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
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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Help! Now help! ASAP!I’ll make you brainly now please
Answer:
Day 2
Step-by-step explanation:
On Day 1, the temperature changed by 24.8 degress fahrenheit. On Day 2, the temperature changed by 32.94 fahrenheit which is more then Day 1.
Answer:
day two
Step-by-step explanation:
-11.31 + 13.49= 2.18
-7.69+ 25.25= 17.56
so day two because there's more distance in temp.
Which number produces an irrational number when added to 0.4?
If correct will award!
Answer: C. 3π
Step-by-step explanation:
Since pi is irrational, (even multiples of pi) if π is added to any number, the sum is irrational.
The other choices are not irrational numbers.
√9 is 3 0.4444 repeating is the decimal equivalent of 4/9
2/7 is a fraction, and by definition all fractions with integers in the numerator and denominator [except 0] are rational numbers.
Bria and Mandy each bought some candy Bria bought 5 packs of skittles for $9.75 Mandy bought 7 packs of skittles for $11.97
(5k − 1 + 2k3) − (6k3 − 3k2 − 8) + (8k3 − 2k2 − 7k)
Answer:
4k^3 + k^2 - 2k + 7
Step-by-step explanation:
Hope this helps, and good luck
Write and solve an equation to find the value of x and the missing angle measures
Answer:
in explanation
Step-by-step explanation:
angle rules say that those angles respond to each other meaning
they will equal each other
so 6x-4=4x+14
now solve for x
x=9
the top angle will be
6(9)-4=50
bottom angle will be 50
4(9)+14=50
Evaluate 2p - 3r + t for p = 10,
r = -4 and t = 5.
13
37
8
Answer:
37Step-by-step explanation:
[tex]2p - 3r + t[/tex]
p = 10
r = -4
t = 5
Substitute values into the given equation
[tex]2(10) - 3( - 4) + 5[/tex]
Simplify
[tex]20 + 12 + 5 \\ \\ = 37[/tex]
Megan buys paint for her artwork. The
graph shows the relationship between the
number of bottles of paint, x, she buys
and the ounces of paint, y, that she has.
y Bottles of Paint
20
15
Paint (ounces)
10
5
0
1 2 3 4
Number of Bottles
What is an equation in terms of x and y
that can be used to model the
proportional relationship?
Answer: y=5x
each 1 ounce of paint is 5 bottles.
Pls help 10th grade math
Answer:
B
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,
⇒ ∠Q ≅ ∠T
We have to given that,
Two triangles PQR and STU are shown in figure.
Now, We have;
⇒ PQ ≅ ST
⇒ ∠P ≅ ∠S
To show the congruency of triangle by using ASA congruent theorem, we need;
⇒ ∠Q ≅ ∠T
As, PQ = ST
Therefore, The correct option for the congruency of triangle by using ASA congruent theorem is,
⇒ ∠Q ≅ ∠T
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Parallel drainage pipes are connected with a third pipe. The connector pipe makes a 65 degree angle with a pipe as shown. What is the measure of the angle it makes with the pipe on the other side of the road. Explain.
Alex has a rectangular piece of red paper that is 4centimeters wide. It's length is twice it's width.she glues a rectangular piece of blue paper on top of the red piece measuring 3 centimeters by 7 centimeters how many square centimeters of red will be paper will be visible on top
Answer:
11 square centimeters
Step-by-step explanation:
1. find the area of the red paper
4 x 8 = 32
2. find the area of the blue paper
3 x 7 = 21
3. subtract area of the blue paper from area of the red paper
32 - 21 = 11
Show your work and write an expression by using these clues:
1. Write a number that is greater than 100, but smaller than 10,000
2. Divide that number by 10, 100 or 1,000
3. The quotient should be a number that is less than 100, but greater than 1
Answer: 10.1
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
Step 3: and 10.1 is less than 100 greater than 1
Answer:10.1
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
Step 3: and 10.1 is less than 100 greater than 1
Step-by-step explanation:
Five added to six times
a number w is the same
as the quotient of 32
and w.
Answer:
6w + 5 = 32/w
Step-by-step explanation:
6 times w = 6w
add 5 = 6w + 5
quotient = division = 32/w
If y varies directly as x, and y is 20 when x is 4, what is the constant of variation for this relation?
01 -
5
05
1
16
Answer:
5
Step-by-step explanation:
y
y=ax
where a is a constant of proportionality;
y=20, x=4
20=4a
a=20/4
a=5
y=5x
The constant of variation is 5
The constant of variation for the given relationship is 5.
What is Direct Variation?Direct variations are defined as the functions of the form y = kx, where k is a constant.
Here when y increases, x increases and if y decreases, x also decreases.
Given that,
y varies directly as x
So the equation will be of the form,
y = kx
Here k is the constant of variation.
Given, y is 20 when x is 4.
So, 20 = 4k
k = 20 / 4 = 5
Hence the constant of variation for the given relationship is 5.
