Which facts are true for the graph of the function below? Check all that apply.<br><br> F(x)=(3/5)^x

The caffeine content (in mg) was examined for a random sample of 50 cups of black coffee dispensed by a new machine. The mean an

Genrish500 [490]

Answer:

We are 98% confident interval for the mean caffeine content for cups dispensed by the machine between 107.66 and 112.34 mg .

Step-by-step explanation:

Given -

The sample size is large then we can use central limit theorem

n = 50 ,

Standard deviation $(\sigma)$ = 7.1

Mean $\overline{(y)}$ = 110

$\alpha =$ 1 - confidence interval = 1 - .98 = .02

$z_{\frac{\alpha}{2}}$ = 2.33

98% confidence interval for the mean caffeine content for cups dispensed by the machine = $\overline{(y)}\pm z_{\frac{\alpha}{2}}\frac{\sigma}\sqrt{n}$

= $110\pm z_{.01}\frac{7.1}\sqrt{50}$

= $110\pm 2.33\frac{7.1}\sqrt{50}$

First we take + sign

$110 + 2.33\frac{7.1}\sqrt{50}$ = 112.34

now we take - sign

$110 - 2.33\frac{7.1}\sqrt{50}$ = 107.66

We are 98% confident interval for the mean caffeine content for cups dispensed by the machine between 107.66 and 112.34 .

5 0

4 years ago

Acrosonic's production department estimates that the total cost (in dollars) incurred in manufacturing x ElectroStat speaker sys

il63 [147K]

Answer:

a) $P(x)=-0.042x^2+530x-18000$

b) $P'(x)=-0.084x+530$

c)

$P'(4000)=194$

$P'(9500)=-268$

Step-by-step explanation:

a)

We know that Revenue is our total income and cost is our total cost. Thus, profit is what's left after cost is subtracted from Income (revenue). Thus, we can say:

P(x) = R(x) - C(x)

Finding Profit Function (P(x)):

$P(x) = R(x) - C(x)\\P(x) = -0.042x^2+800x-(270x+18000)\\P(x)=-0.042x^2+800x-270x-18000\\P(x)=-0.042x^2+530x-18000$

This is the profit function.

b)

The marginal profit is the profit earned when ONE ADDITIONAL UNIT of the product is sold. This is basically the rate of change of profit per unit. We find this by finding the DERIVATIVE of the Profit Function.

Remember the power rule for differentiation shown below:

$\frac{d}{dx}(x^n)=nx^{n-1}$