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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2. A university dean is interested in determining the proportion of students who receive some sort of financial aid. Rather than examine the records for all students, the dean randomly selects 200 students and finds that 118 of them are receiving financial aid. If the dean wanted to estimate the proportion of all students receiving financial aid to within 3% with 99% reliability, how many students would need to be sampled?
Answer:
The number of students to be sampled is [tex]n = 1789 [/tex]
Step-by-step explanation:
From the question we are told that
The margin of error is E = 0.03
Generally the proportion of students that receive financial aid is mathematically represented as
[tex]\^ p = \frac{118 }{200}[/tex]
=> [tex]\^ p = 0.59[/tex]
From the question we are told the confidence level is 99% , hence the level of significance is
[tex]\alpha = (100 - 95 ) \%[/tex]
=> [tex]\alpha = 0.05[/tex]
Generally from the normal distribution table the critical value of [tex]\frac{\alpha }{2}[/tex] is
[tex]Z_{\frac{\alpha }{2} } = 2.58 [/tex]
Generally the sample size is mathematically represented as
[tex]n = [\frac{Z_{\frac{\alpha }{2} }}{E} ]^2 * \^ p (1 - \^ p ) [/tex]
=> [tex]n = [\frac{2.58}{0.03} ]^2 * 0.59(1 - 0.59) [/tex]
=> [tex]n = 1789 [/tex]
Using the margin of error, it is found that 1033 students would need to be sampled.
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the z-score that has a p-value of [tex]\frac{1+\alpha}{2}[/tex].The margin of error is of:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
The dean randomly selects 200 students and finds that 118 of them are receiving financial aid, hence, the estimate is:
[tex]\pi = \frac{118}{200} = 0.59[/tex]
99% confidence level
So [tex]\alpha = 0.99[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.99}{2} = 0.995[/tex], so [tex]z = 2.575[/tex].
The sample size needed is n when M = 0.03, hence:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.03 = 1.96\sqrt{\frac{0.59(0.41)}{n}}[/tex]
[tex]0.03\sqrt{n} = 1.96\sqrt{0.59(0.41)}[/tex]
[tex]\sqrt{n} = \frac{1.96\sqrt{0.59(0.41)}}{0.03}[/tex]
[tex]\sqrt{n}^2 = \left(\frac{1.96\sqrt{0.59(0.41)}}{0.03}\right)^2[/tex]
[tex]n = 1032.5[/tex]
Rounding up, it is found that 1033 students would need to be sampled.
A similar problem is given at https://brainly.com/question/25420216
Heellllpppp plzzzzzzzzzzz
Answer:
3/32
Step-by-step explanation:
the reason it’s 3/32 is because you have to divide 3/4 divide by 8. So that means 3/4x1/8 and that gives you 3/32. I hope that helped you!
2 and 1 over 4 divided by 4 and 3 over 8?
Answer:
42
43
Step-by-step explanation:
that just the answer
In the equation 3j = 75 + 9, what is the next step in the equation solving sequence?
Answer:
Combine 75 and 9
Step-by-step explanation:
3j = 75 + 9
Combine like terms
3j = 84
Answer:
3j = 75+9
3j = 84
j = 84/3
j = 28
The next step is to add, you are adding 75+9.
The value of the the expression:
50 times the sum of 64 and 36?
3,236
2,354
4,104
5,000
Answer:
5000
Step-by-step explanation:
Let's start by evaluating what we are given. 50 times the sum of 64 and 36. Ok, so 50 times which is the way to write x (multiply) and the sum of 64 and 36 is another way to write 64 + 36.
Lets put this together now!
50 x ( 64 + 36 ) = 50 x ( 100 )
= 5000
A 4 2/4
ounce package of trail mix contains nuts and dried fruit. There are
2 3/4 ounces of nuts in the trail mix. How many ounces of dried fruit are in the trail mix
are in the trail mix?
Answer:
1 3/4 ounces of dried fruit.
Step-by-step explanation:
4 2/4 - 2 3/4 is equal to 7/4. 7/4 simplified is 1 3/4.
Emily is saving up to buy a new phone. She already has $75 and can save an additional $7 per week using money from her after school job. How much total money would Emily have after 4 weeks of saving? *
Anwser - 103$$$$$$$$$$$$$$$$
Answer:$28
Step-by-step explanation: 7 x 4
***INCORRECT***
What is the distance between 2 and 3 on the number line? Write the integer only. *
Answer:
1
Step-by-step explanation:
The distance between any two numbers on the number line is their difference:
3 - 2 = 1
_____
Any two consecutive integers have a distance between them of 1 on the number line.
