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3 years ago

Write an explicit formula formula for the sequence 2, 8, 14, 20, 26,...

Mathematics

1 answer:

Degger [83]3 years ago

5 0

Answer:

d. a_n = 6n - 4.

Step-by-step explanation:

The common difference (d) is 8-2 = 14-8 = 20-14 = 26-20 = 6.

This is an Arithmetic Sequence with the first term (a1) is 2.

The general form of the explicit formula is a_n = a1 + d(n - 1) so this sequence has the formula:

a_n = 2 + 6(n - 1)

a_n = 2 + 6n - 6

a_n = 6n - 4.

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3 years ago

Midpoint of the segment between the points (−5,13) and (6,4)

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Answer: $(0.5,8.5)$

Step-by-step explanation:

We need to use the following formula to find the Midpoint "M":

$M=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$

Given the points (-5,13) and (6,4) can identify that:

$x_1=-5\\x_2=6\\\\y_1=13\\y_2=4$

The final step is to substitute values into the formula.

Therefore, the midpoint of the segment between the points (-5,13) and (6,4) is:

$M=(\frac{-5+6}{2},\frac{13+4}{2})\\\\M=(\frac{1}{2},\frac{17}{2})\\\\M=(0.5,8.5)$

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3 years ago

Read 2 more answers

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3 years ago

A survey asked whether respondents favored or opposed the death penalty for people convicted of murder. Software shows the resul

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Answer:

The 95% confidence interval for those opposed is: (0.298, 0.334).

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence level of $1-\alpha$ , we have the following confidence interval of proportions.

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

In which

z is the zscore that has a pvalue of $1 - \frac{\alpha}{2}$ .

For this problem, we have that:

1786 of the 2611 were in favor, so 2611 - 1786 = 825 were opposed. Then

$n = 2611, \pi = \frac{825}{2611} = 0.316$

95% confidence level

So $\alpha = 0.05$ , z is the value of Z that has a pvalue of $1 - \frac{0.05}{2} = 0.975$ , so $Z = 1.96$ .

The lower limit of this interval is:

$\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.316 - 1.96\sqrt{\frac{0.316*0.684}{2611}} = 0.298$

The upper limit of this interval is:

$\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.316 + 1.96\sqrt{\frac{0.316*0.684}{2611}} = 0.334$

The 95% confidence interval for those opposed is: (0.298, 0.334).

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