What are the zeros of the function below? F(x) = 8x(x-6)/(x+2)(x+9)

erastova [34]

Answer:

the correct answer is option ( C )

8 0

3 years ago

WidgCo is a company that produces and sells widgets. Let p denote the price per widget (measured in dollars), and let x be the m

Alecsey [184]

Answer:

The answer to this question can be defined as follows:

i) $\bold{p(x)= -5x^2+ 217x- 1,401} \\$

ii) x=22 units

iii) Maximum profit: 953.45

Step-by-step explanation:

Given value:

p(x) = 211 − 5x \\

C(x) = 1,401 + 16x

The formula for calculating the profit function value:

$\to \bold{P(x)= xp(x) - C(x)}$

$= x(211-5x)- 1,401 + 16x\\\\= 211x -5x^2-1,401+16x\\\\= -5x^2+ 217x- 1,401 \\$

The formula for calculating the value for maximum profit:

$p'(x) = - 10x + 217 =0$

$217= 10x\\\\x= \frac{217}{10}\\\\x= 21.7$

So, the production level is 22 units

Maximum profit:

$\to p(21.7)= - 5 (21.7)^2+217 (21.7) -1,401\\\\$

$=-5 (470.89) +217 (21.7) -1,401\\\\=-2354.45+ 4708.9-1,401\\\\= 953.45$

7 0

3 years ago

In a random sample of 25 people, the mean commute time to work was 33.9 minutes and the standard deviation was 7.2 minutes. Ass

Phoenix [80]

Answer:

$33.9-1.32\frac{7.2}{\sqrt{25}}=31.999$

$33.9+1.32\frac{7.2}{\sqrt{25}}=35.801$

So on this case the 80% confidence interval would be given by (31.999;35.801)

And the margin of error is given by:

$ME = t_{\alpha/2}\frac{s}{\sqrt{n}}$

And replacing we got:

$ME = 1.32\frac{7.2}{\sqrt{25}} =1.9008$

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".

$\bar X=33.9$ represent the sample mean for the sample

$\mu$ population mean (variable of interest)

s=7.2 represent the sample standard deviation

n=25 represent the sample size

Solution to the problem

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

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

In order to calculate the critical value $t_{\alpha/2}$ we need to find first the degrees of freedom, given by:

$df=n-1=25-1=24$

Since the Confidence is 0.80 or 80%, the value of $\alpha=0.2$ and $\alpha/2 =0.1$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.01,24)".And we see that $t_{\alpha/2}=1.32$