1. Suppose that a theater charges a school group $4.50 per student to show a special film. Suppose that the theater's operating expenses include $130 for the staff and a film rental fee of $1.25 per student.
a. What equation relates the number of students x to the theater's income I?
b. What equation relates the theater's operating expenses E to the number of students x?
c. Copy and complete the table below.
Theater Income and Expenses
Number of Students, x 0 10 20 30 40 50 60 70
Income, I ($) box box box box box box box box
Expenses, E ($) box box box box box box box box
d. On the same set of axes, graph the theater's income and operating expenses for any number of students from 0 to 100.
e. Describe the patterns by which income and operating expenses increase as the number of students in a group increases.
f. Write and solve an equation that you can use to answer the question “How many students need to attend the movie so that the theater's income will equal its operating expenses?”
g. Write an equation that represents the theater's profit. Compare your equation to those your classmates wrote.
h. Find the number of students that make each of the following inequality statements true.
i. E < 255
ii. I > 675
Answers
The functions I(x) and E(x) of the theatre's income and expenses are illustrations of linear functions.
The equation of the theatre's incomeThe theatre charges $4.50 per student.
Assume the number of students is x, the equation of the theatre's income would be:
I(x) = 4.5x
The equation of the theatre's expensesThe theatre expense per student is $1.25, and the operating cost on the staff is $130
The equation of the theatre's expenses would be:
E(x) = 1.25x + 130
Complete the tableUsing the formulas I(x) = 4.5x and E(x) = 1.25x + 130, the complete table is:
Students, x 0 10 20 30 40 50 60 70
Income, I 0 45 90 135 180 225 270 315
Expenses, E 130 142.5 155 167.5 180 192.5 205 217.5
The graph of the theatre's income and expensesSee attachment
The pattern by which theatre's income and expenses increaseThe functions I(x) and E(x) are linear functions.
So, the pattern with which the functions increase is a linear pattern.
The number of students when the theatre's income and expenses are equal
This means that:
I(x) = E(x)
So, we have:
4.5x = 1.25x + 130
Subtract 1.25 from both sides
3.25x = 130
Divide both sides by 3.25
x = 40
Hence, the number of students is 40
The theatre profitThis is the difference between the theatre expenses and their income.
So, we have:
P(x) = E(x) - I(x)
This gives
P(x) = 1.25x + 130 - 4.5x
Simplify
P(x) = 130 - 3.25x
Solution to the inequalitiesWe have:
E(x) < 255
This gives
1.25x + 130 < 255
Subtract 130 from both sides and divide by 1.25
x < 100 students
Also, we have:
I(x) > 675
This gives
4.5x > 657
Solve for x
x > 146 students
Hence, the number of students for the inequalities are less than 100 and greater than 146
Read more about linear equations and inequalities at:
https://brainly.com/question/11234618
Related Questions
What is the degree of 9x^3?
9x to the power of 3.
Answers
The largest exponent is the degree.
this only has one exponent so the degree would be 3
A sample of bacteria cells in a petri dish increases by 50% every hour. A scientist starts with a sample of 30 bacteria cells. Write an equation that can be used to determine the number of cells after x hours
Answers
Answer:
divide fifty out of one hundred times thirty. so x equals to fifteen hours
-
nd
According to the line of best fit, about how many words
will Jean have typed when she completes 60 minutes of
typing?
0 2,500
o 2,750
3,000
O
3,250
Answers
Answer:
C. 3000
Step-by-step explanation:
i took the quiz!
also 60 and 3000 line up
Answer:
C 3,000
Step-by-step explanation: It's right on Edge
A small theater had 6 rows of 24 chairs each. Workers just removed 7 of these chairs. How many chairs are left? chairs
Answers
144 - 7 = 137
There is 137 chairs left in the theater. Hope this helps!
Answer:
137 chairs
Step-by-step explanation:
6*24=144.
144-7=137.
please mark as brainliest.
The perimeter of a quarter circle is 10. 71 yards. What is the quarter circle's radius?
Use 3. 14 for
Answers
Answer:
r = 3 yds
Step-by-step explanation:
The perimeter of a quarter circle is 1/4 of a circumference of the circle AND two straight edges that are the length of the radius. see image.
The circumference is given and using 3.14 for pi, we'll then solve for r. see image.
What is the distance between the points (8, 12) and (1, 3)? If necessary, round
your answer to two decimal places.
O A. 130 units
B. 11.40 units
C. 12.08 units
D. 146 units
Answers
Answer:
B
Step-by-step explanation:
(8,12)=(x1, y1)
(1,3)=(X2, y2)
distance=√(x2-x1)^2+(y2-y1)^2
=√(1-8)^2+(3-12)^2
=√(49+81)
√130
=11.40
I need help with this please extra points for the help.
Answers
Answer:
1/3
explanation:
there are total 6 colour boxes.among which 2 are redso probability:
2/61/3[tex]\qquad\qquad\huge\underline{{\sf Answer}}♨[/tex]
Number of Favorable outcomes (red)= 2
Total outcomes = 6
So, the probability of getting red is :
[tex]\qquad \sf \dashrightarrow \: \dfrac{2}{6} [/tex]
[tex]\qquad \sf \dashrightarrow \: \dfrac{1}{3} [/tex]
[tex]・ ．━━━━━━━†━━━━━━━━━．・[/tex]
Find the derivative of 30x² + 7x at x = 2.
Answers
Answer:
127
Step-by-step explanation:
Given :
30x² + 7xOn differentiating,
dy/dx = 2 * 30 * x²⁻¹ + 1 * 7 * x¹⁻¹dy/dx = 60x + 7At x = 2
60(2) + 7120 + 7127First differentiate
d/dx(x^n)=nx^n-1So
[tex]\\ \rm\Rrightarrow \dfrac{d}{dx}(30x^2+7x)[/tex]
[tex]\\ \rm\Rrightarrow 60x+7[/tex]
Put x=2
60(2)+7120+7127what if the ice caps were melting even more rapidly and san francisco was losing about 2% of its land area per year as land and streets went under water. the city is only about 49 square miles in area
Answers
The exponential function that shows San Francisco area after x years is y = 49(0.98)ˣ
What is an exponential function?
An exponential function is in the form:
y = abˣ
Where a is the initial value of y and b is the multiplication factor.
Let y represent the land area of San Francisco after x years. Hence:
The city is only about 49 square miles in area, a = 49. It is losing 2% yearly, hence b = 100% - 2% = 0.98
The equation becomes y = 49(0.98)ˣ
Find out more on exponential function at: https://brainly.com/question/12940982
Lena got a prepaid debit card with $30 on it. For her first purchase with the card, she bought some bulk ribbon at a craft store. The price of the ribbon was 19 cents per yard. If after that purchase there was $27.15 left on the card, how many yards if ribbon did lena buy?
Answers
Step-by-step explanation:
To find out how much she spent:
30 - 27.15 = 2.85
Change it to cents:
2.85 x 100 = 285 cents
Calculate how many yards of ribbon she bought:
285 / 19 = 15
Therefore, she bought 15 yard of ribbon.
63.625 rounded to the nearest tenth
Answers
Answer:
63.6
Step-by-step explanation:
63.625
63.6
Answer:
63.6
Step-by-step explanation:
The tenth's place is one after the decimal point, and since 2 is closer to zero than ten, the 6 stays the same, making the answer 63.6.
Hopefully this helps- let me know if you have any questions!
Which of the following is most likely the next step in the series? 06 O A. OB. ОС. OD.
Answers
The first group has a blue circle followed by a red circle with the first sequential number in it.
The second group has a red number with the next sequential number in it followed by a blue circle.
The third group is a repeat of the first group just with the next sequential number.
This means that the next group should by a repeat of the second group with the next sequential number. That pattern group is displayed in C.
C
What is the area of this figure?
Answers
Answer:
74km
Step-by-step explanation:
7 + 7 = 14
15 + 12 = 27
5 + 8 = 13
9 + 11 = 20
14 + 27 = 41
41 + 13 = 54
54 + 20 = 74
PLEASE ANSWER QUICKLYY IK ITS TEDIOUS CUZ THERES A LOT BUT MATH EXPERTS, HELP
Answers
Step-by-step explanation:
i answered these 3 already.
Please help I'm struggling so bad right now
Answers
Answer:
y = m x + b is the standard form of a straight line
m = (y2 - y1) / (x2 - x1) = (10 - (-8)) / (-3 - 0) = 18 / -3 = -6
When x = 0 y = b from the equation for a line
y = - 8
So our equation is
y = -6 x - 8
As a check let x = -2 then
y = (-6 * -2) - 8 = 12 - 8 = 4
Check on the graph to verify that this equation holds
Please help ASAP
I'll mark Brainliest
Answers
Muriel is considering leasing a car, and she is even thinking about buying it after the lease is up. She's trying to make sense of the terms of the lease before she makes her decision, but she's having a little trouble figuring it all out. The terms of the lease are as follows.
Terms:
Length of lease: 32 months
MSRP of the car: $26,260
Purchase value of the car after lease: $14,330
Down payment: $1270
Security deposit: $605
Acquisition fee: $765
Lease factor: 0.00073
Provide Muriel with some assistance by answering the following questions. 5 points: Part I - 1 point; Part II - 1 point; Part III - 1 point; Part IV - 1 point; Part V - 1 point)
What is the amount of the cash due at signing?
What would be Muriel's monthly payment? What is the total amount of money that Muriel would spend on monthly payments? What is the total cost of leasing the car, assuming that Muriel does not get the security deposit back?
What is the total price of the car if Muriel buys it after leasing, assuming that she does not get the security deposit back
Answers
The amount of cash due based on the terms of the lease that Muriel will pay is $2640.
How to calculate the cash due?The amount of cash due is calculated thus:
= Security deposit + Acquisition fee + Down payment
= $605 + $1270 + $765
= $2640
The monthly lease payment will be:
= Depreciation + Interest
= $133 + $28.7
= $161.70
Depreciation was calculated as:
= ($24990 - $14330) / 32 = $133
Interest was calculated as:
= Capitalized cost + Residual value × Money factor
= ($24990 + $14330) × 0.00073
= $28.70
Learn more about cash on:
https://brainly.com/question/25785586
A triangle has and area of 42 cm2. The height of the triangle is 14cm What is the base and length
Answers
Answer:
Step-by-step explanation:
AREA: 42 cm^2
h = 14 cm
area of a triangle formula:
[tex]\frac{height * base}{2} \\\frac{14 * base}{2} = 42[/tex]
(14)(base) = 42 * 2
(14)(base) /14 = 84 /14
base = 6 cm
Which expression is equivalent to 20c - 8d
Answers
Answer:
4(5c-2d)
Step-by-step explanation:
if you mean in factorization
Graph the inequality of x>15
Answers
Answer:
Hope this helps!
Which graph represents the function f(x) = - |x - 2| - 1?
Answers
Answer:
nsgs6
68÷9
02_3
73929
Step-by-step explanation:
8282×627=628373
Answer:
i hope this helps you!
Step-by-step explanation:
Pls help thanks to who ever does and please do NOT put links
Answers
Answer:
C
Step-by-step explanation:
Remark
The way to solve the problem is to figure out how many cubic feet would be present if the window was not there and then calculate the volume of the window and subtract it. That is the general method used to obtain the answer to the question you have asked.
Volume Original Shape
Each side of the figure is one side of a square.
So the volume of the square face is 6 by 6 or 6*6 = 36 (no window)
The window is 2*2 which is 4.
The volume of the original shape is 36 - 4 = 32
Volume new shape
Each side of the figure is 12 by 12 = 144 With no window
The size of the window is 4 by 4 = 16 With the window (Subtract)
The size of the modified figure is 128
Answer and discussion
The question is a bit ambiguous. I think the question means that the wall has gone from 32 to 128 cubic feet. So you need Subtract to find the difference..
Answer: 128 - 32 = 96 which is C.
Calculate the difference between the average rates of change of Function B and Function A from x=2 to x=4.
Answers
Answer:
-4
Step-by-step explanation:
-8/2=-4
So you do -8-2/4-2, which is the average rate formula.
Which choice shows the graph of the solution set for the inequality p - 2 > 6?
(A
"10
"5
0
5
10
B)
10
5
0
5
10
"10
5
HHHO+++
5 10
0
*10
-5
HHHO++++
0 5 10
Answers
Answer:
p > 8
Step-by-step explanation:
p - 2 > 6
Add 2 to each side
p > 8
help me pleasseeeee!!
Answers
Answer:
-35/91 is the required answer
Hope it helps
make me brainlist
Solve: 3x - 3= x +5
please can someone solve this I will give brainiest
Answers
3x - 3= x + 5
=> 3x - x = 5 + 3
=> 2x = 8
=> x = 8/2
=> x = 4
Answer:
4
Step-by-step explanation:
3x - 3 = x+5
=> 3x = x+5+3 ( transposing method)
=> 3x-x = 5+3
=> 2x = 8
=> x = 8/2
=> x = 4
Lines a and b are parallel.
what is the value of x?
A) 15
B) 16
C) 56
D) 64
Answers
Answer:
56
Step-by-step explanation:
Use the volume formula to find the volume of the prism
Answers
Answer:
B. 9 cubic inches
Step-by-step explanation:
Hey there!
To find the volume of a rectangular prism, you must use the formula:
L * W * H
L is the lengthW is the widthH is the heightTo find the volume we must multiply: 1.5, 4, and 1.5
Let's start!
1.5 * 4 * 1.56 * 1.59The solution is 9 cubic inches (remember that inches * inches * inches is inches³, or cubic inches)
Volume = base area × height
Volume = ( 4 × 1 ½ ) × 1 ½
[tex]v = (4 \times \frac{3}{2} ) \times \frac{3}{2} \\ [/tex]
[tex]v = \frac{12}{2} \times \frac{3}{2} \\ [/tex]
[tex]v = \frac{36}{4} \\ [/tex]
[tex]v = 9[/tex]
Thus C is the correct option.
Have a great day ♡
It’s kinda confusing?
Answers
Please help me my teacher hasn't been helping me I really need your help
Answers
Answer:
550.5323531336038
Step-by-step explanation:
I have a hint: if you ever need help with triangle trigonometry questions go to carbside depot trigonometry calculator it is a literal life savor