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4 years ago

15

Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. Write the polynomial in s

tandard form.
4, -8, and 2 + 5i

1 answer:

Elena L [17]4 years ago

6 0

X=- 8x=4 x=2+5i
(x+8)(x-4)(x-(2+sqrt(-25))
x^2+4x-32(x-2+sqrt(-25))
x^3+4x^2-32x-2x^2+8x-64+x^2(5i)+4x5i-32(5i)
now simplify

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A sample of 25 commuters in the Washington, D.C., area yielded the sample mean commute time of 27.97 minutes and sample standard

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The 99% confidence interval for the mean commute time of all commuters in Washington D.C. area is between 22.7994 minutes and 33.1406 minutes. The interpretation is that we are 99% sure that the true mean ommute time of all commuters in Washington D.C. area is between 22.7994 minutes and 33.1406 minutes.

Step-by-step explanation:

We have that to find our $\alpha$ level, that is the subtraction of 1 by the confidence interval divided by 2. So:

$\alpha = \frac{1-0.99}{2} = 0.005$

Now, we have to find z in the Ztable as such z has a pvalue of $1-\alpha$ .

So it is z with a pvalue of $1-0.005 = 0.995$ , so $z = 2.575$

Now, find M as such

$M = z*\frac{\sigma}{\sqrt{n}}$

In which $\sigma$ is the standard deviation of the population and n is the size of the sample.

$M = 2.575*\frac{10.04}{\sqrt{25}} = 5.1706$

The lower end of the interval is the mean subtracted by M. So it is 27.97 - 5.1706 = 22.7994 minutes

The upper end of the interval is the mean added to M. So it is 6.4 + 0.3944 = 33.1406 minutes.

The 99% confidence interval for the mean commute time of all commuters in Washington D.C. area is between 22.7994 minutes and 33.1406 minutes. The interpretation is that we are 99% sure that the true mean ommute time of all commuters in Washington D.C. area is between 22.7994 minutes and 33.1406 minutes.

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