A university is trying to determine what price to charge for tickets to football games. At a price of $20 per ticket, attendance averages 40,000 people per game. Every decrease of $4 adds 10,000 people to the average number. Every person at the game spends an average of $4.00 on concessions. What price per ticket should be charged in order to maximize revenue? How many people will attend at that price? What is the price per ticket? $ What is the average attendance? people
Answers
The price per ticket that maximizes revenue is $10.
The average attendance at a price of $10 per ticket is 60,000 people.
The second derivative of the revenue equation with respect to x:
R''(x) = -20
What price per ticket should be charged in order to maximize revenue?Let's denote the price per ticket as x, and the average attendance as y. We can model the relationship between x and y as follows:
y = -10(x-20) + 40
This equation represents the fact that every decrease of $4 in price (x-20) adds 10,000 people to the average attendance (the -10 coefficient) from the initial value of 40,000 people when the price is $20.
The revenue generated from ticket sales and concessions is given by:
R = xy + 4y
where 4y represents the total revenue from concessions since each person spends an average of $4.
We can substitute the equation for y into the revenue equation to get:
R = x(-10x + 240) + 4(-10x + 400)
Simplifying this expression, we get:
\(R = -10x^2 + 200x + 1600\)
To find the price per ticket that maximizes revenue, we need to find the vertex of the parabola defined by this equation. The x-coordinate of the vertex is given by:
x = -b/(2a)
where a and b are the coefficients of the quadratic equation. In this case, a = -10 and b = 200, so we have:
x = -200/(2*(-10)) = 10
Therefore, the price per ticket that maximizes revenue is $10.
What is the price per ticket? $ What is the average attendance?To find the average attendance at this price, we can substitute x=10 into the equation for y:
y = -10(10-20) + 40 = 60
Therefore, the average attendance at a price of $10 per ticket is 60,000 people.
How many people will attend at that price?To verify that this is a maximum, we can take the second derivative of the revenue equation with respect to x:
R''(x) = -20
Since this is a negative constant, we know that the revenue function is concave down and the vertex is a maximum.
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Related Questions
what features of the distribution of the hispanic population in us counties are apparent in the map but not in the histogram? what features are apparent in the histogram but not the map?
Answers
The map visually represents the spatial distribution of the Hispanic population across U.S. counties, allowing for the identification of patterns and clusters. On the other hand, the histogram provides a quantitative representation of the distribution, illustrating the frequency or density of Hispanic population within specific ranges or categories.
The map reveals certain features that may not be apparent in the histogram. For instance, it allows us to observe spatial concentrations or clusters of Hispanic population, such as regions with high densities of Hispanic residents or areas where the Hispanic population is more dispersed. These spatial patterns can provide insights into factors like immigration patterns, cultural heritage, or historical settlement patterns that influence the distribution of the Hispanic population in the United States.
Conversely, the histogram highlights features that may not be readily visible in the map. The histogram enables a more detailed examination of the distribution within specific population ranges or categories. It can reveal the frequency or density of the Hispanic population within each range, allowing for comparisons across different counties or regions. By examining the histogram, one can identify variations in the size or proportion of the Hispanic population in different areas, potentially indicating demographic disparities or variations in population growth rates.
In summary, the map provides a visual understanding of the spatial distribution of the Hispanic population, highlighting clusters and patterns, while the histogram offers a quantitative representation, revealing variations in population density within specific ranges or categories. Both tools are valuable for analyzing and interpreting the distribution of the Hispanic population in U.S. counties, providing complementary perspectives for understanding demographic trends and patterns.
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*EASY* SOLVE WITH STEPS *WILL MARK BRAINLIEST*
Answers
Answer:
(6, 1)
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Algebra I
Solving systems of equations using substitution/eliminationStep-by-step explanation:
Step 1: Define Systems
3x - 5y = 13
x + 4y = 10
Step 2: Rewrite Systems
x + 4y = 10
Subtract 4y on both sides: x = 10 - 4yStep 3: Redefine Systems
3x - 5y = 13
x = 10 - 4y
Step 4: Solve for y
Substitution
Substitute in x: 3(10 - 4y) - 5y = 13Distribute 3: 30 - 12y - 5y = 13Combine like terms: 30 - 17y = 13Isolate y terms: -17y = -17Isolate y: y = 1Step 5: Solve for x
Define equation: x + 4y = 10Substitute in y: x + 4(1) = 10Multiply: x + 4 = 10Isolate x: x = 6Answer:
(6,1) x=6 and y=1
Step-by-step explanation:
EASY we can use Elimination or Substitution process
We are going to solve by
Elimination process
Subtract each other
(3x-5y=13)
(x+4y=10)
3x-5y=13;x+4y=10
To solve this multiply (x-4y=10) by 3 to get rid of the x
3x-12y=30
now u can subtract both
3x-12y=30 minus
3x-5y=13
17y=17
Divide both sides by 17
y=1
Now we have y lets plug it in to find x
x+4(1)=10
x+4=10
subtract 4 from both sides
x=6
x=6 and y=1
Find m∠CBD.
i’ll give a brainist
Answers
Answer:
<M<CBD=M<CDB=34° BASE ANGLE OF ISOSCELES TRIANGLE
What is the answer to this?
Answers
Answer:
(c) III
Step-by-step explanation:
If you simplify the equations and the left side is identical to the right side, then there are an infinite number of solutions: the equation is true for all values of x.
Another way to simplify the equation is to subtract the right side from both sides. If that simplifies to 0 = 0, then there are an infinite number of solutions.
__
I.2x -6 -6x = 2 -4x . . . . eliminate parentheses
-4x -6 = -4x +2 . . . . no solutions (no value of x makes this true)
__
II.x +2 = 15x +10 +2x . . . . eliminate parentheses
x +2 = 17x +10 . . . . one solution (x=-1/2)
__
III.4 +6x = 6x +4 . . . . eliminate parentheses
6x +4 = 6x +4 . . . . infinite solutions
__
IV.6x +24 = 2x -4 . . . . eliminate parentheses; one solution (x=-7)
The soccer team voted on what they wanted to eat. There are 20 members on the team. Six members voted for pizza, 10 voted for chicken, and the rest voted for hot dogs.
Which ratio represents the number of votes for hot dogs to chicken?
Responses
1/5
2/5
3/5
5/2
Answers
The ratio representing the number of votes for hot dogs to chicken is 2/5.
Define the term ratios of the number?An set of points of integers a and b, represented as a / b, is a ratio if b is not equal to 0. A proportion is indeed an equation that sets two ratios at the same value.Ratios contrast two figures by ordinarily dividing them. A/B would be your formula if you were comparing each data point (A) to some other data point (B).For the stated question.
Total votes = 20.
Pizza = 6
Chicken = 10
Hot dogs = 20 - 16 = 4
Then,
Ratio = votes for hot dogs/ votes for chicken
Ratio = 4/10
Ratio = 2/5
Thus, the ratio representing the number of votes for hot dogs to chicken is 2/5.
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Hannah notices that segment HI and segment KL are congruent in the image below: Two triangles are shown, GHI and JKL. G is at negative 3, 1. H is at negative 1, 1. I is at negative 2, 3. J is at 3, 3. K is at 1, 3. L is at 2, 1. Angle I and L are shown as congruent. Which step could help her determine if ΔGHI ≅ ΔJKL by SAS? (5 points) segment IG ≅ segment LJ segment GH ≅ segment KL ∠G ≅ ∠ K ∠L ≅ ∠ H
Answers
Answer:
segment IG ≅ segment LJ
Step-by-step explanation:
Please refer to the attached image as per the triangles as given in the question statement.
\(\triangle HGI, \triangle JKL\)
\(G\left(-3,1\right),\ H\left(-1,1\right),\ I\left(-2,3\right)\)
\(J\left(3,3\right),K\left(1,3\right),L\left(2,1\right)\)
Given that:
\(HI\cong KL\) and
\(\angle I \cong \angle L\)
SAS congruence between two triangles states that two triangles are congruent if two corresponding sides and the angle between the two sides are congruent.