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Find x if f(x) = 2x + 7 and f(x) = -1.
A.5
B.-4
C.-4
Answer:
x = - 4
Step-by-step explanation:
Hi there !
if f(x) = 2x + 7 and f(x) = -1 =>
2x + 7 = - 1
2x = - 1 - 7
2x = - 8
x = - 8 ÷ 2
x = - 4
Good luck !
how many miles can a airplane fly in 2 hours
Answer:
It depends on how many miles the airplane flew per mile. It also depends on atmospheric conditions specifically wind speed and direction.
0.007 divided by 10 equivalent to 0.07
Does 0.007/10=0.07
true or false?
Answer:
NO if you wanted to get 0.07 you would have to multiply not divide.
Step-by-step explanation:
0.007/10=0.0007
Find a function, g(x) that transform f (x) = 3 sqrt x by shifting f (x) right 3 units
Given
The function is
[tex]f(x)=3\sqrt{x}[/tex]
The function g(x) transform by shifting f(x) right 3 units.
To find:
The function g(x).
Step-by-step explanation:
The translation is defined as
[tex]g(x)=f(x+a)+b[/tex]
where, a is horizontal shift and b is vertical shift.
If a>0, then the graph shifts a units left and if a<0, then the graph shifts a units right.
If b>0, then the graph shifts b units up and if b<0, then the graph shifts b units down.
The function f(x) shifts only 3 units right. So,
[tex]a=-3,b=0[/tex]
Now,
[tex]g(x)=f(x+(-3))+0[/tex]
[tex]g(x)=f(x-3)[/tex]
[tex]g(x)=3\sqrt{x-3}[/tex] [tex][\because f(x)=3\sqrt{x}][/tex]
Therefore, the required function is [tex]g(x)=3\sqrt{x-3}[/tex].
area of a 18cm wide rectangle is 342 cm squared. what is the length?
3. The math department needs to buy new textbooks and laptops for their
classrooms. The textbooks cost $116.00 each and the laptops cost
$439.00 each. If they need to purchase 30 textbooks and have $6500
to spend, what is the greatest number of laptops they can buy?
Write an inequality and solve.
Let they be x.
Cost of textbooks + laptops cant greater than total amount.
(cost of 1 textbooks * number of textbooks) + (cost of 1 laptop * number of laptops ≤ 6500
(30*116) + (x*439) ≤ 6500
3480 + 439x ≤ 6500
439x ≤ 3020
x ≤ 6.8(approx)
Last natural number is 6, says, they can buy 6 laptops at max.
PLEASE HELP!!!!!!!!!! I HAVE BEEN ON THIS QUESTION FOR HOURS!!!! What is 1 + 1?
Answer:
it ius literally 2
Step-by-step explanation:
Answer:
21!
Step-by-step explanation: JK If you are fr 2
You spend $4.50 on 5 pounds of apples. What is the unit rate in dollars per pound?
Answer:
$0.90/pound
Step-by-step explanation:
4.5$ ÷ 5 pounds = $0.90 / pound
what is
3 3/5+(-1 4/9)+1/5
Answer: 2 and 16/45 or 2 (16/45)
Step-by-step explanation:brainlest please
is 2.35 the answer
PLEASE PLEASE HELP ME I WILL GIVE BRAINLIEST
Answer:
D
Step-by-step explanation:
-16p + 37 = 49 -21p
-16p +21p = 49 - 37
5p = 12
p = 12/5
A.
-55 + 12p = 5p + 16
7p = 71
p = 71/7
B.
2+1.25p = -3.75p +10
5p = 8
p = 8/5
C.
-14 + 6p = -9 -6p
12p = 5
p = 5/12
D.
1.5p - 5 + 2.25p = 7 - 1.25p
5p = 12
p = 12/5
Answer:
d
Step-by-step explanation:
ddddddddddddddddddddddddddddddddddddddddddddddddddddddddd
When we carry out a chi square test of Independence the alternate hypothesis states that the two relevant classification blank
Answer: that's false
Step-by-step explanation:
degrees of freedom=(r-1)(c-1)
If I'm wrong I'm sorry
In your own words, describe the negative property. Use complete sentences.
Answer:
The negative property is a sign used when a number goes below zero
Step-by-step explanation:
if that is the negative you are talking about
create a truth table for The Logical statement
9514 1404 393
Answer:
see below
Step-by-step explanation:
The not (~) changes T to F and vice versa.
The a→b implication is False for a=T and b=F, and true otherwise.
The soccer team can have no more than 26 players. How many more players can make the team if the coach has already chosen 12 players? Write an inequality where x represents the number of players
that can still be added to the team.
Answer: >14 I think
Explanation:
Simplify: (8 2/3)^4
Answer:
8^8/3
Step-by-step
A tennis racket normally costs $70. The tennis racket is on sale for 30% off. What is the sale price of the tennis racket?
What is a good topic to research for linear regression?
Answer:
Growth rate of plants compared to average daily temperature.
Step-by-step explanation: