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svetoff [14.1K]
2 years ago
6

3.The monopolist faces a demand curve given by D(p) = 10p-3 . Its cost function is c(y) = 2y. What is its optimal level of outpu

t and price?.
Mathematics
1 answer:
shusha [124]2 years ago
5 0
<span>-> R (y) = (10y -3) 2y = 20y² - 6y -> R' (y) = 40y - 6 Optimal level of output when R' (y) = C'(y) -> 40y - 6 = 2 => 40y = 8 => y = 8/40 = .2 by using differential calculus w got its optimal level and price</span>
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Given that a function, g, has a domain of -1 ≤ x ≤ 4 and a range of 0 ≤ g(x) ≤ 18 and that g(-1) = 2 and g(2) = 8, select the st
notka56 [123]

Options

  • (A)g(5) = 12
  • (B)g(1) = -2
  • (C)g(2) = 4
  • (D)g(3) = 18

Answer:

(D)g(3) = 18

Step-by-step explanation:

Given that the function, g, has a domain of -1 ≤ x ≤ 4 and a range of                       0 ≤ g(x) ≤ 18 and that g(-1) = 2 and g(2) = 8

Then the following properties must hold

  1. The value(s) of x must be between -1 and 4
  2. The values of g(x) must be between 0 and 18.
  3. g(-1)=2
  4. g(2)=9

We consider the options and state why they are true or otherwise.

<u>Option A: g(5)=12</u>

The value of x=5. This contradicts property 1 stated above. Therefore, it is not true.

<u>Option B: g(1) = -2 </u>

The value of g(x)=-2. This contradicts property 2 stated above. Therefore, it is not true.

<u>Option C: g(2) = 4 </u>

The value of g(2)=4. However by property 4 stated above, g(2)=9. Therefore, it is not true.

<u>Option D: g(3) = 18</u>

This statement can be true as its domain is in between -1 and 4 and its range is in between 0 and 18.

Therefore, Option D could be true.

3 0
2 years ago
The box office took in a total of $2905 in paid admissions for the high-school musical. Adult tickets cost $8 each, and student
Svet_ta [14]
There are no equations to choose from but it should look like the following.

a= # of adult tickets
s= # of student tickets

QUANTITY EQUATION
a + s= 560

COST EQUATION
$8a + $3s= $2905

***If you have to also solve for the number of adults and students, here are the steps.

STEP 1:
multiply quantity equation by -8

-8(a + s)= -8(560)
-8a - 8s= -4480

STEP 2:
add cost equation and step 1 equation

$8a + $3s= $2905
-8a - 8s= -4480
a term cancels out to zero
-5s= -1575
divide both sides by -5
s= 315 students

STEP 3:
substitute s=315 in quantity equation
a + s= 560
a + 315= 560
subtract 315 from both sides
a= 245 adults

ANSWER:
Quantity Equation
a + s= 560

Cost Equation
$8a + $3s= $2905

Hope this helps! :)
7 0
2 years ago
Each airline passenger and his or her luggage must be checked to determine whether he or she is carrying weapons on to the airpl
Dafna1 [17]

Answer:

a

P_k  = 0.83

b

 N_{\mu} \approx  4 \ passengers

c

T_{\lambda} =  0.5 \ minutes

Step-by-step explanation:

From the question we are told that

The average number of passengers that arrive per minute is \lambda = 10

The average number of check that can be carried out in one minute is \mu= 12

Generally the probability that a passenger will have to wait before being checked for weapons is mathematically represented as

        P_k  = \frac{\lambda }{ \mu }

=>    P_k  = \frac{10 }{ 12}

=>    P_k  = 0.83

Generally the number of passengers are waiting in line to enter the checkpoint is mathematically represented as

     N_{\mu} =  \frac{\lambda^2}{\mu (\mu -\lambda) }

=>  N_{\mu} =  \frac{10^2}{12 (12 -10) }

=>  N_{\mu} \approx  4 \ passengers

Generally the average time a passenger spend at the checkpoint is mathematically represented as

      T_{\lambda} = \frac{ \frac{\lambda}{(\mu - \lambda)} }{ \lambda}

=>   T_{\lambda} = \frac{ \frac{ 10}{(12 - 10)} }{10}

=>   T_{\lambda} =  0.5 \ minutes

5 0
1 year ago
Mike is preparing refreshments for a party. To make a smoothie, he will mix 3 1⁄2 quarts of strawberry puree with 2 pints of lem
Shkiper50 [21]
Let's convert all volumes into pint:

1 Quart  = 2 pints → 3.5 quart of strawberry = 2 x 3.5 = 7 pints Strawberry
1 Gallon = 8 pints →1.25 Ga. water = 1.25 x 8 = 10 pints Water
2 pints of limonade = 2 pints of limonade 

Add up all pints Total = 7+10+2 = 19 pints of smoothie

Or in quart 9.5

Or in Gal 2.375

7 0
2 years ago
Read 2 more answers
suppose you could make a single "lump sum" deposit of $3679, in an investment that provides an annual percentage rate(apr) of 4%
yaroslaw [1]

Answer:

\$5,698.30  

Step-by-step explanation:

The compound interest formula is equal to  

A=P(1+\frac{r}{n})^{nt}  

where  

A is the Final Investment Value  (future value)

P is the Principal amount of money to be invested  

r is the rate of interest  in decimal

t is Number of Time Periods  

n is the number of times interest is compounded per year

in this problem we have  

t=11\ years\\ P=\$3,679\\ r=4\%=4/100=0.04\\n=365  

substitute in the formula above

A=3,670(1+\frac{0.04}{365})^{365*11}  

A=\$5,698.30  

3 0
2 years ago
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