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vlada-n [284]
3 years ago
12

A restaurant operator in Accra has found out that during the lockdown,if she sells a plate of her food for Ghc 20 each,she can s

ell 300 plates but for each Ghc5 she raises the price,10 less plates are sold. A.Draw a table relating 5 different price levels with their corresponding number of plates sold.
B.Use the table to find the slope of the demand

C.Find the equation of the demand fraction.

D.Use your equation to determine the price in Ghc if she sells one plate of food to maximize her revenue
Mathematics
1 answer:
ella [17]3 years ago
3 0

The demand equation illustrates the price of an item and how it relates to the demand of the item.

  • The slope of the demand function is -1/2
  • The equation of the demand function is: R(x) = (300 - 10x) \times (20 + 5x)
  • The price that maximizes her revenue is: Ghc 85

From the question, we have:

Plates = 300

Price = 20

The number of plates (x) decreases by 10, while the price (y) increases by 5. The table of value is:

\begin{array}{cccccc}x & {300} & {290} & {280} & {270} & {260} \ \\ y & {20} & {25} & {30} & {35} & {40} \ \end{array}

The slope (m) is calculated using:

m = \frac{y_2 - y_1}{x_2 - x_1}

So, we have:

m = \frac{25-20}{290-300}

m = \frac{5}{-10}

m = -\frac{1}{2}

The equation of the demand is as follows:

The initial number of plates (300) decreases by 10 is represented as: (300 - 10x).

Similarly, the initial price (20) increases by 5 is represented as: (20 + 5x).

So, the demand equation is:

R(x) = (300 - 10x) \times (20 + 5x)

Open the brackets to calculate the maximum revenue

R(x) =6000 + 1500x - 200x - 50x^2

R(x) =6000 + 1300x - 50x^2

Equate to 0

6000 + 1300x - 50x^2 =0

Differentiate with respect to x

1300 - 100x =0

Collect like terms

100x =1300

Divide by 100

x =13

So, the price at maximum revenue is:

Price= 20 + 5x

Price= 20 + 5 * 13

Price= 85

In conclusion:

  • The slope of the demand function is -1/2
  • The equation of the demand function is: R(x) = (300 - 10x) \times (20 + 5x)
  • The price that maximizes her revenue is: Ghc 85

Read more about demand equations at:

brainly.com/question/21586143

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ANswer to c is 720.

a) Number who liked  chicken and laksa = (3/8 + 1/4) * 720  =  450 Answer

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A bag contains 31 checkers—13 red and 18 black. Determine whether the events "a red checker is selected, not replaced and then a
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Answer:

dependent, 39/155

Step-by-step explanation:

Since the checkers are not replaced, the events are dependent since the number of checkers in the bag  when you pick the second time depends on the first pick.

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P(red) = red/ total

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2 years ago
Select the curve generated by the parametric equations. Indicate with an arrow the direction in which the curve is traced as t i
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Answer:

length of the curve = 8

Step-by-step explanation:

Given parametric equations are x = t + sin(t) and y = cos(t) and given interval is

−π ≤ t ≤ π

Given data the arrow the direction in which the curve is traces means

the length of the curve of the given parametric equations.

The formula of length of the curve is

\int\limits^a_b {\sqrt{\frac{(dx}{dt}) ^{2}+(\frac{dy}{dt}) ^2 } } \, dx

Given limits values are −π ≤ t ≤ π

x = t + sin(t) ...….. (1)

y = cos(t).......(2)

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\frac{dx}{dt} = 1+cost

differentiating equation (2)  with respective to 'y'

\frac{dy}{dt} = -sint

The length of curve is

\int\limits^\pi_\pi  {\sqrt{(1+cost)^{2}+(-sint)^2 } } \, dt

\int\limits^\pi_\pi  \,   {\sqrt{(1+cost)^{2}+2cost+(sint)^2 } } \, dt

on simplification , we get

here using sin^2(t) +cos^2(t) =1 and after simplification , we get

\int\limits^\pi_\pi  \,   {\sqrt{(2+2cost } } \, dt

\sqrt{2} \int\limits^\pi_\pi  \,   {\sqrt{(1+1cost } } \, dt

again using formula, 1+cost = 2cos^2(t/2)

\sqrt{2} \int\limits^\pi _\pi  {\sqrt{2cos^2\frac{t}{2} } } \, dt

Taking common \sqrt{2} we get ,

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<u>conclusion</u>:-

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And we can find this probability on this way:

P(0.2

And in order to find these probabilities we can find tables for the normal standard distribution, excel or a calculator.  

P(0.2

b) P(X\geq 23)=P(\frac{X-\mu}{\sigma}\geq \frac{23-\mu}{\sigma})=P(Z\geq \frac{23-29}{5})=P(Z\geq -1.2)

And in order to find these probabilities we can find tables for the normal standard distribution, excel or a calculator.  

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c) P(X> 40)=P(\frac{X-\mu}{\sigma}> \frac{40-\mu}{\sigma})=P(Z\geq \frac{40-29}{5})=P(Z> 2.2)

And in order to find the probabilitiy we can use tables for the normal standard distribution, excel or a calculator.  

P(Z>2.2)=1-P(Z

Step-by-step explanation:

Previous concepts

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".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

2) Part a

Let X the random variable that represent the number of viewers for the American Idol TV of a population, and for this case we know the distribution for X is given by:

X \sim N(29,5)  

Where \mu=29 and \sigma=5 with the values on this case representing millions

We are interested on this probability :

P(30

And the best way to solve this problem is using the normal standard distribution and the z score given by:

z=\frac{x-\mu}{\sigma}

If we apply this formula to our probability we got this:

P(30

And we can find this probability on this way:

P(0.2

And in order to find these probabilities we can use tables for the normal standard distribution, excel or a calculator.  

P(0.2

Part b

We are interested on this probability :

P(X\geq 23)

P(X\geq 23)=P(\frac{X-\mu}{\sigma}\geq \frac{23-\mu}{\sigma})=P(Z\geq \frac{23-29}{5})=P(Z\geq -1.2)

And in order to find the probabilitiy we can use tables for the normal standard distribution, excel or a calculator.  

P(Z\geq -1.2)=1-P(Z

Part c

We are interested on this probability :

P(X> 40)

P(X> 40)=P(\frac{X-\mu}{\sigma}> \frac{40-\mu}{\sigma})=P(Z\geq \frac{40-29}{5})=P(Z> 2.2)

And in order to find the probabilitiy we can use tables for the normal standard distribution, excel or a calculator.  

P(Z>2.2)=1-P(Z

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