Eva is reading a book that is 400 pages.She has read 336 pages so far.What percentage of the book does she have left to read?
Plz tell me the answer I need helpp
Answer:
Eva has 16% of the book left to read
Step-by-step explanation:
Answer:
16%
Step-by-step explanation:
400-336=64
64÷400= 0.16
0.16x100=16
16% is your answer
Which of the following coordinates exists on the line y = 2x - 4?
O A. (1,-2)
O B. (-1,2)
O C. (-3,-5)
O D. (2,-4)
(1, -2) is the coordinates that exists on the line y = 2x - 4
What is an equation?An equation is a mathematical statement that shows that two mathematical expressions are equal.
Given is an equation of a line, we need to find that on which of the given points it lies,
So, we will put the points one by one, the point which stratify the equation will be the answer.
The equation :- y = 2x-4
1) (1, -2)
Put x = 1, y = -2 in the equation,
2(1)-4
= 2-4 = -2
LHS = RHS
Since, point (1, -2) satisfy the equation therefore, the line will pass through it.
Hence, (1, -2) is the coordinates that exists on the line y = 2x - 4
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please help with this question
whats 8+0 lol
njxzzzzzzzzzzzzzaK
Answer:
8
Step-by-step explanation:
6299 round to neaRest hundred
Answer:
6300
Step-by-step explanation:
plz give me a harder answer next time :)
What is the quotient? (6x10) divided (1.5 x 10-4)
Answer:
5.4 hope this help
According to Siri every 5 inches of the map represents 3 miles of trails in the park how many inches on the map represents 9 miles on the park trails
Answer:
15 inches
Step-by-step explanation:
If 3 miles represents 5 inches and you want to know what represents 9 miles Just multiply 5*3 to get 15
Study the grid closely and name the ordered pairs of the 4 red points A, B, C, D on this coordinate system. Will the line joining A &
B pass through D? How would you prove that it does or does not? Answer in the discussion below!
9514 1404 393
Answer:
A(0, 0), B(1, 1), C(5, 1), D(8, 7)no; Dx ≠ DyStep-by-step explanation:
1) Upon studying the grid, we see that A is at the intersection of the x- and y-axes, and that all of the other points are in the first quadrant. The distance between minor grid lines in either direction is taken to be 1 unit. That is, B is 1 unit right and 1 unit up from A(0, 0), so has coordinates B(1, 1).
The coordinates of C and D can be found by counting grid lines. We find them to be C(5, 1) and D(8, 7).
__
2) The line joining A and B is a line whose points have their x-coordinate equal to their y-coordinate. The coordinates of D are not equal, so will not be on that line.
What would the phrase "three times the sum of a number and 4" look like as a
variable expression?
3x +4
O3(3x +4)
O3(x + 4)
3x -4
A recipe for 1 batch of spice mix says, “Combine 3 teaspoons of mustard seeds, 5 teaspoons of chili powder, and 1 teaspoon of salt." How many batches are represented by the diagram? mustard seeds (tsp) chili powder (tsp) salt (tsp)
you need to put a picture again
sorry i cant answer because it doesnt show diagram
Let f(x)=2x+ 3 find f (2b)
Answer:
14
Step-by-step explanation:
Answer:
4b +3
Step-by-step explanation:
you would replace f(x) with f(2b), so
f(2b) = 2(2b)+3
4b +3
Can someone please help. I'm offering a lot of points because this answer needs an explanation. Statement proof style would be helpful, but it's not totally needed
Answer:
See below
Step-by-step explanation:
Given∠A ≅ ∠B and CD⊥ABTo prove CD bisects ∠ACBSolutionAs CD⊥AB, ∠BDC = ∠ADC = 90°
∠BDC ≅ ∠ADC
∠BCD = 180 - (∠BDC + ∠DBC)and
∠ACD = 180 - (∠ADC + ∠DAC)We can substitute ∠ADC with ∠BDC and ∠DAC with ∠DBC
Then we get same equation for ∠BCD and ∠ACD
Therefore ∠BCD = ∠ACD = 1/2∠ACB
It proves that CD bisects ∠ACB
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
A dog trainer is trying to find a triangular area behind his house that encloses 1800 square feet for his dog to run. He has the first two fence posts at (6, 0) and at (0, 25). The final fence post is on the property line at x = 30. Find the point where the trainer can place the final fence post.
