the arlington drama club is selling tickets to an upcoming play. They can sell at most 250 tickets. The adult tickets for $15 each and student tickets costs $5 each. They would like to raise at least $2000. It x represents the number of adult tickets and y represents the number of student tickets.
Number of adult tickets = 75
Number of student tickets = 175
Solution:
Let x represents the number of adult tickets and
y represents the number of student tickets.
Total number of tickets sold = 250
⇒ x + y = 250 – – – – (1)
Cost of adult ticket = $15
Cost of student ticket = $5
Total cost of collection = $2000
15x + 5y = 2000 – – – – (2)
Multiply equation (1) by 5
⇒ (1) × 5 5x + 5y = 1250 – – – – (3)
Subtract equation (3) from equation (2), we get
15x + 5y – 5x – 5y = 2000 – 1250
⇒ 10x = 750
⇒ x = 75
Substitute x = 75 in equation (1), we get
⇒ 75 + y = 250
⇒ y = 250 – 75
⇒ y = 175
Number of adult tickets = 75
Number of student tickets = 175
Test corner points for maximum revenue. The optimal solution is 250 adult tickets and 0 student tickets, yielding $3750.
To solve this problem, let's set up the equations based on the given information:
1. The total number of tickets sold cannot exceed 250:
[tex]\[ x + y \leq 250 \][/tex]
2. The total revenue must be at least $2000:
[tex]\[ 15x + 5y \geq 2000 \][/tex]
Now, let's solve this system of inequalities step by step:
Step 1: Graph the constraints:
Let's graph the lines corresponding to the equations:
x + y = 250 and 15x + 5y = 2000
Step 2: Find the feasible region:
The feasible region is the area that satisfies all the given constraints. In this case, it will be the region below or on the lines ( x + y = 250 ) and ( 15x + 5y = 2000 ), and within the boundaries of the axes.
Step 3: Identify the corner points:
The corner points of the feasible region are the points where the lines intersect or touch the boundary lines.
Step 4: Test the corner points:
Substitute the coordinates of each corner point into the objective function (the total revenue) to find which one yields the maximum revenue.
Let's start with the calculations:
1. **Graph the constraints:**
We'll need to find the intercepts of each line and draw them on the graph.
For ( x + y = 250 ):
When ( x = 0 ), ( y = 250 )
When ( y = 0 ), ( x = 250 )
For ( 15x + 5y = 2000 ):
When ( x = 0 ), ( y = 400 )
When ( y = 0 ),[tex]x = \frac{2000}{15} = \frac{400}{3} \)[/tex]
Now, let's plot these points and draw the lines.
2. **Find the feasible region:**
Shade the region below or on the lines ( x + y = 250 ) and ( 15x + 5y = 2000 ), and within the boundaries of the axes.
3. **Identify the corner points:**
The corner points of the feasible region are the points where the lines intersect or touch the boundary lines.
4. **Test the corner points:**
Substitute the coordinates of each corner point into the objective function ( R = 15x + 5y ) to find which one yields the maximum revenue.
Let's calculate the corner points:
Corner Point 1: (0, 0)
[ R = 15(0) + 5(0) = 0 ]
Corner Point 2: (250, 0)
[ R = 15(250) + 5(0) = 3750 ]
Corner Point 3: (0, 400)
[ R = 15(0) + 5(400) = 2000 ]
Now, let's compare the revenues:
- Corner Point 1: $0
- Corner Point 2: $3750
- Corner Point 3: $2000
The maximum revenue is $3750, which occurs at the corner point (250, 0).
Therefore, to maximize revenue while satisfying the given constraints, the Arlington Drama Club should sell 250 adult tickets and 0 student tickets.
a book store cost $80 a day to keep open, and it spends $15 for each book that it sells. if each book sells for $23, what is the break-even point for this booksotre?
The break even point for this book store is 10
Solution:
Given that, book store cost $80 a day to keep open, and it spends $15 for each book that it sells
Cost to open the book store = $ 80
The formula for solving the break even point (BEP) is:
[tex]BEP = \frac{\text{Fixed cost}}{\text{Selling price - variable cost}}[/tex]
Fixed Cost is the cost that remains constant whether the services provided or products sold increases or decreases
Variable Cost is the cost that varies or differs in proportion to the products or services produced, whether they increased or decreased
In this problem,
Fixed cost = $ 80
Selling price = $ 23
Variable cost = $ 15
Therefore,
[tex]BEP = \frac{80}{23-15}\\\\BEP = \frac{80}{8}\\\\BEP = 10[/tex]
Thus break even point for this book store is 10
In order for the bookstore to continue its business, it should sell at least 10 books to meet its $80 cost
Answer:p=10
Step-by-step explanation:
Suppose that y varies directly with x
and y = 10 when x = 20. What is y
when x = 15?
It’s a fraction
Answer:
15/2
Step-by-step explanation:
y varies directly as x can be written as:
y & x
y = Kx
K = y/x
But from the question, we were told that:
y = 10
X = 20
K = y/x
K = 10/20
K = 1/2
The formula for the expression is:
y = Kx
y = 1/2 x
Now let us solve for y, when:
x = 15
y = 1/2 x
y = 1/2 x 15
y = 15/2
Final answer:
To find the value of y when x = 15, we first determined the constant of proportionality (k) using the given y and x values, which was found to be 0.5. We then plugged x = 15 into the direct variation formula y = kx, resulting in y = 7.5.
Explanation:
If y varies directly with x and y = 10 when x = 20, then we can write this direct variation as y = kx, where k is the constant of proportionality. To find k, we substitute the known values of x and y and solve for k:
10 = k × 20
k = 10 / 20
k = 0.5
With k found, we can now determine what y is when x = 15:
y = k × x
y = 0.5 × 15
y = 7.5
Why wouldn’t you use a division to find an equivalent fraction for 7/15
To simplify a fraction by division you must have common factors between the denominator and the neominator to divide (or cancel) them
a relation contains the points (-5,-10) (-2,-4) (-1,-2) (4,8) (5,10) is this a function?
Answer:
This is a function and there is no value of x for which we will get two or more different values of y.
Step-by-step explanation:
A relation contains the points (-5,-10), (-2,-4), (-1,-2), (4,8), and (5,10).
So, if we want to model the equation that includes those points then we will get the equation of a straight line passing through the origin {Since the rate of change of y with respect to x is uniform.
The equation is y = 2x
Now, this is a function and there is no value of x for which we will get two or more different values of y. (Answer)
If you get a loan of $1,500 at an interest rate of 10% and the monthly payment is $131.85, what is the new principal after the first payment? (please explain how you got it)
Answer:
The new principal after the first payment is $ 1,380.65
Step-by-step explanation:
1. We calculate the amount of interest to pay in the first payment, this way:
Interest = Amount of loan * (interest rate/months in a year)
Replacing with the real values we know:
Interest = 1,500 * (0.1/12)
Interest = 1500 * 0.0083 = $ 12.50
2. Now we subtract the Interest from the monthly payment, as follows:
Payment to principal = 131.85 - 12.50
Payment to principal = $ 119.35
3. Finally we subtract that 1st payment to principal from the initial principal to get the new principal, this way:
New Principal = 1,500 - 119.35
New Principal = $ 1,380.65
The new principal after the first payment is $ 1,380.65
estimate the sum 7.234 + 3.9 + 6.56
7.234 + 3.9 + 6.56
7.234 + 10.46
17.694 (actual)
17.69 (rounded to the hundredths place)
17.7 (rounded to the tenths place)
18 (rounded to the ones place)
Hope this helps! ;)
Find the geometric mean of
6 and 24.
Answer:
15
Step-by-step explanation:
6+24=30
30÷2=15
the formula for calculating the mean is the total of the numbers ÷ the number of numbers
Sanchez applied 6 fluid Ounces of an herbicide per acre on 300 acres of com. How many gallons
did he apply
Click here to enter text.
Answer:
Sanchez applied 1,800 fluid ounces of herbicide to his 300 acres of corn.
Step-by-step explanation:
Let's identify what we already know:
1) Sanchez has 300 acres of corn
2) For every 1 acre, Sanchez applies 6 fluid ounces of an herbicide.
So, we need to figure out how many fluid ounces Sanchez used for the entire six acres. We can create a formula for this:
300 acres x 6 fluid ounces = x
x equals total number of fluid ounces. We multiple the number of acres by the fluid ounces, to get 1,800 fluid ounces for the entire 300 acres of corn.
Final answer:
Sanchez applied a total of 14.0625 gallons of herbicide on 300 acres of corn, after converting the total amount of herbicide from fluid ounces to gallons using the equivalence of 1 gallon equal to 128 fluid ounces.
Explanation:
Sanchez applied 6 fluid ounces of herbicide per acre on 300 acres of corn. To determine how many gallons he applied, we'll use the unit equivalence that 1 gallon = 128 fluid ounces. First, we'll calculate the total amount of herbicide in fluid ounces by multiplying the rate of application by the number of acres:
6 fluid ounces/acre imes 300 acres = 1800 fluid ounces total.
Next, we'll convert fluid ounces to gallons:
1800 fluid ounces imes (1 gallon / 128 fluid ounces) = 14.0625 gallons.
Therefore, Sanchez applied 14.0625 gallons of herbicide on the 300 acres of corn.
The diagram represents the factorization of x2 – 9x + 18. It is partially completed.
A 2-column table with 2 rows. First column is labeled x with entries x squared, question mark. Second column is labeled negative 3 with entries question mark, 18. First row is labeled x with entries x squared, question mark. Second row is labeled negative 6 with entries question mark, 18.
Which two terms are missing from the diagram?
–x and –8x
–2x and –7x
–3x and –6x
–4x and –5x
Answer:
The missing terms are - 3x and - 6x.
Step-by-step explanation:
The table represents the factorization of x2 – 9x + 18. It is partially completed.
So, the unknown term in the first row and second column will be the product of -3 and x i.e. -3x.
And the unknown term in the second row and first column will be the product of -6 and x i.e. -6x.
Therefore, the missing terms are - 3x and - 6x. (Answer)
The two terms that are missing in the diagram are –3x and –6x
How to determine the missing term Method 1The two missing term can be obtained as follow:
Multiply –3 and x together. The result is –3xMultiply –6 and x together. The result is –6xThus, the two missing term are –3x and –6x
Method 2The missing term can be obtained by doing a partial factorisation of the expression. This can be obtained as follow:
x² – 9x + 18
Multiply the 1st term (i.e x²) and the last term (i.e 18) together. The result is 18x².Find the two factors of 18x² such that the sum of the factors is equal to –9xThe factors are –3x and –6xSubstitute –3x and –6x in place of –9x in the equation above. We havex² – 9x + 18
x² – 3x – 6x + 18
Thus, the missing terms are –3x and –6x
Complete question:
See attached photo
Learn more about factorisation:
https://brainly.com/question/22248251
Can you do 985.2 divided by 100
Answer:
OF course!Dividing by 100 just means move the decimal two places to the left, so the answer is 9.652
Step-by-step explanation:
Answer:
=9.852
Step-by-step explanation:
985.2/100
=9.852
What is the answer to 1-2x=-3x+2
Answer:
x=1
Step-by-step explanation:
1-2x=-3x+2
-1=-x
1=x
Answer:
8
Step-by-step explanation:
plus 6 plus 3 look iam just trying to cheat I got stuff to do
If the 3 longest bulletin boards were side by side, what would their total length be?
The total length of the three longest bulletin boards when placed side by side would be 180 inches.
To calculate the total length of the three longest bulletin boards when placed side by side, we first need to determine the average length of a bulletin board and then multiply it by three.
The length of bulletin boards can vary widely depending on their purpose, but let's assume a standard size commonly found in schools or offices.
A typical bulletin board might measure around 4 feet (48 inches) in length.
However, some bulletin boards can be longer, reaching up to 6 or 8 feet.
Let's take a conservative estimate of 5 feet (60 inches) for our calculations.
So, if we have three bulletin boards each measuring 5 feet (60 inches) in length, the total length when placed side by side would be:
Total length = Length of one bulletin board × Number of bulletin boards
Total length = 60 inches × 3
Total length = 180 inches
Therefore, the total length of the three longest bulletin boards when placed side by side would be 180 inches.
PLEASE ANSWER
The graphs shown are of two different functions.
A. Both Graph A and Graph B have multiple y-intercepts.
B. Both Graph A and Graph B have only one x-intercept.
C. Graph A is a linear function because it has a constant rate of change.
D. Graph B is not a linear function but also has a constant rate of change.
Answer:
C: Graph A is a linear function and Graph B is also a function but a low and high constant rate
Find the volume of the program. Round to the nearest tenth if necessary
This is pretty much half the volume of a rectangular prism, so we multiply 4.8*2.5*3.4 to get 40.8 mm^3
Then we take half of that to get 20.4 mm^3
Hope that helped you to understand!
Ty sells signs in a monthly craft fair,and he can make 7 signs every 2 hours. Harrison can sign 15 signs every 4 hours. Who has the greater rate?
Answer:
If Ty can make 7 signs in 2 hours that means in 4 hours he could double that output to make 14 signs. Harrison, on the other hand, makes 15 signs every 4 hours. Therefore, by default - Harrison makes 1 more sign every 4 hours than Ty. Harrison has the greater rate. You have to figure out how many signs Ty can make in 4 hours, by multiplying 2 x 7 = 14. Hope that helps.
Step-by-step explanation:
HELP ME FOR A BRAINLIST AND 20 POINTS
Answer:
Area = [tex]\frac{5}{12}[/tex] x²
Step-by-step explanation:
The area (A) of a triangle is calculated as
A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the perpendicular height )
Here b = [tex]\frac{5}{6}[/tex] x and h = x, thus
A = [tex]\frac{1}{2}[/tex] × [tex]\frac{5}{6}[/tex] x × x = [tex]\frac{5}{12}[/tex] x²
Find the solution of the system of equations.
- 8x - 3y = 46
- 8x + 9y = 22
Answer:
x=-5, y=-2. (-5, -2).
Step-by-step explanation:
-8x-3y=46
-8x+9y=22
----------------
3(-8x-3y)=3(46)
-8x+9y=22
--------------------------
-24x-9y=138
-8x+9y=22
-------------------
-32x=160
x=160/-32
x=-5
-8(-5)-3y=46
40-3y=46
3y=40-46
3y=-6
y=-6/3
y=-2
Answer:
(-5, -2)
Step-by-step explanation:
You can find the solution to the system by either doing substitution or elimination. Since it is already it standard form, the easier way that I am showing you is elimination.
- 8x - 3y = 46 First you subtract! not add because you must
- 8x + 9y = 22 cancel 8 them out.
---- 6y=24
6 6
y=-2
to find x, just plug into either equation!
Can someone please answer this question please answer my question and answer it correctly and show work please
Answer:
Hours inequality (solution set): 0 ≤ x ≤ 7
Cost inequality: $2 ≤ y ≤ $100
Step-by-step explanation:
The babysitter charges $14 dollars per hour + bus fare
Price per hour = $14
Bus fare = $2
Mr. Tyler wants to spend no more than $100
Subtract the bus fare from the total amount, as that will not contribute to the babysitter's hours
$100 - $2 = $98
Divide by $14 per hour
$98 ÷ $14 = 7 hours
The maximum amount of time that Mr. Tyler could hire the babysitter for is 7 hours
This means that the hours cannot be greater than 7. It is given that x cannot be less than 0, because the babysitter cannot work negative hours.
