Answers
The revenue function when the assumed values and parameters are used is F(x) = (60 + 8x)(250 - 30x)
The assumed valuesTicket price = $60 per ticketPeople = 250Increase in price = 8Decrease in people = 30The revenue functionLet the number of people be x, and the revenue function be F(x).
Using the assumed values, the revenue function is:
F(x) = (60 + 8x)(250 - 30x)
The maximum fundsWe have:
F(x) = (60 + 8x)(250 - 30x)
Expand
F(x) = 15000 - 1800x + 2000x - 240x²
Differentiate the function
F'(x) = -1800 + 2000 - 480x
Evaluate
F'(x) = 200 - 480x
Set to 0
200 - 480x = 0
This gives
480x = 200
Divide both sides by 480
x = 0.42
Substitute x = 0.42 in F(x)
F(x) = (60 + 8 * 0.42)(300 - 30* 0.42)
Evaluate
F(x) = 18210
Hence, the maximum revenue is $18210, at a rate of $0.42 per person.
Would they raise $5000?We start by setting F(x) to 5000.
So, we have:
15000 - 1800x + 2000x - 240x² = 5000
Evaluate the like terms
10000 + 200x - 240x² = 0
Using a graphing tool, we have:
x = 6.89
Hence, they would reach their goal at a rate of $6.89 per ticket.
The cost function
We have:
People = x
Cost per person = 20
So, the cost function is:
C(x) = 20x
The profit functionProfit is calculated using:
P(x) = F(x) - C(x)
So, we have:
P(x) = 15000 - 1800x + 2000x - 240x² - 20x
Evaluate
P(x) = 15000 + 180x - 240x²
The break even priceThis is the point where P(x) = 0.
So, we have:
15000 + 180x - 240x² = 0
Using a graphing tool, we have:
x = 8.29
Hence, the break even price is $8.29
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Related Questions
Frank bought 6 pens and 3 highlighters in the school store and paid $21 for the whole purchase. His friend, Andy, paid $19 for 2 pens and 4 highlighters. If all pens cost the same and all highlighters cost the same, what is the price of one pen?
Answers
Answer:one pen = $1.50
Step-by-step explanation:
See picture for the math if that helps
Using p for pens, h for highlighter,
A for first equation
B for second equation
I used equation A to reduce to a usable substitute by dividing all by 3
And then isolating “h”.
Now substitute the value of “h” into equation B and solve for “p”
P=$1.50
To check your work, substitute p ($1.50) into equation B and solve for “h”
h=$4.00
Now substitute the p and h values into either equation A or B and solve, they equal the numbers given
An 8in x 11in photo is enlatged by 200% what are the Dimensions of the enlargement?
Answers
Answer:
16in x 22in
Step-by-step explanation:
8in = 100%
x = 200%
(200*8) / 100 = 16
11in = 100%
X = 200%
(200*11) / 200 = 22
The trick is to cross multiply (without multiplying the X) and then divide by the number that was not multiplied :)
Answer:
16 in by 22 in
Step-by-step explanation:
Each dimension is multiplied by the scale factor when a photo is enlarged or reduced.
__
The enlarged photo will have dimensions ...
(200% × 8 in) by (200% × 11 in) = 16 in by 22 in
_____
Additional comment
The factor 200% is equal to 200/100 = 2. (% and /100 are interchangeable)
Please help me with this
Answers
Answer:
1 and 4
Step-by-step explanation:
(x²+1)(x²-4) = x^4 -3x²-4
The green blank is 1 and the blue/purple is 4.
Hope this helped and brainliest please
The quadratic function
d=-9x² + 40 models a
skateboarder's distance, in
feet, from the bottom of a hill
x seconds after the skateboarder
starts moving down the hill.
After how many seconds is the
skateboarder 4 ft from the
bottom of the hill?
A) 3s B) 4s C) 2s D) 3.5s
Please help!! Also if you could explain that would be great! Tysm!
Answers
Answer:
C
Step-by-step explanation:
equate d to 4 and solve for t , that is
- 9x² + 40 = 4 ( subtract 40 from both sides )
- 9x² = - 36 ( divide both sides by - 9 )
x² = 4 ( take square root of both sides )
x = [tex]\sqrt{4}[/tex] = 2
It takes 2 seconds for the skateboarder to be 4m from bottom of hill
Graph the inverse of the line provided on the graph.