We are given that one angle and one sides are congruent in the given triangles.
We need to prove that other sides that makes this angle are also congruent.
To show the triangles are congruent i.e. \(\triangle GHI \cong \triangle JKL\) by SAS congruence we need to prove that
segment IG ≅ segment LJ
Let us use Distance formula to find IG and LJ:
\(D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)
\(IG =\sqrt{(-2+3)^2+(3-1)^2} =\sqrt5\ units\)
\(LJ =\sqrt{(2-3)^2+(1-3)^2} =\sqrt5\ units\)
Hence, segment IG ≅ segment LJ
\(\therefore\) ΔGHI ≅ ΔJKL by SAS
Diego put $15,000 into a savings account 6 years ago.
- The account earned 3.25% simple annual interest.
He made no additional deposits or withdrawals.
Based on this information, what is the balance in dollars and cents in Diego's savings account at the end of these 6 year
$18.173.21
B $2,925.00
$17,925.00
D $3,173.21
Answers
Answer: The answer is option C: $17,925.00.
Step-by-step explanation: Using the simple interest formula:
I = Prt
where I is the interest, P is the principal, r is the interest rate, and t is the time in years.
We can find the interest earned over the 6 years:
I = P * r * t = $15,000 * 0.0325 * 6 = $2,925
Adding the interest to the principal, we get the balance at the end of the 6 years:
Balance = Principal + Interest = $15,000 + $2,925 = $17,925
Therefore, the answer is option C: $17,925.00.
Simplify. 2√(6√−10−−√) 23√−25√ −22√ 32√−25√ 23√−52√
Answers
Answer:
i think it is \(18400\sqrt{4290}i\)
Step-by-step explanation
Answer:
3√2 − 2√5
Step-by-step explanation:
v
Is ozone harmful to health?
Answers
Ozone can be both harmful and beneficial to health, depending on its location in the atmosphere and the levels at which it is present.
In the stratosphere (the layer of the atmosphere that is located about 10-50 kilometers above the Earth's surface), ozone is a beneficial gas that protects life on Earth by absorbing harmful ultraviolet (UV) radiation from the sun. However, at ground level, ozone can be harmful to health, particularly for people with respiratory problems such as asthma.
Exposure to high levels of ozone can irritate the respiratory system and cause coughing, throat irritation, and chest pain. It can also worsen bronchitis, emphysema, and other lung diseases. Ozone can also reduce lung function and inflame the linings of the lungs, leading to more serious health problems.
It is important to note that ground-level ozone is not emitted directly into the air, but is formed when pollutants from sources such as vehicle exhaust, power plants, and industrial facilities react with sunlight and heat.
Therefore, Ozone can be both harmful and beneficial to health.
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Use the Integral Test to determine whether the series is convergent or divergent.
[infinity] n
n2 + 6
n = 1
Evaluate the following integral.
[infinity] 1
x
x2 + 6
dx
Answers
The series ∑ₙ=₁ to ∞ (n/n² + 6) is divergent.
To determine whether the series ∑ₙ=₁ to ∞ (n/n² + 6) is convergent or divergent, we can use the Integral Test.
The Integral Test states that if f(x) is a continuous, positive, and decreasing function on the interval [1, ∞) and f(n) = aₙ for all positive integers n, then the series ∑ₙ=₁ to ∞ aₙ and the integral ∫₁ to ∞ f(x) dx either both converge or both diverge.
In this case, let's consider the function f(x) = x/(x² + 6). We can check if it meets the conditions of the Integral Test.
Positivity: The function f(x) = x/(x² + 6) is positive for all x ≥ 1.
Continuity: The function f(x) = x/(x² + 6) is a rational function and is continuous for all x ≥ 1.
Decreasing: To check if the function is decreasing, we can take the derivative and analyze its sign:
f'(x) = (x² + 6 - x(2x))/(x² + 6)² = (6 - x²)/(x² + 6)²
The derivative is negative for all x ≥ 1, which means that f(x) is a decreasing function on the interval [1, ∞).
Since the function f(x) = x/(x² + 6) satisfies the conditions of the Integral Test, we can evaluate the integral to determine if it converges or diverges:
∫₁ to ∞ x/(x² + 6) dx
To evaluate this integral, we can perform a substitution:
Let u = x² + 6, then du = 2x dx
Substituting these values, we have:
(1/2) ∫₁ to ∞ du/u
Taking the integral:
(1/2) ln|u| evaluated from 1 to ∞
= (1/2) ln|∞| - (1/2) ln|1|
= (1/2) (∞) - (1/2) (0)
= ∞
The integral ∫₁ to ∞ x/(x² + 6) dx diverges since it evaluates to ∞.
According to the Integral Test, since the integral diverges, the series ∑ₙ=₁ to ∞ (n/n² + 6) also diverges.
Therefore, the series ∑ₙ=₁ to ∞ (n/n² + 6) is divergent.
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Incomplete question:
Use the Integral Test to determine whether the series is convergent or divergent.
∑ₙ=₁ to ∞ = n/n² + 6
Evaluate the following integral ∫₁ to ∞ x/x²+6 . dx
A set of Numbers is shown below.
Answers
Answer: A
Step-by-step explanation:
write 132 as a product of prime factors.
Answers
Answer:
132
Step-by-step explanation:2 x 2 x 3 x 11
HELP PLEASE QUICKLY HELP -h
Answers
Answer:
3rd option.
Step-by-step explanation:
Make the denominators equal
10/18+11/18
21/18
Simplify
7/6
Option c when turned in mixed fraction
Answer:
1 1/6
Step-by-step explanation:
5/9 + 11/18
5/9= 10/18
10/18 + 11/18 = 21/18 or 1 3/18
3/18 can be simplified to 1/6 so our final answer is 1 1/6
How can you decompose the composite figure to determine its area? as a circle, three rectangles, and a triangle as a circle, a trapezoid, and four triangles as a semicircle, three rectangles, and a square as a semicircle, a trapezoid, and two rectangles.
Answers
Answer:
The best way to decompose the composite figure to determine its area is as a semicircle, a trapezoid, and two rectangles. This way, we can use the following formulas to find the area of each part:
Area of a semicircle = 21πr2, where r is the radius of the circle.
Area of a trapezoid = 21(b1+b2)h, where b1 and b2 are the bases and h is the height of the trapezoid.
Area of a rectangle = l×w, where l is the length and w is the width of the rectangle.
Then, we can add up the areas of each part to find the total area of the composite figure. The other options are not as convenient because they either involve more parts or more complicated shapes. For example, option A would require finding the area of a triangle, which involves using trigonometry or the Pythagorean theorem. Option B would require finding the area of four triangles, which is more tedious than finding the area of two rectangles. Option C would require finding the area of a square, which is redundant because a square is a special case of a rectangle.
Step-by-step explanation:
The composite figure can be decomposed into a semicircle, a trapezoid, and two rectangles.
Option D is the correct answer.
What is a trapezium?It is a quadrilateral that has one pair of parallel sides and a height.
The area is calculated as: 1/2 x sum of the parallel sides x height.
Examples:
Area of a trapezium that has the parallel sides as 3 cm and 4 cm and a heght o 5 cm.
Area = 1/2 x (3 + 4) x 5
Area = 1/2 x 7 x 5
Area = 35/2 = 17.5 cm^2
We have,
The given figure can be decomposed into the following figure.
- Semicircle
- Trapezoid
- Two rectangles
Thus,
A semicircle, a trapezoid, and two rectangles.
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Katrina sketches the graphs of four functions on a coordinate plane. Which of the following functions is linear?
Answers
The function that is linear is the function that is a straight line
How to determine the function that is linearA linear function can be identified on a graph by its shape.
A linear function will always have a straight line. So, if the graph of several functions, then the linear function would be a straight line.
To confirm that it is a linear function, you can check if it has the form y = mx + b, where m and b are constants.
In this form, m represents the slope of the line, which is a measure of how steep the line is. and b is the y-intercept
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Use the similar triangles to find the slope on the lines??? Hello plzzz
Answers
Answer:
the slope is 1/4 my friend
Answer:
We can use line segments QR and the points on it to find the slope.
The equation for slope is y2 - y1 / x2 - x1 where x1 is the x value of the first point you chose, y2 is the y value of the second point you chose and so on.
By using this eqution we can pick any 2 points on the line. I will pick q which is (1, 3) and R which is (5, 4)
y2 - y1 / x2 - x1
4 - 3 / 5 - 1
1/4 is the slope
Step-by-step explanation:
Dividing the given equations into factors
Answers
Answer:
a) 16=2x=0 b)68×55[$$]4=0
If x = 7+3 root 5 by 7 - 3 root 5 , find the value of x^2 + 1 by x^2
Answers
Answer:
6 because why not
Step-by-step explanation:
Can someone help geometry assp
Answers
Answer:
24°
Step-by-step explanation:
66°+b=90°(right angle)
or,b=90°-66°
or,b=24°
hope this helps you
5 apples for $6.25 or 8 apples for $9.25. Which is the better deal?
Answers
The option that is the better deal between both deals for apples, is 8 apples for $9.25.
How to find the better deal?The better deal on the apples would be the deal that gives the lower amount per apple. This means that the deal that leads to each individual apple having a lower price is the deal that should be considered best.
To find the price of an apple, you would need to divide the price of the deal given, by the number of apples in the deal.
The first deal would therefore have a per apple price of :
= Price of deal / Number of apples
= 6. 25 / 5 apples
= $ 1. 25 per apple
The second deal would be :
= Price of deal / Number of apples
= 9. 25 / 8 apples
= $ 1. 16 per apple
The better deal is therefore 8 apples for $9.25.
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3x + 160y<=1120 written in slope intercept form
Answers
I can find the perimeter and area of the rectangle
Answers
Answer:
A = 72, P = 38
Step-by-step explanation:
Area can be found by getting the area of the overall figure, and then subtracting the blank space in the corner
12 * 7 = 84
3 * 4 = 12(invisible rectangle in top right)
84 - 12 = 72
Perimeter can be found by adding all of the sides
12 + 7 + (12-4) + 3 + 4 + (7-4)
The numbers in brackets are the unlabeled sides on the top and left.
Answer:
\(P=38\\ A=72\)
Step-by-step explanation:
To find the perimeter (P), add up all of the side lengths of the figure:
(numbers in parenthesis are the unlabeled values in the figure).
\(12+7+(8)+3+4+(4)=38\)
To find the area of the figure (A), multiply the length and width of the original rectangle \((12*7=84)\). Then, subtract this amount (84) minus the area of the missing rectangle in the top left corner \((4*3=12)\).
Subtract the required values: \(84-12=72\).
Therefore, the perimeter of the figure is 38 units, and the area of the figure is 72 units.
What is the side length of the square garden with an area of 4w^2?
Answers
Answer:
2w
Step-by-step explanation:
The area of a square is given by a formula; A = a²
Substitute the A with the area 4w² and solve for the side length (a).
a = 2w
What transformation was not done to the linear parent function, f(x) = x, to get the function g(x) = - 5(x - 3) - 8 ? A. Reflection over the x-axis B. Shift down 8 units C. Horizontal stretch by a factor of 5 D. Shift right 3 units
Answers
Answer:
A. Reflection over the x-axis.
Step-by-step explanation:
Now, we present how to transform \(f(x) = x\) into \(g(x) = -5\cdot (x-3)-8\) below:
1) \(f(x) = x\) Given.
2) \(f(x-3) = x - 3\) Horizontal shift to the right.
3) \(-5\cdot [f(x-3)] = -5\cdot (x-3)\) Vertical scale factor.
4) \(-5\cdot f(x-3)-8 = -5\cdot (x-3)-8\) Vertical shift downwards.
5) \(g(x) = -5\cdot (x-3)-8\) Definition/Result
In consequence, the only transformation which was not done to the linear parent function was a reflection over the x-axis. The correct answer is A.
I need help with the problem x/-9 ≥ 3 Simplify. Thanks!
Answers
Answer:
x ≤ -27
Step-by-step explanation:
\(\frac{x}{-9}\) ≥ 3
to isolate the 'x' we need to multiply each side by -9
whenever you multiply or divide an inequality by a negative you must reverse the inequality symbol, therefore:
x ≤ -27
The standard deviation is _____ when the data are all concentrated close to the mean, exhibiting little variation or spread.
Answers
The standard deviation is relatively small when the data are all concentrated close to the mean, exhibiting little variation or spread.
The standard deviation could be a degree of the changeability or spread of a set of information. It is calculated by finding the square root of the normal of the squared contrasts between each information point and the cruel(mean).
In other words, it tells us how much the information values are scattered around the mean.
When the information is all concentrated near the cruel(mean), it implies that the contrasts between each information point and the cruel are moderately little.
This comes about in a little while of squared contrasts, which in turn leads to a little standard deviation. On the other hand, when the information is more spread out, it implies that the contrasts between each information point and the cruel are bigger.
This comes about in a bigger entirety of squared contrasts, which in turn leads to a bigger standard deviation.
For case, let's consider two sets of information:
Set A and Set B.
Set A:
2, 3, 4, 5, 6
Set B:
1, 3, 5, 7, 9
Both sets have the same cruel(mean) (4.0), but Set A encompasses a littler standard deviation (1.4) than Set B (2.8).
This is because the information values in Set A are all moderately near to the cruel(mean), while the information values in Set B are more spread out.
Subsequently, we will say that the standard deviation is generally small when the information is all concentrated near the mean, showing a small variety or spread.
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What is3/5written as a percent?
Answers
Answer:
60%
Step-by-step explanation:
5÷3=0.6
0.6×100=60
Turn it into a percent.
60%
Could I please have BRAINLIEST?
Answer:
60%
Step-by-step explanation:
Pete found 5/6 of a party sand which in the refrigerator. He took 1/2 of the 5/6 of the sand which to his neighbors. How much of the original sand which did pete take to his neighbors.
Answers
Answer:
1/2
Step-by-step explanation:
Pete found 5/6 of a party sand which in the refrigerator. He took 1/2 of the 5/6 of the sand which to his neighbors.
This is calculated as:
1/2 × 5/6
= 5/12
Hence, he took 5/12 of the sand
How much of the original sand which did pete take to his neighbors.
Let the original sand be represented as 1
Hence:
5/6 = 5/12 sand
1 = x
Cross Multiply
5/6x = 1 × 5/12
x = 5/12 ÷ 5/6
x = 5/12 × 6/5
x = 1/2
Therefore, pete took 1/2 of the original sand to his neighbors.
How would you use the Distributive Property to write an equivalent expression, with no spaces, for x(3x+2)?
Answers
Answer:
\(x(3x + 2) = 3x^2 + 2x\)
Step-by-step explanation:
Given
\(x(3x + 2)\)
Required
Apply distributive property
\(x(3x + 2)\)
Distribute
\(x(3x + 2) = x * 3x + x * 2\)
\(x(3x + 2) = 3x^2 + 2x\)
A scientist has two solutions, which she has labeled Solution A 60% and Solution B 75% Each contains salt. She knows that Solution A is salt and Solution B is salt. She wants to obtain ounces of a mixture that is salt. How many ounces of each solution should she use
Answers
Answer:
The answer is "180".
Step-by-step explanation:
Please find the complete question in the attached file.
Let's
x = ounces solution of A
y = ounces solution of B
\(x + y = 180 \\\\y = 180 - x\\\\0.60x + 0.85y = 0.75(180)\\\\0.60x + 0.85y = 135\\\\\)
Multiply both sides of the equation by 100 to remove the decimal points.
\(60x + 85y = 13500\\\\60x + 85(180 - x) = 13500\\\\60x + 15300 - 85x = 13500\\\\-25x = -1800\\\\x = 72\ \ ounces\\\\y = 180 - 72 \\\\y = 108 \ \ ounces\\\\\)