0 ≤ x ≤ 7
This inequality shows that the Mr. Tyler will not have the babysitter work for less than 0 hours, or more than 7 hours. He will have to pay $2 minimum, or $100 max. Below is the inequality to represent this:
(y represents amount Mr. Tyler will pay)
$2 ≤ y ≤ $100
Hope this helps :)
Aaron runs a distance of 7.2km in the SE direction. How Far East has Aaron run?
– 2(– 3х + 4) + 3x — 3 = — 29
Answer:
x = - 2
Step-by-step explanation:
– 2(– 3х + 4) + 3x — 3 = — 29
6x - 8 + 3x - 3 = - 29
9x = - 29 + 8 + 3
9x = - 18
x = - 18 : 9
x = - 2
Answer:
x = -2
Step-by-step explanation:
– 2(– 3х + 4) + 3x — 3 = — 29 multiply -2 with inside the parenthesis remember negative sign multiplied by negative sign is positive
6x - 8 + 3x - 3 = - 29 add the like terms
9x - 11 = -29
9x = -29 + 11
9x = -18
x = -2
2/3 year is how many months
Answer:
2/3 of a year is 8 months.
Step-by-step explanation:
Since there is 12 months in a year, divide 12 by 3.
12÷3= 4
Now, multiply 4 by 2.
4×2= 8
This gives you the answer of 8 months.
Answer: 8 months
Step-by-step explanation: multiply denominator and numerator by 4 so it can be equivalent to 12 months.
What is an equivalent fractions to 5/12
Answer:
exact form is 5/12
decimal form is 0.416666
Step-by-step explanation:
Equivalent fractions are fractions that have the same value or proportion. To find an equivalent fraction to a given fraction, you multiply or divide both the numerator and the denominator by the same number. Therefore, 10/24 and 15/36 are equivalent fractions to 5/12.
Explanation:To find an equivalent fraction to 5/12, you simply multiply or divide both the numerator (the top number) and the denominator (the bottom number) by the same non-zero number. An equivalent fraction will have a different numerator and denominator, but it will represent the same value or proportion. For example, if we multiply both the numerator and the denominator of 5/12 by 2, we get 10/24. Therefore, 10/24 is an equivalent fraction to 5/12.
Similarly, if we multiply 5 (the numerator) and 12 (the denominator) by 3, we get the equivalent fraction 15/36.
So, 5/12 = 10/24 = 15/36 in terms of value or proportion.
Learn more about Equivalent Fractions here:https://brainly.com/question/23075364
#SPJ3
What is 20 = f - 27.
Answer: 47
Step-by-step explanation:
Just add 27 and 20 then you get f
Just use inverse operations
Tom has read 2 books for school. Tom read 1/2 of the first book on Thursday and 5/12 of the second book on Friday. What total fraction of these two books has Tom read
Answer:
35/12
Step-by-step explanation:
1 1/2+1 5/12
=3/2+17/12
=3*6+17*1/12
=18+17/12
=35/12
Tom read a total of 11/12 of the two books combined by reading 1/2 of the first book and 5/12 of the second book, after finding a common denominator to add the fractions.
Explanation:To calculate the total fraction of the two books that Tom has read, we need to add the fractions of each book he has read together. Tom read 1/2 of the first book and 5/12 of the second book.
To add these fractions, they need to have a common denominator. The lowest common denominator between 2 and 12 is 12.
Therefore, we convert 1/2 into 6/12 so that both fractions have the same denominator.
Now, the fractions to be added are 6/12 (from the first book) and 5/12 (from the second book).
Adding these fractions, we get:
6/12 + 5/12 = 11/12
So, Tom has read a total of 11/12 of the two books combined. This method of finding a common denominator and then adding the numerators is an effective strategy to add fractions with different denominators, providing a clear, step-by-step approach to solving such problems in mathematics.
A college student borrows $1500 for 9 months to pay for a semester of school . if the interest is $92.81 find the monthly payment
The monthly payment for the loan of $1500 with $92.81 interest over 9 months is $176.98.
To calculate the monthly payment for a $1500 loan with $92.81 in interest over 9 months, we must first find the total amount to be paid back, which includes both the principal and the interest. The total repayment amount will be $1500 (the original loan) plus $92.81 (the interest), making the total amount $1592.81.
We can then divide this total amount by the number of months the loan will be held to find the monthly payment:
Monthly Payment = Total Repayment Amount ÷ Total Months
Monthly Payment = $1592.81 ÷ 9
Monthly Payment = $176.98
Therefore, the student needs to pay $176.98 every month to pay off the loan in 9 months.
Suppose f(x) = x+1. Find the graph of f(1/4x)
The graph of the equation [tex]f(\dfrac{1}{4}x)=\dfrac{1}{4}x+1[/tex] has a slope of 1/4 and y-intercept of 1.
What is the graph of a linear equation.
The graph of a linear equation is a straight line graph. It can be expressed as function of x i.e. f(x) = y = mx + b.
Given that: f(x) = x + 1, we are to graph the function of f(1/4x). We will have to replace (1/4x) into the original equation.
[tex]f(\dfrac{1}{4}x)=\dfrac{1}{4}x+1[/tex]
It implies that the graph of f(1/4x) has a slope of 1/4 and the y-intercept is 1. So it will be less steeper than the equation f(x) = x + 1.
HELP ASAP! what is the answer for 8x^2 + 25y?
Answer:
Step-by-step explanation:
There is no answer because this is a formula
We need an equation — something that equals something else
Assuming you mean
[tex]8x^2 + 25y = 0\\25y = -8x^2\\y = -\frac{8}{25}x^2[/tex]
jeffery plans to rent a beach house for his sister's birthday and will use his savings pay for it. The company charges a $25.00 cleaning fee plus $10.00 per hour for the house . if he rents the house for 6 hours, what will be the change in jeffery's saving?
Answer:
-$85
Step-by-step explanation:
The charge will be $25 + ($10/h)(6 h) = $25 +60 = $85.
Jeffrey's savings will decrease by $85, so the net change is -$85.
Which of these strategies would eliminate a variable in the system of equations?
\begin{cases} 8x + 5y = -7 \\\\ -7x + 6y = -4 \end{cases}
⎩
⎪
⎪
⎨
⎪
⎪
⎧
8x+5y=−7
−7x+6y=−4
Choose all answers that apply:
Choose all answers that apply:
(Choice A)
A
Multiply the top equation by 666, multiply the bottom equation by -5−5minus, 5, then add the equations.
(Choice B)
B
Multiply the bottom equation by 888, then add the equations.
(Choice C)
C
Multiply the top equation by 777, then add the equations.
Multiply the top equation by 6 and and the bottom equation by –5 and then add the equations is the correct answer.
Solution:
Given system of equations:
8x + 5y = –7 – – – – (1)
–7x + 6y = –4 – – – – (2)
Multiply top equation by 6 and and bottom equation by –5
(1) × 6 ⇒ 48x + 30y = –42
(2) × –5 ⇒ 35x – 30y = 20
Now add these two equations, we get
(48x + 30y) + (35x – 30y) = –42 + 20
48x + 35x + 30y – 30y = –42 + 20
83x = –20
The variable y is eliminated.
Therefore Multiply the top equation by 6 and and the bottom equation by –5 and then add the equations is the correct answer.
Answer:
Multiply the top equation by −5, then add the equations.
Step-by-step explanation:
Did it on Khan Academy