Drawing Tools
Click on a tool to begin drawing.
Answers
Use the listing method to represent the following set. {x | x I, x ≤ 3}
....,0,1,2,3
4,5,6,7...
3,4,5,6....
Answers
Here the set given is
{x|x,x≤3}So the set should be
(-oo,3]The set elements are
{..,1,2,3}
Answer:
{ ..., 0, 1, 2, 3}
Step-by-step explanation:
Set notation is used in math to list numbers, objects or outcomes.
It uses curly brackets called "braces". Objects placed within the braces are the elements of the set.
Given set notation: { x | x ∈ I, x ≤ 3 }
The ∈ symbol means "is an element of".
Therefore, x ∈ I means that x is an element of the set of integers. (Integers are whole numbers that can be positive, negative, or zero).
The ≤ symbol means "less than or equal to".
Therefore, x ≤ 3 means that x is less than or equal to 3.
Therefore, the given set notation means:
x is an element of the set of integers less than or equal to 3
The listing method of set notation simply lists the numbers in the set.
The three dots "..." means it is infinite (goes on forever).
Therefore:
{ x | x ∈ I, x ≤ 3 } = { ..., 0, 1, 2, 3}
What is the exact volume of the sphere?
56.3¯π ft³
274.625π ft³
366.16¯π ft³
1464.6¯π ft³
Answers
Answer:
1150.35 ft^3
Step-by-step explanation:
4/3πr^3 is the equation to find the volume of a sphere.
we know the radius is 6.5 feet so all we have to do is input it and calculate.
please give brainliest!
hope this helps
Explain how to solve
Answers
Answer:
198 cm^3
Step-by-step explanation:
volume = 22/7 * 3^2 * 7
volume = 22/7 * 7 * 3^2
volume = 22 * 3^2
volume = 22 * 9
volume = 198
I need help with this question . I have 1 answer and this question has 4 answers I already found 1.
Answers
Answer:
A , C , E , F
Step-by-step explanation:
If you have to write the solution, just tell me.
this question confuses me any help
Answers
Answer:
42.25π m²
Step-by-step explanation:
Let's solve!
⇒ Take the radius of the lawn to be 'r'
===========================================================
Then, area of the path equals :
⇒ Area of (lawn + path) - Area of lawn
⇒ π (r + 2)² - πr² = 30π
⇒ πr² - πr² + 4πr + 4π = 30π
⇒ 4πr = 26π
⇒ r = 6.5 m
===========================================================
Area of the lawn :
⇒ Area = πr²
⇒ Area = π × (6.5)²
⇒ Area = 42.25π m²
Which of the following is not a triangle congruence theorem?
AAA
AAS
ASA
Answers
Answer:
A. (AAA)
Step-by-step explanation:
.....(AAA) "does not work because it can produce similar but not congruent triangles"
.....(AAS) "If two angles and the non-included side of one triangle are congruent to the corresponding parts of another triangle, the triangles are congruent."
.....(ASA)"triangles are congruent if any two angles and their included side are equal in the triangles."
Hope This Helped
Write the equation of the trigonometric graph
Answers
The equation for the trigonometric graph given above is:
y = 4sin(2x + (π/2))
y = 4 cos 2x
It is to be noted that the domain value of θ is displayed on the horizontal x-axis and the range value is depicted on the vertical y-axis in the graphs of trigonometric functions.
What is the step-by-step solution to the question?Note that
y = A Sin (Bx - C) + D
The vertical shift → D
Horizontal [Phase] shift → C/B
Wavelength [Period] → (2/B) π
Amplitude → | A |
Vertical Shift → 0
Horizontal | Phase | Shift → C/B → [- (π/4)] → (-π/2/2)
Wavelength | Period | → (2/B)π → π → (2/2)π
Amplitude → 4
Hence, working the above further we get:
y = 4sin(2x + (π/2))
y = 4 cos 2x
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Answer(s):
[tex]\displaystyle y = 4sin\:(2x + \frac{\pi}{2}) \\ y = -4cos\:(2x \pm \pi) \\ y = 4cos\:2x[/tex]
Step-by-step explanation:
[tex]\displaystyle y = Asin(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow 0 \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \hookrightarrow \boxed{-\frac{\pi}{4}} \hookrightarrow \frac{-\frac{\pi}{2}}{2} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{\pi} \hookrightarrow \frac{2}{2}\pi \\ Amplitude \hookrightarrow 4[/tex]
OR
[tex]\displaystyle y = Acos(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow 0 \\ Horisontal\:[Phase]\:Shift \hookrightarrow 0 \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{\pi} \hookrightarrow \frac{2}{2}\pi \\ Amplitude \hookrightarrow 4[/tex]
You will need the above information to help you interpret the graph. First off, keep in mind that although this looks EXACTLY like the cosine graph, if you plan on writing your equation as a function of sine, then there WILL be a horisontal shift, meaning that a C-term will be involved. As you can see, the photograph on the right displays the trigonometric graph of [tex]\displaystyle y = 4sin\:2x,[/tex]in which you need to replase "cosine" with "sine", then figure out the appropriate C-term that will make the graph horisontally shift and map onto the cosine graph [photograph on the left], accourding to the horisontal shift formula above. Also keep in mind that the −C gives you the OPPOCITE TERMS OF WHAT THEY REALLY ARE, so you must be careful with your calculations. So, between the two photographs, we can tell that the sine graph [photograph on the right] is shifted [tex]\displaystyle \frac{\pi}{4}\:unit[/tex]to the right, which means that in order to match the cosine graph [photograph on the left], we need to shift the graph BACKWARD [tex]\displaystyle \frac{\pi}{4}\:unit,[/tex]which means the C-term will be negative, and by perfourming your calculations, you will arrive at [tex]\displaystyle \boxed{-\frac{\pi}{4}} = \frac{-\frac{\pi}{2}}{2}.[/tex]So, the sine graph of the cosine graph, accourding to the horisontal shift, is [tex]\displaystyle y = 4sin\:(2x + \frac{\pi}{2}).[/tex]Now, with all that being said, in this case, sinse you ONLY have a graph to wourk with, you MUST figure the period out by using wavelengths. So, looking at where the graph WILL hit [tex]\displaystyle [-1\frac{1}{4}\pi, 0],[/tex]from there to [tex]\displaystyle [-\frac{\pi}{4}, 0],[/tex]they are obviously [tex]\displaystyle \pi\:units[/tex]apart, telling you that the period of the graph is [tex]\displaystyle \pi.[/tex]Now, the amplitude is obvious to figure out because it is the A-term, but of cource, if you want to be certain it is the amplitude, look at the graph to see how low and high each crest extends beyond the midline. The midline is the centre of your graph, also known as the vertical shift, which in this case the centre is at [tex]\displaystyle y = 0,[/tex]in which each crest is extended four units beyond the midline, hence, your amplitude. So, no matter how far the graph shifts vertically, the midline will ALWAYS follow.
I am delighted to assist you at any time.
What are the values of x and y?
A- x=56, y=68
B- x=68, y=56
C- x=57, y=66
D- x=66, y=57
Answers
Option c,
x = 57° and y=66°
Explanation ;-
Kindly check the attachment below
The value of "x" and "y".
Solution:Let's solve "x" first.
Given is a supplementary angle so it should add up to 180°
[tex]x=180-123[/tex]
[tex]\large\boxed{x=57°}[/tex]
Now, we can solve "y"
Given is an isosceles triangle so the opposite sides will be equal.
[tex]57+57[/tex]
[tex]114°[/tex]
Angle sum of triangle is 180° so, it should add up to 180°
[tex]y=180-114[/tex]
[tex]\large\boxed{y=66°}[/tex]
Therefore, the correct answer is option C
Choose the best selection for the
quadrilateral with vertices at the
following points:
(4,0), (8,0), (4,-4), (8,-4)
Hint: Start by graphing the points.
Distance Formula: d= √(x2-x1)² + (y2-y1)²
A. Rectangle
B. Square
C. Rhombus
D. Trapezoid
Answers
Answer:
B. Square
Step-by-step explanation:
Finding the side lengths :
Side 1
⇒ d₁ = √(-4 - 0)² + (8 - 8)²
⇒ d₁ = √16
⇒ d₁ = 4
=============================================================
Side 2
⇒ d₂ = √(-4 + 4)² + (8 - 4)²
⇒ d₂ = √16
⇒ d₂ = 4
===========================================================
Side 3
⇒ d₃ = √(-4 - 0)² + (4 - 4)²
⇒ d₃ = √16
⇒ d₃ = 4
============================================================
Side 4
⇒ d₄ = √(0 - 0)² + (8 - 4)²
⇒ d₄ = √16
⇒ d₄ = 4
As all sides of the figure are equal, and it creates 4 right angles, it is a square.
