How do you factor n^3+1000

1 answer:

8 0

N^3 + 1000
Steps
you have to apply the sum of cubes rule: x^3 + y^3 = (x + y)(x^2 - xy + y^2)
which is... n^3 + 1000 = (n + 10)(n^2 - 10n + 10^2)
= (n + 10)(n^2 - 10n + 10^2)
Simplify
= (n = 10)(n^2 - 10n + 100)

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How many weeks of data must be randomly sampled to estimate the mean weekly sales of a new line of athletic footwear? We want 98

Irina18 [472]

Answer:

$n=(\frac{2.33(1400)}{400})^2 =66.50 \approx 67$

So the answer for this case would be n=67 rounded up

Step-by-step explanation:

Information given

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

$\mu$ population mean

$\sigma=1400$ represent the sample standard deviation

n represent the sample size

Solution to the problem

The margin of error is given by this formula:

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

And on this case we have that ME =400 and we are interested in order to find the value of n, if we solve n from equation (a) we got:

$n=(\frac{z_{\alpha/2} \sigma}{ME})^2$ (b)

The critical value for 98% of confidence interval now can be founded using the normal distribution. And the critical value would be $z_{\alpha/2}=2.33$ , replacing into formula (b) we got: