A dance studio has fixed monthly costs of $1500 that include rent, utilities, insurance, and advertising. The studio charges $60 for each private lesson but has a variable cost for each lesson of $35 to pay the instructor.

Answers

Answer 1

Answer:

a)C(x)=1500+35x

b)R(x)=60 x

c)P(x)=25x-1500

d)The number of lessons that must be held for the studio to break even ia 60

e)The studio will make 550 if 82 lessons are held

Step-by-step explanation:

Monthly cost that include rent, utilities, insurance, and advertising = $1500

The studio charges $60 for each private lesson but has a variable cost for each lesson of $35 to pay the instructor.

a)Write a linear cost function representing the cost to the studio C(x) to hold x private lessons  for a given month

Fixed monthly cost = $1500

Variable cost of trainer for each lesson = $35

Variable cost of trainer for x lessons = 35x

So, C(x)=1500+35x

b)Write a linear revenue function representing the cost to the revenue R(x) to hold x private lessons  for a given month

Charge for 1 lesson = 60

Charge for x lessons = 60 x

So, R(x)=60 x

c)Write a linear profit function representing the cost to the profit P(x) to hold x private lessons  for a given month

Profit = Revenue - Cost

P(x)=R(x)-C(x)

P(x)=60x-1500-35x

P(x)=25x-1500

d)Determine the number of lessons that must be held for the studio to break even

R(x)=C(x)

60x=1500+35x

25x=1500

x=60

So, the number of lessons that must be held for the studio to break even ia 60

e) If 82 lessons are held during a month how much money will the studio make or lose

P(x)=25x-1500

P(82)=25(82)-1500

P(82)=550

So, The studio will make 550 if 82 lessons are held

Answer 2

1)Profit function P(p)=25p-1500

2) For the break-even number of lessons to be held is 60 lessons.

3)Profit, when 82 sessions are held is $550.

The fixed monthly cost of the dance studio= $1500

The variable cost of the trainer for each lesson = $35

So, Variable cost of trainer for 'p' lessons = 35a

So, Total cost =1500+35p

Charge for 1 private lesson = 60

Charge for 'p' lessons = 60p

So, Revenue =60p

We know that, Profit = Revenue - Cost

So, Profit =60p-(1500+35p)

Profit=25p-1500

What is the break-even point?

The break-even point is the point at which total cost and total revenue are equal.

For break-even

Cost = Revenue

1500+35p = 60p

p =60

So, for the break-even number of lessons to be held = 60 lessons

Profit when 82 sessions are held

Profit = 25p-1500

Profit = 25*82-1500

Profit = $550

Therefore, 1)Profit function P(p)=25p-1500

2) For the break-even number of lessons to be held is 60 lessons.

3)Profit, when 82 sessions are held is $550.

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Answers

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Step-by-step explanation:

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Answers

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Step-by-step explanation:

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Answers

Answer:

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Step-by-step explanation:

[tex]2p - 3r + t[/tex]

p = 10

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[tex]2(10) - 3( - 4) + 5[/tex]

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Answers

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Step-by-step explanation:

each side is corresponded to the other so Q=U and P=S

The correct option for the congruency of triangle by using ASA congruent theorem is,

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Answers

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Answers

Answer:

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Step-by-step explanation:

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Answers

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Step-by-step explanation:

Step 1:  1,000 is greater than 100 but smaller then

Step 2:  10,000     1,000 is divided by 10,100 which =10.1                                                                  

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Step-by-step explanation:

Step 1:  1,000 is greater than 100 but smaller then

Step 2:  10,000     1,000 is divided by 10,100 which =10.1                                                                  

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Step-by-step explanation:

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Answers

Answer:

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Step-by-step explanation:

6 times w = 6w

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Answers

Answer:

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Step-by-step explanation:

y

y=ax

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What is Direct Variation?

Direct variations are defined as the functions of the form y = kx, where k is a constant.

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Answers

Answer:

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Step-by-step explanation:

Hi there !

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Answers

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Answers

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Step-by-step explanation:

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Answers

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Step-by-step explanation:

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Answers

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Answers

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Answers

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Step-by-step explanation:

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B.

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Answer:

d

Step-by-step explanation:

ddddddddddddddddddddddddddddddddddddddddddddddddddddddddd

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Step-by-step explanation:

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If I'm wrong I'm sorry  

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Answers

Answer:

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Step-by-step explanation:

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