What is the diameter of a pond if the area is 4069. 44

Mathematical Statistics with Applications Help Homework

Mars2501 [29]

7.43: Let $X$ denote the random variable for height and $\overline X$ for the sample mean. Then if $\mu$ is the mean of

So the probability that the difference between the sample and population means does not exceed 0.5 inch is

$P(|\overline X-\mu|\le0.5) = P\left(\left|\dfrac{\overline X-\mu}{0.25}\right|\le\dfrac{0.5}{0.25}\right) = P(|Z|\le 2) \approx \boxed{0.95}$

per the empirical or 68/95/99.7 rule.

7.44: For a sample of size n, the sample standard deviation would be $\frac{2.5}{\sqrt n}$ . We want to find n such that

$P(|\overline X-\mu| < 0.4) = 0.95$

Comparing to the equation from the previous part, this means we would need

$\dfrac{0.4}{\frac{2.5}{\sqrt{n}}} = 0.16\sqrt n = 2 \implies \sqrt n = 12.5 \implies n = 156.25$

so a sample of at least 157 men would be sufficient.

7 0

3 years ago

A bakery finds that the price they can sell cakes is given by the function p = 580 − 10x where x is the number of cakes sold per

dexar [7]

Answer:

The total revenue is $TR=580x-10x^2$ .

The marginal revenue is $MR=580-20x$ .

The fixed cost is $900.

The marginal cost function is $MC=50x+300$ .

Step-by-step explanation:

The Total Revenue ( $TR$ ) received from the sale of $x$ goods at price $p$ is given by

$TR=p\cdot x$

The Marginal Revenue ( $MR$ ) is the derivative of total revenue with respect to demand and is given by

$MR=\frac{d(TR)}{dx}$

From the information given we know that the price they can sell cakes is given by the function $p=580-10x$ , where $x$ is the number of cakes sold per day.

So, the total revenue is

$TR=(580-10x)\cdot x\\TR=580x-10x^2$

And the marginal revenue is

$MR=\frac{d}{dx}(580x-10x^2) \\\\\mathrm{Apply\:the\:Sum/Difference\:Rule}:\quad \left(f\pm g\right)'=f\:'\pm g'\\\\MR=\frac{d}{dx}\left(580x\right)-\frac{d}{dx}\left(10x^2\right)\\\\MR=580-20x$

The Fixed Cost ( $FC$ ) is the amount of money you have to spend regardless of how many items you produce.

The Marginal Cost ( $MC$ ) function is the derivative of the cost function and is given by

$MC=\frac{d(TC)}{dx}$

We know that the total cost function of the company is given by $C=(30+5x)^2$ , which it is equal to

$\mathrm{Apply\:Perfect\:Square\:Formula}:\quad \left(a+b\right)^2=a^2+2ab+b^2\\a=30,\:\:b=5x\\\\\left(30+5x\right)^2=30^2+2\cdot \:30\cdot \:5x+\left(5x\right)^2=25x^2+300x+900\\\\C=25x^2+300x+900$

From the total cost function and applying the definition of fixed cost, the fixed cost is $900.

And the marginal cost function is

$MC=\frac{d}{\:dx}\left(25x^2+300x+900\right)\\\\MC=\frac{d}{dx}\left(25x^2\right)+\frac{d}{dx}\left(300x\right)+\frac{d}{dx}\left(900\right)\\\\MC=50x+300+0=50x+300$

4 0

3 years ago

If f(1) = 2 and f(n) = 5f(n − 1) then find the value of f(5). -

Juliette [100K]

Answer:

f ' (n) = 5f

Step-by-step explanation:

1- Take the derivative

2- remove the parenthesis

3- use differentiation rules

4- Differentiate

5- Simplify

8 0

2 years ago

If it is 1pm today and school holidays officially begin on Saturday at 9 amHow many hours away are school holidays?

adell [148]

Answer:

68 hours

Step-by-step explanation:

Going by the time frame and date attached to this question, if school holidays should begin by Saturday 9 am, then from 1pm today we are 68 hours away from holiday.

3 0

3 years ago

Read 2 more answers

To help racecar drivers safely negotiate turns, racetracks are banked at the curves. At one location, a 58 ft track is banked su

zmey [24]

The correct answer is Choice B: 53.0 feet.

If you draw a picture of the cross section, you will have a right triangle. The hypotenuse is 58 and one of the legs is 23.6. All you have to do is use the Pythagorean Theorem and solve for the missing side.

x^2 + 23.6^2 = 58^2

7 0

3 years ago