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3 years ago

Find the common difference of the following sequence.

Mathematics

1 answer:

Darya [45]3 years ago

3 0

You have the correct answer. It is choice B) -1/4

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Explanation:

This is because we're adding -1/4 to each term to get the next one. In other words, we're subtracting 1/4 from each term to get the next one.

term2 = term1+(d) = 1/2 + (-1/4) = 1/2 - 1/4 = 2/4 - 1/4 = 1/4
term3 = term2+(d) = 1/4 + (-1/4) = 1/4 - 1/4 = 0
term4 = term3+(d) = 0 + (-1/4) = 0 - 1/4 = -1/4
term5 = term4+(d) = -1/4 + (-1/4) = -2/4 = -1/2

and so on.

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To find the common difference, all we have to do is subtract any term from its previous one.

For example:

d = (term2) - (term1)

d = (1/4) - (1/2)

d = (1/4) - (2/4)

d = (1-2)/4

d = -1/4

The order of subtraction matters, so we cannot say d = term1-term2.

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Supposing that the stock increases in 37 days, the 95% confidence interval for the proportion of days JMJ stock increases is: (0.484, 0.7292)

The lower bound is of 0.484.
The upper bound is of 0.7292.

The interpretation is that we are 95% sure that the true proportion of all days in which the JMJ stock increases is between 0.484 and 0.7292.

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence level of $\alpha$ , we have the following confidence interval of proportions.

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

In which

z is the z-score that has a p-value of $\frac{1+\alpha}{2}$ .

Supposing that it increases on 37 out of 61 days:

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95% confidence level

So $\alpha = 0.95$ , z is the value of Z that has a p-value of $\frac{1+0.95}{2} = 0.975$ , so $z = 1.96$ .

The lower limit of this interval is:

$\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.6066 - 1.96\sqrt{\frac{0.6066(0.3934)}{61}} = 0.484$

The upper limit of this interval is:

$\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.6066 + 1.96\sqrt{\frac{0.6066(0.3934)}{61}} = 0.7292$

The 95% confidence interval for the proportion of days JMJ stock increases is (0.484, 0.7292), in which 0.484 is the lower bound and 0.7292 is the upper bound.

The interpretation is that we are 95% sure that the true proportion of all days in which the JMJ stock increases is between 0.484 and 0.7292.

A similar problem is given at brainly.com/question/16807970

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2 years ago

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Answer:

Step-by-step explanation:

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