.

179 out of 523 members indicated they would buy the new product at the proposed price, hence:

$\pi = \frac{179}{523} = 0.3423$

Then the bounds of the interval are found as follows:

$\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.3423 - 1.96\sqrt{\frac{0.3423(0.6577)}{523}} = 0.3016$

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More can be learned about the z-distribution at brainly.com/question/25890103

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