(8x2 - 4x-8)(2x +3x+2)

Mathematics

1 answer:

MArishka [77]2 years ago

8 0

Answer:

(8x2−4x−8)(2x+3x+2)

=(8x2+−4x+−8)(2x+3x+2)

=(8x2)(2x)+(8x2)(3x)+(8x2)(2)+(−4x)(2x)+(−4x)(3x)+(−4x)(2)+(−8)(2x)+(−8)(3x)+(−8)(2)

=16x3+24x3+16x2−8x2−12x2−8x−16x−24x−16

=40x3−4x2−48x−16

Step-by-step explanation:

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Researchers are interested if a school breakfast program leads to taller children. Assume that the population of all 5 year-old

DedPeter [7]

Answer:

$39-1.96\frac{1}{\sqrt{25}}=38.608$

$39+1.96\frac{1}{\sqrt{25}}=39.392$

So on this case the 95% confidence interval would be given by (38.608;39.392)

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

$\bar X=39$ represent the sample mean for the sample

$\mu$ population mean (variable of interest)

$\sigma=1$ represent the population standard deviation

n=25 represent the sample size

Solution to the problem

The confidence interval for the mean is given by the following formula:

$\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$ (1)

The margin of error is given by:

$ME= z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$

Since the Confidence is 0.95 or 95%, the value of $\alpha=0.05$ and $\alpha/2 =0.025$ , and we can use excel, a calculator or a tabel to find the critical value. The excel command would be: "=-NORM.INV(0.025,0,1)".And we see that $z_{\alpha/2}=1.96$