Answer:
[tex]C = (30,500)[/tex]
Step-by-step explanation:
Given
[tex]Area = 1800ft^2[/tex]
[tex]A = (6,0)[/tex]
[tex]B = (0,25)[/tex]
[tex]C(x,y) = (30,y)[/tex]
Required
Determine the coordinates of C
The area of triangle is calculated as thus:
[tex]Area = \frac{|A_x(B_y - C_y) + B_x(C_y - A_y) + C_x(A_y - B_y)|}{2}[/tex]
This gives:
[tex]1800= \frac{|6(25 - y) + 0(y - 0) + 30(0 - 25)|}{2}[/tex]
[tex]1800= \frac{|6(25 - y) + 30(0- 25)|}{2}[/tex]
[tex]1800= \frac{|6(25 - y) + 30(-25)|}{2}[/tex]
[tex]1800= \frac{|150 - 6y -750 |}{2}[/tex]
[tex]1800= \frac{|150 -750- 6y |}{2}[/tex]
[tex]1800= \frac{|-600- 6y |}{2}[/tex]
Multiply through by 2
[tex]2 * 1800= |-600- 6y|[/tex]
[tex]3600= |-600- 6y|[/tex]
[tex]3600= |-(600+ 6y)|[/tex]
[tex]3600= 600+ 6y[/tex]
Solve for 6y
[tex]6y = 3600 - 600[/tex]
[tex]6y = 3000[/tex]
Solve for y
[tex]y = 3000/6[/tex]
[tex]y = 500[/tex]
Hence:
The point is:
[tex]C = (30,500)[/tex]
Zoé compró 3 quesos de 3/5 cada uno. ¿cuántos Kilogramos de queso tiene en total?
Answer:
Huh?
Step-by-step explanation:
?
Determine the intercepts of the line
X-intercept: (__ , __)
Y-intercept: (__, __)
Answer:
x-int: (-1.2, 0)
y-int: (0, -0.7)
Step-by-step explanation:
The x-intercept is the x value when y = 0.
Another way to reword that is when the graph crosses the x-axis.
The y-intercept is the y value when x = 0.
Another way to reword that is when the graph crosses the y-axis.
According to the graph, when y = 0 and when the line crosses the x-axis, the x-value is -1.2. Therefore, our x-intercept is (-1.2, 0).
According to the graph, when x = 0 and when the line crosses the y-axis, the y-value is -0.7. Therefore, our x-intercept is (0, -0.7).
Rewrite as a square or a cube:
0.001
Answer:
10^-3*1/3 = 10^-1=0.1
Tamara has $30,000, part or all of which she wants to invest into a combination of corporate bonds and municipal bonds. She wants to invest no less than $8,000 into corporate bonds, and at least three times as much into corporate bonds than into municipal bonds. Let x be the amount invested in corporate bonds, and let y be the amount invested in municipal bonds. Which system of inequalities describes Tamara’s investment options?
Answer:
The system of inequalities describes Tamara’s investment options are as follows:
[tex]8000\leq x[/tex]
[tex]3y\leq x[/tex]
Step-by-step explanation:
Total amount with Tamara = $30,000
Let [tex]x[/tex] be the amount invested in corporate bonds, and let [tex]y[/tex] be the amount invested in municipal bonds.
She wants to invest no less than $8,000 into corporate bonds.
So, the inequality is [tex]8000\leq x[/tex]
Also, she wants to invest at least three times as much into corporate bonds than into municipal bonds.
[tex]3y\leq x[/tex]
The system of inequalities describes Tamara’s investment options are as follows:
[tex]8000\leq x[/tex]
[tex]3y\leq x[/tex]
Find the number such that the sum of that number and 25 is 48
Answer:
x = 23
Step-by-step explanation:
x + 25 = 48
x = 23....
Answer:
23
Step-by-step explanation:
You subtract 25 from 48
48 - 25 = 23
your thinking
2. A shipping box should weigh 1.0 pound. If
there is a 10% error on the weight, what is the
range of acceptable weight?
Answer:
.9 pounds to 1.1 pounds
Step-by-step explanation:
10% of 1.0 is .1, so it allows for a .1 addition or subtraction to the weight of the box
Answer:
the answer is 0.9-1.0
Step-by-step explanation:
the answer is that because my teacher gave me the answer
∠A and ∠ B ∠B are vertical angles. If m ∠ A = ( 5 x − 4 ) ∘ ∠A=(5x−4) ∘ and m ∠ B = ( 2 x − 1 ) ∘ ∠B=(2x−1) ∘ , then find the value of x.
Answer:
x=1
Step-by-step explanation:
vertical angles are equal
therefore a=b
5x-4=2x-1= 3x=3
x=1
help ????????!???????????!???????
Answer:
1/8= 12.50
1/4 =250 apologize for not being able to answer the last one
