18 rolls of paper towels cost $25.99. Determine the cost of one roll of
toilet paper.

Answer:

a) x = 798   is the quantity that maximizes the profit

b)po(x) = 401 $/unit

c)P(max ) = 636105 $

Step-by-step explanation:

The weekly demand function is equal to the price by unit and the Revenue function is weekly demand times quantity of units then:

R(x) = p(x) * x

R(x) = ( 800 - 0,5*x ) * x

R(x) = 800*x - 0,5*x²

The equation for the profit is:

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

P(x) = 800*x - 0,5*x² - ( 300 + 2*x)

P(x) = 798*x - 0,5*x² - 300

a) P(x) = 798*x - 0,5*x² - 300

Taking derivatives on both sides of the equation:

P´(x) = 798 - x

If P´(x) = 0     then    798 - x = 0

x = 798   is the quantity that maximizes the profit

b) Selling price for the optimal quantity is:

p(x) = 800 - 0,5*x

p(x) = 800 - 0,5* 798

po (x) = 800 - 399

po(x) = 401 $/unit

c) Pmax = ?

P(x) = 798*x - 0,5*x² - 300    by subtitution of  x = 798

P(max) = 636804 - 399 - 300

P(max ) = 636105 $

a) The quantity that will maximize profit is [tex]100 \ units[/tex].

b) The selling of at this optimal quantity is [tex]\[/tex][tex]750[/tex] per unit.

c) So, the maximum profit is [tex]\[/tex][tex]25000[/tex].

A demand function is a mathematical equation that expresses the demand for a product or service as a function of its price and other factors such as the prices of the substitutes and complementary goods, income, etc.

The given demand function,

[tex]P=800-\frac{1}{2}x[/tex]

So, the revenue function is,

[tex]R(x)=p.x\\R(x)=800-x-\frac{1}{2}x^{2}[/tex]

[tex]\Rightarrow[/tex]Average cost is

[tex]\bar{C}=300+2x[/tex]

So, the total cost function is,

[tex]C\left ( x \right )=\bar{C}.x \\ C\left ( x \right )=300x+2x^{2}[/tex]

a) Profit function:

[tex]P\left ( x \right )=R\left ( x \right )-C\left ( x \right ) \\ =800x-\frac{1}{2}x^{2}-300x-2x^{2} \\ P\left ( x \right )=500x-\frac{5}{2}x^{2}[/tex]

For maximum,

[tex]{P}'\left ( x \right )=0 \\ 500\left ( 1 \right )-\frac{5}{2}\left ( 2x \right )=0 \\ 500-5x=0 \\ x=100[/tex]

b) Selling Price:

[tex]P=800-\frac{1}{2}x \\ at \ x=100 \\ P=800-\frac{1}{2}\left ( 100 \right ) \\ =\$ 750[/tex]

c) Maximum Profit:

[tex]P\left ( x \right )=500x-\frac{5}{2}x^{2} \\ P\left ( 100 \right )=500\left ( 100 \right )-\frac{5}{2}\left ( 100 \right )^{2} \\ P\left ( 100 \right )=\$ 25000[/tex]

Learn more about of Demand Function: https://brainly.com/question/25938253

Answer:

y=3/2x

Step-by-step explanation:

The equation of the required line as per slope-intercept form is 3x - 2y = 0.

The equation of a line that passes through points (x₁, y₁) and (x₂, y₂) is defined as:  

m = (y₂ - y₁)/(x₂ - x₁)

Here, 'm' is the slope and 'c' is the y-intercept of the given line.

Therefore, the slope of a line that passes through (6, 9) and (0, 0) is

= (0 - 9)/(0 - 6)

= 3/2

Now, the general form of a line is y = mx + c. Here, 'm' is the slope and 'c' is the y-intercept of the line.

The line passes through the point (0, 0).

Therefore, 0 = (3/2) × 0 + c

⇒ c = 0

Now, the equation of the straight line is

y = (3/2)x + 0

⇒ 2y = 3x

⇒ 3x - 2y = 0

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Step-by-step explanation:

ummm where is the pic? like bruh

Answer:

48 cm

Step-by-step explanation:

Multiply 4x2x6 and get the answer of 48 cm.

Answer:

y = 4/5x -1/5

Step-by-step explanation:

4x -5y = 1

-5y = -4x + 1

5y = 4x - 1

y = 4/5x - 1/5

Answer:

81

Step-by-step explanation:

Answer/Step-by-step explanation:

Score 1:

3, 7, 5, 4, 5, 6, 7, 8, 6, 5

Mean = [tex] \frac{3 + 7 + 5 + 4 + 5 + 6 + 7 + 8 + 6 + 5}{10} = \frac{56}{10} = 5.6 [/tex]

Median: order the data from least to the greatest.

3, 4, 5, 5, 5, 6, 6, 7, 7, 8

The median is average of the fifth and sixth data value in the data set

Median = (5 + 6)/2 = 11/2 = 5.5

Mode = value with the highest frequency = 5

Score 2:

34, 54, 17, 26, 34, 25, 14, 24, 25, 23

Mean = sum of all values/10

Mean = 276/10 = 27.6

Median: order the data set from min to max.

14, 17, 23, 24, 25, 25, 26, 34, 34, 54

The median is average of the fifth and sixth data value in the data set

Median = (25 + 25)/2 = 50/2 = 25

Mode = 25 and 34 (both have frequencies of 2)

Score 3:

154, 167, 132, 145, 154, 145, 113, 156, 154, 123

Mean = sum of all values/10

Mean = 1443/10 = 144.3

Median: order the data set from min to max.