A soup can lid has a diameter of 8 cm and it is 15 cm tall. what is the area of the lid?
Answers
Answer:
50.27
Step-by-step explanation:
area for a circle is (pie)r^2
r^2=16
16xpie=50.27
What is the standard form of y=2x-2
Answers
Answer:
A standard form of a linear equation would look like this Ax+ By = C A x + B y = C
Step-by-step explanation:
Find g(x), where g(x) is the translation 8 units left of f(x)=x
Answers
Using translation concepts, it is found that function g(x) is given by:
g(x) = x + 8.
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
In this problem, function g(x) is a translation 8 units left of f(x) = x, hence x -> x + 8 and:
g(x) = f(x +8) = x + 8.
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Write 320 g as a fraction of 2 kg. Give your answer in its simplest form.
Answers
Answer:
4/25
Step-by-step explanation:
Let's make the units the same :
2 kg = 2000 g
Now lets simplify this fraction :
Divide top and bottom by 2 until you can't :
320/2000 = 160/1000
160/1000 = 80/500
80/500 = 40/250
40/250 = 20/125
Now we divide top and bottom by 5 as 2 is not a factor of 125 :
20/125 = 4/25
This is our final answer
Hope this helped and brainliest please
40% of the students in a class are girls and the number of boys is 24 find the total number of students and the number of girls
Answers
Answer:
Girls = 16
Total students = 40
Step-by-step explanation:
40% of the students are girls, this means 60% of the students are boys.
To find the number of girls, setup a proportion using the percentages and actual number of students in the class. I am going to make the numerator the numbers that go with the girls and the denominator will be the numbers that go with the boys.
Also let's convert the percentages to decimals by moving the decimal two places left.
40% = 0.4 and 60% = 0.6
[tex]\frac{.4}{.6} =\frac{g}{24} \\.6g=9.6\\\frac{.6g}{.6} =\frac{9.6}{.6} \\g=16[/tex]
Now let's find the total number of students by adding the number of girls to the number of boys.
16 + 24 = 40
The function f(x) = 5x - 4 is changed to f(x) = 5x + 3. What is the result?
Answers
Answer: move up or add 7 in positive direction
HELP
Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real world and mathematical problems in two and three dimensions
Answers
You did not provide any question. I will give general advice.
Pythagorean Theorem: a² + b² = c²
If you know two sides, you know ll three sides.
A house sits in the shade.
The house is 18 feet tall. The shadow is 24 feet long. What is the hypotenuse of this triangle?
We know a and b here! a=18, b=24.
18 * 18 = 324.
24 * 24 = 576.
324+576 = 900
The square root of 900 is what will be your answer:
18*18 + 24*24 = 30*30.
I hope this helps!
Find the equation of a line that passes through the points (-4, -2) and (6, 3).
Answers
Answer:
[tex]y=\frac{1}{2} x[/tex]
Step-by-step explanation:
The equation of a line through two points can usually (except when the line is a vertical line) be written in slope intercept form, [tex]y=mx+b[/tex] , where "m" is the slope of the line, and "b" is the y-intercept of the line.
General outlineFind the slopeFind the y-interceptStep 1. Find the slope
To find "m", use the formula for slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m=\dfrac{(3)-(-2)}{(6)-(-4)}[/tex]
[tex]m=\dfrac{3+2}{6+4}[/tex]
[tex]m=\dfrac{5}{10}[/tex]
[tex]m=\dfrac{1}{2}[/tex]
So, the slope is 1/2 and we know that the equation for the line that passes through these two points should look like: [tex]y=\frac{1}{2} x+b[/tex]
Step 2. Find the y-interceptTo find "b", substitute one of the known points, and solve for "b":
[tex]y=\frac{1}{2} x+b[/tex]
[tex](3)=\frac{1}{2} (6)+b[/tex]
[tex]3=3+b[/tex]
Subtracting 3 from both sides to isolate the "b"...
[tex](3)-3=(3+b)-3[/tex]
[tex]0=b[/tex]
So, the y-intercept is 0. Substituting into our line equation, [tex]y=\frac{1}{2} x+(0)[/tex] which simplifies to [tex]y=\frac{1}{2} x[/tex]
Can somebody please help me with this?
Answers
Answer:
The slope of the line is:
[tex]-\frac{3}{4}[/tex]
Slope of a parallel line is the same:
[tex]-\frac{3}{4}[/tex]
Slope of a perpendicular line, invert the sign and fraction:
[tex]\frac{4}{3}[/tex]
Hope this helps
G
ewrite the equation in Ax+By=C form.
se integers for A, B, and C.
y+4= -4(x-2)
Answers
Step-by-step explanation:
y + 4 = -4(x - 2) = -4x + 8
y - 4 = -4x
-4x - y = -4
4x + y = 4
A scientist cools some water at a constant rate. The graph and table show
how the temperature of the water changes with time.
Which function models this situation?
Water Temperature
8
7
8
Time (minutes)
Temperature (°C)
2899 228 229
55
50
45
40+
35+
30
25
20
15
10
5
Time (minutes)
Temperature (°C)
A. a(n) = 46-n-(4-1)
B. a(n) = 46 - 40+1
C. a(n) = 46-(n-1)-4
D. a(n) = 46-47-1
9 10
5
30
6
26
Answers
The correct function that matches the data in the graph is a(n) = 46-(n-1)-4 (option C)
How to choose the correct option?The only way is to verify the function matches the data by replacing n.
For example, we know at 5 seconds the temperature is 30. Let's use 5 (n) to verify the function.
a(n) = 46-(5-1) x 4a(n) = 46- 4x 4a(n) = 46- 16a (n) = 30This option matches the value of the temperature.
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Presently, Victor is three times as old as Maria. Ten years ago, Victor was seven times as old as Maria. How old is each person now?
Answers
Step-by-step explanation:
v = Victor's age
m = Maria's age
v = 3m
v - 10 = 7(m - 10)
3m - 10 = 7m - 70
60 = 4m
m = 15
v = 3m = 3×15 = 45
Victor is 45 years old. Maria is 15 years old.
2. Given 4x² + bx + 25, select a possible b value that will make this factorable. [A] b=-50 [B] b = -29 [C] b = 10 [D] b= 100
Answers
Answer:
b = 40 and -40
General form of Perfect square trinomial is
a
2
+
2
a
b
+
b
2
Therefore from
16
x
2
−
b
x
+
25
a
2
=
√
16
x
2
,
b
2
=
25
, then
a
=
±
4
x
,
b
=
±
5
take consideration a=4x and b=-5 (different sign), then
−
b
x
=
2
(
4
x
)
(
−
5
)
−
b
x
=
−
40
x
b
=
40
The perfect square is
(
4
x
−
5
)
2
=
16
x
2
−
40
x
+
25
.
if we consider a=4x and b=5 (same sign), then
−
b
x
=
2
(
4
x
)
(
5
)
−
b
x
=
40
x
b
=
−
40
The perfect square is
(
4
x
+
5
)
2
=
16
x
2
+
40
x
+
25
.
The first solution
(
4
x
−
5
)
2
is the best solution after comparing the expression given.
1 Pound brown sugar is equivalent to _____ cups
Answers
Answer:
3 1/2 or said as 3.5 cups is equal to 1 pound
Step-by-step explanation:
1 Pound brown sugar is equivalent to ___3 1/2 or 3.5 __ cups
Hope This Helped
Mr. Franco's class wants to raise at least $750 for a fundraiser. Let r be the amount of money, in dollars, the class raised.help ASAP..
Answers
Answer:
>
Step-by-step explanation:
Cause 750 was the least they could raise
Answer:
>=
Step-by-step explanation:
>= because the teacher wants AT LEAST 750. at least meaning you can raise 750 or MORE
Solve number 8 please
Answers
Answer:
see explanation
Step-by-step explanation:
the equation of a circle in standard form is
(x - h)² + (y - k )² = r²
where (h, k ) are the coordinates of the centre and r is the radius
given
x² + y² - 8x + 8y + 23 = 0
collect the x and y terms together and subtract 23 from both sides
x² - 8x + y² + 8y = - 23
using the method of completing the square
add ( half the coefficient of the x / y terms )² to both sides
x² + 2(- 4)x + 16 + y² + 2(4)y + 16 = - 23 + 16 + 16
(x - 4)² + (y + 4)² = 9 ← in standard form
with centre = (4, - 4 ) and r = [tex]\sqrt{9}[/tex] = 3
this is shown in graph b