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3 years ago

Plz answer hurry. 20 points for right answer

Mathematics

2 answers:

BlackZzzverrR [31]3 years ago

8 0

First, we need to define the function of (fog)(x)
(fog)(x) = f(g(x))
it means we need to substitute the x in the function f(x) with g(x)

f(x) = x + 7
change x with g(x)
fog(x) = g(x) + 7
fog(x) = $\cfrac{1}{x-13}$ + 7

equalize the denominators
fog(x) = $\cfrac{1}{x-13}$ + 7
fog(x) = $\cfrac{1}{x-13}+\cfrac{7(x-13)}{x-13}$

simplify
fog(x) = $\cfrac{7x-91+1}{x-13}$
fog(x) = $\cfrac{7x-90}{x-13}$

Second, determine the domain of the function
If the function is in fraction form, the denominator of the fraction can't be equal to zero.
x - 13 ≠ 0
x ≠ 13
The domain is {x| x≠13}
The answer is last option

lapo4ka [179]3 years ago

3 0

Did You Figure This Out I Need Help Too. Lol

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the performing arts department put in its spring show on Friday and Saturday nights. the price of a ticket was the same both nig

Galina-37 [17]

Let $p=$ the price of a ticket
Let $c=$ the cost to put on the show

Formula:
(profit) = (ticket price) * (number of people) - (cost to put on show)
We have two equations here:
$500=120p-c$
$400=100p-c$
Solve:
$100=20p$
⇒ $p=5$
⇒ $400=100(5)-c$
⇒ $400=500-c$
⇒ $c=100$

So the price of a ticket is $5, and the cost to put on the show is $100.

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3 years ago

I need help i don’t know the answer

Julli [10]

Answer:

3x - 4 and 2x + 15

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers

A company manufactures and sells x television sets per month. The monthly cost and price-demand equations are C(x)equals72 com

solmaris [256]

Answer:

Part (A)

1. Maximum revenue: $450,000

Part (B)

2. Maximum protit: $192,500

3. Production level: 2,300 television sets

4. Price: $185 per television set

Part (C)

5. Number of sets: 2,260 television sets.

6. Maximum profit: $183,800

7. Price: $187 per television set.

Explanation:

0. Write the monthly cost and price-demand equations correctly:

Cost:

$C(x)=72,000+70x$

Price-demand:

$p(x)=300-\dfrac{x}{20}$

Domain:

$0\leq x\leq 6000$

1. Part (A) Find the maximum revenue

Revenue = price × quantity

Revenue = R(x)

$R(x)=\bigg(300-\dfrac{x}{20}\bigg)\cdot x$

Simplify

$R(x)=300x-\dfrac{x^2}{20}$

A local maximum (or minimum) is reached when the first derivative, R'(x), equals 0.

$R'(x)=300-\dfrac{x}{10}$

Solve for R'(x)=0

$300-\dfrac{x}{10}=0$

$3000-x=0\\\\x=3000$

Is this a maximum or a minimum? Since the coefficient of the quadratic term of R(x) is negative, it is a parabola that opens downward, meaning that its vertex is a maximum.

Hence, the maximum revenue is obtained when the production level is 3,000 units.

And it is calculated by subsituting x = 3,000 in the equation for R(x):

R(3,000) = 300(3,000) - (3000)² / 20 = $450,000

Hence, the maximum revenue is $450,000

2. Part (B) Find the maximum profit, the production level that will realize the maximum profit, and the price the company should charge for each television set. 

i) Profit(x) = Revenue(x) - Cost(x)

Profit (x) = R(x) - C(x)

$Profit(x)=300x-\dfrac{x^2}{20}-\big(72,000+70x\big)$

$Profit(x)=230x-\dfrac{x^2}{20}-72,000\\\\\\Profit(x)=-\dfrac{x^2}{20}+230x-72,000$

ii) Find the first derivative and equal to 0 (it will be a maximum because the quadratic function is a parabola that opens downward)

Profit' (x) = -x/10 + 230

-x/10 + 230 = 0

-x + 2,300 = 0

x = 2,300

Thus, the production level that will realize the maximum profit is 2,300 units.

iii) Find the maximum profit.

You must substitute x = 2,300 into the equation for the profit:

Profit(2,300) = - (2,300)²/20 + 230(2,300) - 72,000 = 192,500

Hence, the maximum profit is $192,500

iv) Find the price the company should charge for each television set:

Use the price-demand equation:

p(x) = 300 - x/20

p(2,300) = 300 - 2,300 / 20

p(2,300) = 185

Therefore, the company should charge a price os $185 for every television set.

3. Part (C) If the government decides to tax the company $4 for each set it produces, how many sets should the company manufacture each month to maximize its profit? What is the maximum profit? What should the company charge for each set?

i) Now you must subtract the $4 tax for each television set, this is 4x from the profit equation.

The new profit equation will be:

Profit(x) = -x² / 20 + 230x - 4x - 72,000

Profit(x) = -x² / 20 + 226x - 72,000

ii) Find the first derivative and make it equal to 0:

Profit'(x) = -x/10 + 226 = 0

-x/10 + 226 = 0

-x + 2,260 = 0

x = 2,260

Then, the new maximum profit is reached when the production level is 2,260 units.

iii) Find the maximum profit by substituting x = 2,260 into the profit equation:

Profit (2,260) = -(2,260)² / 20 + 226(2,260) - 72,000

Profit (2,260) = 183,800

Hence, the maximum profit, if the government decides to tax the company $4 for each set it produces would be $183,800

iv) Find the price the company should charge for each set.

Substitute the number of units, 2,260, into the equation for the price:

p(2,260) = 300 - 2,260/20

p(2,260) = 187.

That is, the company should charge $187 per television set.

7 0

3 years ago

Barbara, Mark, and Carlos participated in the third heat of “The Big Race”. Barbara thought she could win with a 3 meter head st

steposvetlana [31]

Distance to travel = 20 m.
Let us determine the time, t, that each participant took to complete 20 m.

Barbara:
Average speed = (3 m)/(2 s) = 1.5 m/s
t = 20/1.5 = 13.3 s

Mark:
t = 5 s

Carlos:
y = x + 1
where
y = 20 m
x = time, t
Therefore
t =x = y - 1 = 20 - 1 = 19 s

Summary:
Barbara: 13.3 s
Mark: 5 s
Carlos: 19 s

Answer:
The winner is Mark

7 0

4 years ago

How is a finance charge calculated

GuDViN [60]

Answer:

option A. Multiply the unpaid balance by the monthly interest rate

Step-by-step explanation:

Finance charges are the monthly service fee charged by lender on the credit used by borrower if they wish to skip the payment of monthly bill and carry forward it to next month.

So, we can calculate finance charges as monthly interest accrued on the unpaid balance.

Finance charges = Unpaid balance x Monthly interest rate.

Hence, option A is correct, i.e. Multiply the unpaid balance by the monthly interest rate.

6 0

4 years ago