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3 years ago

Given the following Demand Curve: P = 24 - 8Q

Mathematics

1 answer:

KatRina [158]3 years ago

4 0

Answer:

Maximum value of total revenue = 18

Step-by-step explanation:

Express this Demand Curve in terms of Q.

P = 24 - 8Q (it is the same equation)

Find P, if Q=2

P= 24-8(2)

P=24-16

P=8

Find Q if P = 8.

P = 24 - 8Q

8= 24 - 8Q

8Q= 24-8

8Q=16

Q=16/8

Q=2

Total revenue in terms of Q

Total revenue is P times Q, that is

P*Q=TR=(24-8Q)*Q

TR=24Q-8Q^2

$TR=24Q-8Q^{2} \\\\$

Marginal Revenue

It is the first derivative of TR

TR'(Q)= 24-16Q

Find the values of P and Q that will maximize total revenue.

To find them first TR'(Q)=0, that is

0=24-16Q

16Q=24

Q=24/16

Q=3/2

Q=1.5

and we plug in 1.5 in P=24-8Q, which is,

P=24-8Q

P=24-8(1,5)

P=24-12

P=12

Calculate this maximum value of total revenue

P=12 Q=1.5

P*Q=Total Revenue

12*1.5=Total Revenue

18=Total Revenue

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rjkz [21]

Answer:

\mu = 14.5\\

\sigma = 5.071\\

k = 1.084

Step-by-step explanation:

given that a statistician uses Chebyshev's Theorem to estimate that at least 15 % of a population lies between the values 9 and 20.

i.e. his findings with respect to probability are

$P(9$

Recall Chebyshev's inequality that

$P(|X-\mu |\geq k\sigma )\leq {\frac {1}{k^{2}}}\\P(|X-\mu |\leq k\sigma )\geq 1-{\frac {1}{k^{2}}}\\$

Comparing with the Ii equation which is appropriate here we find that

$\mu =14.5$

Next what we find is

$k\sigma = 5.5\\1-\frac{1}{k^2} =0.15\\\frac{1}{k^2}=0.85\\k=1.084\\1.084 (\sigma) = 5.5\\\sigma = 5.071$

Thus from the given information we find that

$\mu = 14.5\\\sigma = 5.071\\k = 1.084$

5 0

3 years ago

Dividing the polynomial P(x) by x-6 yields a quotient by Q(x) and a remainder of 5.

bazaltina [42]

Dividing the given polynomial by (x -6) gives quotient Q(x) and remainder 5 then for Q(-6) = 3 , P(-6) = -31and P(6) =5.

As given in the question,

P(x) be the given polynomial

Dividing P(x) by divisor (x-6) we get,

Quotient = Q(x)

Remainder = 5

Relation between polynomial, divisor, quotient and remainder is given by :

P(x) = Q(x)(x-6) + 5 __(1)

Given Q(-6) = 3

Put x =-6 we get,

P(-6) = Q(-6)(-6-6) +5

⇒ P(-6) = 3(-12) +5

⇒ P(-6) =-36 +5

⇒ P(-6) = -31

Now x =6 in (1),

P(6) = Q(6)(6-6) +5

⇒ P(6) = Q(6)(0) +5

⇒ P(6) = 5

Therefore, dividing the given polynomial by (x -6) gives quotient Q(x) and remainder 5 then for Q(-6) = 3 , P(-6) = -31and P(6) =5.

The complete question is:

Dividing the polynomial P(x) by x - 6 yields a quotient Q(x) and a remainder of 5. If Q(-6) = 3, find P(-6) and P(6).

Learn more about polynomial here

brainly.com/question/11536910

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