A store has been selling 200 DVD burners sold per week at 400 each. A market survey indicates that for each $ 20 rebate offered to buyers, the number of units sold will increase by 40 a week. Find the demand function and the revenue function. How large a rebate should the store offer to maximize its revenue

Answers

Answer 1

Answer:

The answer is "50".

Step-by-step explanation:

Let,

[tex]\to p(200) = 400[/tex]

If we assume the $20 reduction would raise the number of items sold to $40 so the increment is (x - 200) if x is the number of units sold.

[tex]\to (\frac{1}{40}) \times 20 = 0.5[/tex]

[tex]\to D(x) = 400 - 0.5 \times ( x - 200 ) \\\\ \ and \\ \to R(x) = x \times (D(x) \\\\[/tex]

            [tex]= x \times [ 400 - 0.5\times ( x - 200 )]\\\\ = x\times[400 - 0.5x - 100]\\\\= x\times [300 - 0.5 x]\\\\= 300x - 0.5 x^2[/tex]

[tex]R(x)= 300x- \frac{1}{2} x^2\\\\R'(x)=300-x\\[/tex]

if R'(x)=0

x=300

if  0 < x  < 300  and R(x) > 0 then R(x) for maximum x is = 300

[tex]D(300) = 400 - 0.5\times ( x - 200 )\\\\[/tex]

            [tex]= 400 - 0.5\times ( 300- 200 )\\\\ = 400 - 150+ 100\\\\ = 500 - 150 \\\\=350[/tex]

The rebate must be  : 400 - 350  = 50


Related Questions

6-6x = 5x-9x + 15
The value of x is

Answers

Answer:

[tex]Exact Form\\x= -\frac{9}{2} \\\\Decimal form:\\x= -4.5\\\\Mixed number form:\\x=-4\frac{1}{2}[/tex]

Hope this helps :)

Can someone help I numbered them poorly also there will be some left over numbers that weren’t used, I’ll mark brainliest if u give a small explanation

Answers

Answer:

Step-by-step explanation:

Slope m = rise / run = ([tex]y_{2}[/tex] - [tex]y_{1}[/tex]) / ([tex]x_{2}[/tex] - [tex]x_{1}[/tex])

1). (-4,3)

   (4, - 1)

m = (-1 - 3) / (4 + 4) = - 1/2

2). (-1, 1)

    (2, - 5)

m = (- 5 - 1) / (2 + 1) = - 2  

3). (6, 4)

    (5, 4)

m = (4 - 4) / (5 - 6) =  0  (graph is horizontal line)

4). (1, 4)

    (4, 1)

m = (1 - 4) / (4 - 1) = - 1

5). - 3/4

6). 4/3

Now is your turn. You can do it!!!

7). (1, 1)

   (2, 2)

m = ____

8). ( __ , __ )

  ( __ , __ )

m = _____  

9). (0, 2)

   (0, 4)

m = (4 - 2) / (0 - 0) = undefine slope or no slope (graph is vertical line)

10).

819 ÷ ________ = 8.19 (3 points)

a
101

b
102

c
103

d
104

Answers

Are those the only options because 819 divided by 100 is 8.19

£810 is divided between Paul, Brian & Colin so that Paul gets twice as much as Brian, and Brian gets three times as much as Colin. How much does Brian get?

Answers

Answer:

Step-by-step explanation:

Step by step

5x+2y=16 in function form

Answers

Answer:

y=-2.5x+8

Step-by-step explanation:

Subtract 5x from both sides

2y=-5x+16

divide both sides by two

y=-2.5x+8

5 divided by 1/10 is what?

Answers

50...................

4.(03.06) Choose the point-slope form of the equation below that represents the line that passes through the points (-3, 2) and (2, 1). O y + 3 = -5(x - 2) Oy - 2 = -5(x + 3) Oy+3 = - ] (x - 2) Oy-2=-****​

Answers

Answer:the answer is D y-2= 1/5(x+3)

Step-by-step explanation:I took the test

y-2=-1/5(x+3) is the  point-slope form of the equation below that represents the line that passes through the points (-3, 2) and (2, 1).

What is Slope of Line?

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

The given two points are (-3, 2) and (2, 1)

m=1-2/2+3

=-1/5

So slope is -1/5.

Now let us find the point slope form

y-y₁=m(x-x₁)

y-2=-1/5(x+3)

Hence, y-2=-1/5(x+3) is the  point-slope form of the equation below that represents the line that passes through the points (-3, 2) and (2, 1).

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A pair of shoes is currently priced at $55.00. If the store manager marks it down to $22.00, by what percent did he mark down the shoes?

Answers

Answer:

60%

Step-by-step explanation:

55 - 22 = 33

33/55 = 0.6

0.6*100 = 60%

5.82-1.76 rounded to the nearest whole number

Answers

Answer:

4.06 = 4

Step-by-step explanation:

Question 6
5 pts
Maria and Sarah were in charge of selling tickets to the class play. Maria sold 91
tickets and Sarah sold 70 tickets. What is the ratio of the number of tickets Maria sold
to the total number of tickets sold?

Answers

Answer:

Maria sold 56.5% of the total quantity of tickets sold.

Step-by-step explanation:

Given that between Maria and Sarah they both sold 161 tickets (91 + 70), and that of those 161 Maria sold 91 while Sarah sold 70, to determine the percentage of tickets that Maria sold over the total amount, the following crossed multiplication must be performed:

161 = 100

91 = X

((91 x 100) / 161) = X

9,100 / 161 = X

56.5 = X

Therefore, Maria sold 56.5% of the tickets sold.

When discordant pairs exceed concordant pairs in a P-Q relationship, Kendall's tau reports a(n) ________ association between the variables under study.a. positive.
b. weak.
c. negative.
d. strong.
e. inverse.

Answers

Answer:

a. positive.

Step-by-step explanation:

Matching and discordant pairs are used to describe the relationship between pairs of observations. To calculate matched and discordant pairs, data is treated as ordinal values. Therefore these are suitable for your application. The number of concordant and discordant pairs is used in Kendall's tau calculations, whose purpose is to determine the relationship among two ordinal variables.

If the direction of the classifications is the same, the pairs are concordant.

A pair of observations is discordant, suppose the subject being with an increased value on one variable is lower on the other.

SO; When discordant pairs exceed concordant pairs in a P-Q relationship, Kendall's tau reports a(n) positive association between the variables under study.

How many cups of whole wheat flour are required to make 35 biscuits?

Answers

Answer:

8 baby

Step-by-step explanation:

see image help me as fast as possible, please

Answers

20 would be the answer

Jenny and Chris share some prize money in the ratio 2:4. The prize money totaled $3000. How much did Chris win?




Help please need it today

Answers

Solution for What is 2.4 percent of 3000:

2.4 percent *3000 =

(2.4:100)*3000 =

(2.4*3000):100 =

7200:100 = 72
Maybe i dont know tbh

How do you do 20 / 4/5

Answers

Answer:

25

Step-by-step explanation:

you can write this equation as 20 ÷ [tex]\frac{4}{5}[/tex]

so change the division sign to multiplication by flipping the divisor ( [tex]\frac{4}{5}[/tex] )

this means you now have 20 x [tex]\frac{5}{4}[/tex]

so you can simplify 20 and 4, this makes the 4 into a 1 and the 20 into a 5

you now have 5 x [tex]\frac{5}{1}[/tex]

this is the same thing as 5 x 5

multiply it, and you can see that the answer is 25

A random sample of 300 circuits generated 13 defectives. Use the data to test the hypothesis Upper H Subscript 0 Baseline colon p equals 0.05 against Use . Find the P-value for the test.

Answers

Complete Question

A random sample of 300 circuits generated 13 defectives. a. Use the data to test

                            [tex]H_o : p = 0.05[/tex]

Versus

 

                          [tex]H_1 : p \ne 0.05[/tex]

Use α = 0.05. Find the P-value for the test

   

Answer:

The  p-value is  [tex]p-value = 0.5949[/tex]        

Step-by-step explanation:

From the question we are told that

  The sample size is  n = 300

    The number of defective circuits is  k = 13

Generally the sample proportion of defective circuits is mathematically represented as

        [tex]\^ p = \frac{k}{n}[/tex]

=>     [tex]\^ p = \frac{13}{300}[/tex]

=>     [tex]\^ p = 0.0433[/tex]

Generally the standard Error is mathematically represented as

       [tex]SE = \sqrt{\frac{p(1- p)}{n} }[/tex]

=>     [tex]SE = \sqrt{\frac{0.05(1- 0.05)}{300} }[/tex]

=>     [tex]SE = 0.0126[/tex]

Generally the test statistics is mathematically represented as

       [tex]z = \frac{\^ p - p }{SE}[/tex]

=>     [tex]z = \frac{0.0433 - 0.05 }{0.0126}[/tex]

=>     [tex]z = -0.5317[/tex]

From the z table  the area under the normal curve to the left  corresponding to  -0.5317  is

         [tex](P < -0.5317 ) = 0.29747[/tex]

Generally the p-value is mathematically represented as

       [tex]p-value = 2 * P(Z < -0.5317 )[/tex]

=>     [tex]p-value = 2 * 0.29747[/tex]

=>     [tex]p-value = 0.5949[/tex]        

     

If a fair coin is tossed 9 times, what is the probability, to the nearest thousandth, of

getting exactly 4 tails?

Answers

Answer:

=0.444

Step-by-step explanation:

probability= expected outcome  =   4

                        total outcome            9

4 into decimal  = 0.444( to the nearest thousandths- 3dp)

9

The probability is 24.609%

What is probability?

The mathematical subject of probability deals with the outcomes of random events. The term "probability" refers to the possibility or chance of an outcome. It clarifies the likelihood of a particular occurrence. We use phrases like "It will probably rain today," "he will probably pass the test," "there is very little chance of getting a storm tonight," and "most probably the price of onion will go high again" all the time.

Given a coin is tossed 9 times, and to find the probability of exact four heads,

the probability for condition given by  binomial probability ⁿCₓ[(p)ˣ(q)ⁿ⁻ˣ]

where p is probability of tail = 1/2 (favorable outcome)

q is probability of head = 1/2: (1 - p)

n = total outcome = 9

x = 4

ⁿCₓ[(p)ⁿ(q)ⁿ⁻ˣ] = ⁹C₄[(1/2)⁴(1/2)⁵]

= [tex]\frac{9!}{4!(9 - 4)!}[/tex] [1/16 x 1/32]

= [tex]\frac{9 x 8 x7 x 6 x 5!}{4! x 5!}[/tex](512)

126/512 = 0.24609

= 24.609%

Hence the probability, to the nearest thousandth is 24.609%.

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Michaela solved a system of linear equations that had no solution. One of the equations was x + y = 5. The other equation had a y-intercept of −2. What was the other equation?

Answers

Answer:

We have a system of equations with no solutions.

One of the equations is:

x + y = 5.

Isolating y in one side of the equation, we get:

y = 5 - x

And the other equation has an y-intercept of -2, the equation can be written as:

y = a*x - 2.

Then the system will be:

y = -1*x + 5

y = a*x - 2

The solution of a system of equations is a point where the graphs of both functions intersect.

Then if both of these lines are parallel, the lines will never intersect, then the second equation must be parallel to the first one.

And two lines are parallel if they have the same slope.

Then the other equation will be:

y = -x - 2

There are 18 green, 11 white, 15 purple, and 7 blue gum balls in a gum ball machine.



What is the probability that you will get a purple OR a blue gum ball if one is selected at random?



P(Purple OR Blue Gum ball) = ?



Make sure your answer is a SIMPLIFIED FRACTION if possible.


I WILLLLL GIVE THE FIRST 3 PPL THAT ANSWER A BRAINLIEST!!!!!!!!!

Answers

Answer:

%43

Step-by-step explanation:

I'm pretty sure? Its just what I think

The number of bacteria present in a culture was 1,000. Each hour , the number of bacteria in the culture was eight times the number that was present at the start of the preceding hour, as shown in the table

Answers

Answer:

the answer is d

Step-by-step explanation:

if you go threw your toutorial you will see that

A​ 2.5-meter piece of framing lumber has been used to cut a piece 1.65 meters long. How much of the original piece of lumber​ remains, in​ meters?

Answers

Answer:

0.85 of the original piece of lumber remains.

Step-by-step explanation:

Well, this lumber piece of lumber started as 2.5 meters long. Then, a 1.65 meter piece was cut off of it. All we need to do is subtract.

2.5 - 1.65 =

2.50 - 1.65 = 0.85.

Therefore, 0.85 of the original piece of lumber remains.

Hope this helps! :)

Help Please ( and leave on how you solved it ) ":(
view pic below

Answers

Answer:

The value of x = 10.

Step-by-step explanation:

From the given triangle,

The value of angle M = (3x + 28)°The value of angle K = (5x - 18)°The value of angle L = 90°

We know that the sum of a triangle is 180°.

i.e.

K + L + M = 180°

(5x - 18)° + 90° + (3x + 28)° = 180°

[tex]5x-18+90+3x+28=180[/tex]

[tex]5x+3x-18+90+28=180[/tex]

[tex]8x-18+90+28=180[/tex]

[tex]8x+100=180[/tex]

[tex]8x=80[/tex]

[tex]\frac{8x}{8}=\frac{80}{8}[/tex]

[tex]x=10[/tex]

Therefore, the value of x = 10

What is the answer, view the picture above

Answers

The answer is B Reflection and Translation

Andre has a summer job selling magazine subscriptions. He earns $25 per week plus $3 for every subscription he sells. Andre hopes to make at least enough money this week to buy a new pair of soccer cleats. The least expensive pair of cleats Andre wants costs $68.

a.) Write an inequality to find the number of subscriptions he needs to sell so that he can buy a pair of cleats.

b.) Solve the inequality from part (a).

c.) Interpret (what does it mean) and graph the solution.

Answers

Answer:

68≥25+3x

x≥15

Step-by-step explanation:

the overall goal is to have $68, so the goal needs to be less then or equal to the weekly $25 plus each additional subscription at $3 (x represents the needed amount of subscriptions he sells) the inequality would look something like 68≥25+3x because he wants the money this week.

to solve the inequality you would subtract the 25 from the 68, leaving you with 43≥3x as the new inequality, now you need to divide both sides by 3. Which comes out to 14.33333..... since we cant sell a fraction of a subscription you must round up giving you the new inequality of x≥15

this means that in order for Andre to get the cleats this week, he must sell at least 15 subscriptions

hope this helped

a.)   25x + 3y ≥ 68

b.) x = 1, y = 43

c.) As x increases, y decreases

What is a linear inequality?

A linear inequality is a mathematical relation which gives the range of values a variable or a function can take.

Given,

Wage per week= $25

Subscription earning = $3

Let x and y be the number of weeks and number of subscriptions.

Therefore, 25x + 3y ≥ 68

Hence, 25x + 3y ≥ 68 is the required inequality.

Let x = 1

Therefore  minimum value of y = 43.

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Help me please!! I forgot how to do it!

Answers

Answer:

i think the answer is 79

Step-by-step explanation:

im not really sure,

Given Z1 and Z2, find the
distance between them.
Z1 = 2 – 3i and Z2 = 4 + i

Answers

Answer:

The distance between given points is: √20

Step-by-step explanation:

The given numbers are complex numbers. In order to find the distance between two numbers in complex plain, their difference is taken and then modulus is applied.

Given numbers are:

[tex]z_1 = 2-3i\\z_2 =4+i[/tex]

The difference will be calculated as:

[tex]z_2-z_1 = (4+i)-(2-3i)\\= 4+i-2+3i\\=2+4i[/tex]

The distance will be:

[tex]d = \sqrt{(2)^2+(4)^2}\\= \sqrt{4+16}\\=\sqrt{20}[/tex]

Hence,

The distance between given points is: √20

Help?? What decimal place value is .7 in

Answers

Answer:

tenth

Step-by-step explanation:

it just is

tenths place because behind a decimal theres isn’t a oneth place, there’s no such thing so it would be the tenths place

Linear, exponential, or neither?
y = 4(1+.04)*

Answers

I guess it’s neither.

Choose the slope-intercept equation of the line that passes through the point shown and is perpendicular to the line shown.
a) y = x + 1
b) y = - x -
c) y = - x - 3
d) y = x +

Answers

Answer:

c

Step-by-step explanation:

Just trust me ive had ths question before

A submarine descends into the ocean at a
constant rate of 120 feet per minute. Which
equation best describes the depth of the
submarine, y, after x minutes?

Answers

18 mins.
Explanation:
Time taken to travel 20 m = 1 min
Time taken to travel 360m = x min
therefore:
1/20=x/360

(cross multiply)
20 x =360(isolate x by dividing both sides by 20)
x = 360
20 x
= 18 mins.
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