66768 in scientific notation

the school newspaper has a circulation of 500 and sells for $.035 a copy. the students decide to raise the price to increase the

Alik [6]

Let x be the number of times they raise the price on the newspaper. Then the new cost of the newspaper is

$.35+.05x$

Let y be the newspaper they sell, then the income will be

$y(.35+.05x)$

Now, we know that the circulation is of 500, assuming that they sold every newspaper at the original price now the number the will sell will be

$y=500-20x$

Plugging the value of y in the first expression we have that the income will be

$\begin{gathered} f(x)=(500-20x)(.35+\text{0}.5x)=175+25x-7x-x^2 \\ =-x^2+18x+175 \end{gathered}$

Then the income is given by the function

$f(x)=-x^2+18x+175$

To find the maximum value of this functions (thus the maximum income) we need to take the derivative of the function,

$\begin{gathered} \frac{df}{dx}=\frac{d}{dx}(-x^2+18x+175) \\ =-2x+18 \end{gathered}$

no we equate the derivative to zero and solve for x.

$\begin{gathered} \frac{df}{dx}=0 \\ -2x+18=0 \\ -2x=-18 \\ x=\frac{-18}{-2} \\ x=9 \end{gathered}$

This means that we have an extreme value of the function when x=9. Now we need to find out if this value is a maximum or a minimum. To do this we need to take the second derivative of the function, then

$\begin{gathered} \frac{d^2f}{dx^2}=\frac{d}{dx}(\frac{df}{dx}) \\ =\frac{d}{dx}(-2x+18) \\ =-2 \end{gathered}$

Since the second derivative is negative in the point x=9, we conclude that this value is a maximum of the function.

With this we conclude that the number of times that they should raise the price to maximize the income is 9. This means that they will raise the price of the newspaper (9)($0.05)=$0.45.

Therefore the price to maximize the income is $0.35+$0.45=$0.80.

4 0

1 year ago

Including a 6% sales tax, an inn charges $155.82 per night. Find the inn's nightly cost before tax is added.

Feliz [49]

we know the Inn is charging 155.82 and that's 100% plus 6%, namely 106% of an amout of say that is "x", being the 100%.

since we know that 155.82 is 106%, what is "x"?

$\begin{array}{ccll} amount&\%\\ \cline{1-2} 155.82&106\\ x&100 \end{array}\implies \cfrac{155.82}{x}=\cfrac{106}{100}\implies \cfrac{155.82}{x}=\cfrac{53}{50} \\\\\\ 7791=53x\implies \cfrac{7791}{53}=x\implies 147=x$

3 0

2 years ago

Breyers is a major producer of ice cream and would like to test the hypothesis that the average American consumes more than 17 o

zhenek [66]

Answer:

The p-value would be 0.0939

Step-by-step explanation:

We can set a standard t-test for the Null Hypothesis that $H_0: 18.2\geq 17$

The test statistic then takes the form

$t=\frac{18.2-17}{3.9/\sqrt{15}}=1.317$

with this value we then can calculate the probability that is left to the right of this value $P(X>1.317)$ . From theory we know that t follows a standard normal distribution. Then $P(X>1.317)=0.0939$ which is smaller than the p-value set by Breyers of 0.10

3 0

3 years ago

Which polygon is always regular?

aleksley [76]

Square <span>polygon is always regular, other have some scenarios which makes them regular but they are not always regular.</span>

3 0

3 years ago

HURRY!!!!!!!!!!!!! 20PTS!!!! AND BRAINLIEST!!!!!!!!!!!!!!!!!!

Sedaia [141]

Answer:

Step-by-step explanation:

The roots of a function are the x-intercepts. By definition, the y-coordinate of points lying on the x-axis is zero. Therefore, to find the roots of a quadratic function, we set f (x) = 0, and solve the equation, ax2 + bx + c = 0.

6 0

3 years ago

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