113, 123, 132, 145, 145, 154, 154, 154, 156, 167

The median is average of the fifth and sixth data value in the data set

Median = (145 + 154)/2 = 299/2 = 149.5

Mode = 154

Answer:

$930.76

Step-by-step explanation:

So if you move the decimal in the percentage over to the right by two then you have your sales tax rate in decimal form (0.065), you can then multiply that by the listed price and you'll have about 56.80675 so this number will be the sales tax price, then you may add this to the listed price and your answer will be 930.75675, then once you round up it will be $930.76.

Answer:

the 1st 2nd and 5th since if there is even one negative in the fraction it makes the whole fraction negative

Answer:

x=53

y=19

Step-by-step explanation:

3x + y-5

3(5)=15

15+y

Answer:

The answer is 1

Step-by-step explanation:

If you look at the number line and start counting from -8 and count 9 to the right then the number that you end on is the answer.

Answer:

Step-by-step explanation:

alternate angles are equal

see attached

The measure of ∠1 is 33° .

When two parallel lines are crossed by a transversal, the pair of angles formed on the inner side of the parallel lines, but on the opposite sides of the transversal are called alternate interior angles. These angles are always equal.

According to the question

As given , lines A and B are parallel lines

therefore ,

∠1 = 33°  

∠3 = 57°

they are between parallel line and opposite of transversal line

So, they are alternate interior angles and are equal .

Hence, The measure of ∠1 is 33°  .

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Answer:

Wow that is great

Step-by-step explanation:

is there a question? uhhhmmmmm

Answer:

[tex]f(0)=-2\\f(1)=e-1[/tex]

Step-by-step explanation:

According to intermediate value theorem, if a function is continuous on an interval [tex][a,b][/tex], and if [tex]k[/tex] is any number between [tex]f(a)[/tex] and [tex]f(b)[/tex], then there exists a  value, [tex]x=m[/tex], where [tex]a<m<b[/tex], such that [tex]f(m)=k[/tex]

In the given question,

Intermediate Value Theorem is used to show that there is a root of the given equation in the specified interval.

Here,

[tex]f(x)=e^x-3+2x[/tex]

Put [tex]x=0[/tex]

[tex]f(0)=e^0-3+2(0)=1-3+0=-2[/tex]

Put [tex]x=1[/tex]

[tex]f(1)=e^1-3+2(1)=e-3+2=e-1[/tex]

Answer:8

Step-by-step explanation:

Answer:

c. the sampling distribution of the sample mean will be approximately normally distributed as long as the sample size is sufficiently large

Step-by-step explanation:

The law of large numbers is a statistical law, that states : As sample size grows, the sample mean tends to go closer to whole population mean.

So, the sampling distribution of the sample mean will be approximately normally distributed as long as the sample size is sufficiently large

Answer:

The final balance is $1,692.94.

The total compound interest is $392.94.

Step-by-step explanation:

1,300 x 0.045=___ x 6

Answer:

A.

Step-by-step explanation:

Answer:

-2( 7x+4)

Step-by-step explanation:

-14x - 8

Factor out -2

-2*7x -2*4

-2( 7x+4)

Answer:

Step-by-step explanation:

[tex] - 14x - 8[/tex]

Write -8 as -4×2

[tex] - 14x + 2 \times 4[/tex]

Factor out common term : 2

[tex]2( - 7x - 4)[/tex]

Answer: Total cost for 1 ride = $11. Total cost for 2 rides = $14. Total cost for 3 rides = $17. Total cost for 4 rides = $20. Total cost for 5 rides = $23

Step-by-step explanation:

Answer:

I can't really answer this question because there is no picture of actual question but 1 foot = 12 inches so for instance we could do 6 inches + 3 inches = 9 inches.      

Step-by-step explanation: How we would solve this problem is simple.

6 + 3 = 9  if you have to turn this into a fraction it would be 9/12 = (3/4).

Answer:

dilation

Step-by-step explanation:

dilation will make the shape larger or smaller which will change the shape.

Answer:

10 times bigger

Step-by-step explanation:

because if you do 4 times 300 thats 1200

and if you do 4 times 30 then you get 120

and 120 times 10 is 1200 so there you go.

HOPED THIS HELPED!!!!!!!!! :D

hope it helps.........

Answer:

# 10 is 4/3 or 1 and 1/3

#11 is 4/10 or 2/5

#12 is 2 and 3/4

#13 is 36/12 or 3 and 1/12

Step-by-step explanation:

i am not 100% sure on #13 btw

hope this helped!

p.s it would be cool if you gave me brainliest.

Answer:

Hey your answers on there are correct.

Step-by-step explanation:

Answer:

Yes

Step-by-step explanation:

The following relation is a function. When graphed, it passes the vertical line test, and you don't go across any two points at the same time. So therefore, it is a function. Another easy way to determine if the relation is a function is by taking a look at the x-coordinates. If any x-coordinates are the same, then it's not a function. If all x-coordinates are the same, then it's a function.

Hope this helps. Please mark brainliest.

Answer:

13/15 > 4/5 is a true stament.

Step-by-step explanation:

The left side is 0.86 repeating turned into a decimal. which means 0.86 is greater than the right which the right is 0.8 turned into a decimal. which in this case this means that the given stament is always true.

Answer:

6-(9-2)+3x6

Step-by-step explanation:

hope it helps

Answer:

area: 153.86

Circumference: 43.96 :D

Step-by-step explanation: