1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
TEA [102]
3 years ago
13

Suppose a certain outlet chain selling appliances has found that for one brand of stereo system, the monthly demand is 240 when

the price is $900. However, when the price is $850, the monthly demand is 315. Assuming that the demand function for this system is linear, write the equation for the demand function. Use p for price and q for quantity.
Mathematics
1 answer:
Doss [256]3 years ago
6 0

Answer: Therefore the demand function can be given as;

q = -3/2p + 1590

Step-by-step explanation:

Given that at;

$900 the monthly demand is 240. ....1

$850 the monthly demand is 315. ....2

Since, the function is a linear function. The demand function would be of the form;

q = mp + c ....5

Where q = quantity demanded

p = price m = slope and c = intercept

Substituting conditions 1 and 2 to the equation.

240 = 900m + c. ...3

315 = 850m+ c ...4

Subtracting eqn 4 from 3

-75 = 50m

m = -75/50

m = -3/2

Substituting m = -3/2 into equation 3;

We have,

240= -3/2(900) + c

c = 240 + 3/2(900)

c = 1590

Therefore the demand function can be given as; substituting m and c into equation 5, we have;

q = -3/2p + 1590

You might be interested in
I need help or I will faill this
kari74 [83]

Answer:

-4x2 + 3x - 225

 ———————————————

        3    

Step-by-step explanation:

Step  1  :

               4

Simplify   —

                3

Equation at the end of step  1  :

        4            

 (x -  (— • x2)) -  75

        3            

Step  2  :

Equation at the end of step  2  :

       4x2      

 (x -  ———) -  75

        3      

Step  3  :

Rewriting the whole as an Equivalent Fraction :

3.1   Subtracting a fraction from a whole

Rewrite the whole as a fraction using  3  as the denominator :

         x     x • 3

    x =  —  =  —————

         1       3  

Equivalent fraction : The fraction thus generated looks different but has the same value as the whole

Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

Adding fractions that have a common denominator :

3.2       Adding up the two equivalent fractions

Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

x • 3 - (4x2)     3x - 4x2

—————————————  =  ————————

      3              3    

Equation at the end of step  3  :

 (3x - 4x2)    

 —————————— -  75

     3          

Step  4  :

Rewriting the whole as an Equivalent Fraction :

4.1   Subtracting a whole from a fraction

Rewrite the whole as a fraction using  3  as the denominator :

         75     75 • 3

   75 =  ——  =  ——————

         1        3    

Step  5  :

Pulling out like terms :

5.1     Pull out like factors :

  3x - 4x2  =   -x • (4x - 3)  

Adding fractions that have a common denominator :

5.2       Adding up the two equivalent fractions

-x • (4x-3) - (75 • 3)     -4x2 + 3x - 225

——————————————————————  =  ———————————————

          3                       3        

Step  6  :

Pulling out like terms :

6.1     Pull out like factors :

  -4x2 + 3x - 225  =   -1 • (4x2 - 3x + 225)  

Trying to factor by splitting the middle term

6.2     Factoring  4x2 - 3x + 225  

The first term is,  4x2  its coefficient is  4 .

The middle term is,  -3x  its coefficient is  -3 .

The last term, "the constant", is  +225  

Step-1 : Multiply the coefficient of the first term by the constant   4 • 225 = 900  

Step-2 : Find two factors of  900  whose sum equals the coefficient of the middle term, which is   -3 .

     -900    +    -1    =    -901  

     -450    +    -2    =    -452  

     -300    +    -3    =    -303  

     -225    +    -4    =    -229  

     -180    +    -5    =    -185  

     -150    +    -6    =    -156  

For tidiness, printing of 48 lines which failed to find two such factors, was suppressed

Observation : No two such factors can be found !!

Conclusion : Trinomial can not be factored

Final result :

 -4x2 + 3x - 225

 ———————————————

        3        

7 0
2 years ago
WORTH 6 POINTS!! Bob has 2 3/4 gallons of lemonade, 3 5/8 gallons of punch, and a 5 gallon's of soda. He invites 20 of his frien
kolezko [41]
So,

We need to convert the gallons into cups.

1 gal. = 16 c.

2 3/4 gal. = 2(16) + 3/4(16) = 32 + 12 = 44

3 5/8 gal. = 3(16) + 5/8(16) = 48 + 10 = 58

5 gal. = 5(16) = 80

There are 20 + 15 = 35 people.  Therefore, Bob's friends will drink a total of 35 cups of lemonade, 35 cups of punch, and 35 cups of soda.  We just need to subtract these amounts from what Bob has.

44 - 35 = 9 cups of lemonade

58 - 35 = 23 cups of punch

80 - 35 = 45 cups of soda

Obviously, then, Bob will have enough drinks.

He has 9 cups of lemonade, 23 cups of punch, and 45 cups of soda left over.  In gallons, he has 9/16 gallons of lemonade, 1 7/16 gallons of punch, and 2 13/16 gallons of soda left over.
7 0
3 years ago
Solve for x 5 x − 9 = 3 x + 3
Musya8 [376]

5x-9 = 3x+3

2x-9 = 3

2x = 12

x= 6

plz mark branliest, hopoe this helps :)

7 0
3 years ago
A word problem for 7x +10y =100
aivan3 [116]

Anwser: 100/17

Decimal term: 5.88235294

Mixed number: 5 15/17

4 0
3 years ago
What function do you know from calculus is such that its first derivative is itself? (Do not use the function f(x) = 0.) f(x) =
Pie

Answer:

ex is the function whose first derivative is itself and Y' = Y is the differential equation

Step-by-step explanation:

The steps is shown in the attachment.

3 0
3 years ago
Other questions:
  • The table shows the speeds of several runners on a track team. What is the speed, in feet per minute, of the fastest runner?
    12·1 answer
  • What is the cotangent of angle G? <br><br> A. 24/10 <br> B. 13/12 <br> C. 5/12 <br> D. 12/10
    9·1 answer
  • Martha just started a new job as an engineer.she is given a $9,000 sign on bonus and paid $4,500 per month . Write and solve an
    15·2 answers
  • The equation x^3+x^2+ax-4=0 has one root equal to -2. Find the value of a.​
    6·1 answer
  • Small packages of raisins contain different numbers of raisins in each package. The dot plot here shows the distribution of the
    8·2 answers
  • The present value of a house is $242,000. The value of the house increases at the rate of 4% every year. A function is shown bel
    12·2 answers
  • Benny wants to buy a new video game that costs $49.95. He already saved $24.65, and his aunt gave him $15 for mowing her lawn. H
    5·1 answer
  • Help ASAP plssss!!!!!
    10·1 answer
  • I need help on this math question
    10·2 answers
  • Find the volume of the sphere
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!