To maximize income for Water World, the admission cost should be increased by $0.75, calculated by finding the vertex of the quadratic equation representing the income as a function of price increase and visitor numbers.
Explanation:To find the amount by which the admission cost to Water World should be increased to obtain maximum income, we can create a quadratic equation to represent the income based on the number of visitors and admission cost.
Step 1: Define variables and equation
Let x represent the increase in dollars to the current admission cost of $7.50. The new admission cost would be (7.50 + x) dollars.
With each $1 increase, the number of visitors decreases by 25. The new average number of visitors per day would be (225 - 25x) visitors.
Step 2: Formulate the income
Income, I, is equal to the admission cost multiplied by the number of visitors, which is I = (7.50 + x)(225 - 25x).
Step 3: Expand and maximize the quadratic equation
I = 1687.5 - 187.5x + 225x - 25x² = -25x² + 37.5x + 1687.5. This is a quadratic equation that opens downward, meaning it has a maximum point at its vertex.
The formula for the x-coordinate of the vertex of a parabola y = ax² + bx + c is -b/(2a). In this scenario, a = -25 and b = 37.5.
Step 4: Find the vertex
The x-coordinate of the vertex (maximum income) is -37.5 / (2 × -25) = 0.75. Therefore, the admission cost should be increased by $0.75 to maximize income.
If you vertically compress the absolute value parent function, f(x) = |x|, by a factor of 3, what is the equation of the new function?
A. g(x) = |x – 3|
B. g(x) = |3x|
C. g(x) = 1/3 |x|
D. g(x) = 3|x|
That is correct. On APEX its C. g(x)= 1/3 |x|
A circle with center (3,5) intersects the y-axis are(0,1). find the radius of the circle, find the coordinates of the other point of intersection with the y-axis. what are the coordinates of the point of intersection of the circle and the x-axis
The coordinates of the other point of intersection with the y-axis will be (0, 9). And the x-intercept is at (3, 0).
What is the equation of circle?Let r be the radius of the circle and the location of the center of the circle be (h, k).
Then the equation of the circle is given as,
(x - h)² + (y - k)² = r²
A circle with center (3,5).
Then the equation of the circle will be
(x - 3)² + (y - 5)² = r²
The circle intersects the y-axis at (0,1).
Then the radius of the circle will be
(0- 3)² + (1 - 5)² = r²
9 + 16 = r²
r² = 25
r = 5
Then the equation of the circle will be
(x - 3)² + (y - 5)² = 5²
Then the other y-intercept of the circle (0, a) will be
(0 - 3)² + (a - 5)² = 5²
9 + (a - 5)² = 25
(a - 5)² = 16
a - 5 = 4
a = 9
The intersection of the circle with x-axis at (b, 0) will be
(b - 3)² + (0 - 5)² = 5²
25 + (b - 3)² = 25
(b - 3)² = 0
b - 3 = 0
b = 3
Thus, the coordinates of the other point of intersection with the y-axis will be (0, 9). And the x-intercept is at (3, 0).
The graph is given below.
More about the equation of circle link is given below.
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what type of triangle has two angles at 70 degrees and one at 40 degrees
Introduction to addition or subtraction of fractions with different denominator 3/5+1/3
Round $0.6848 to the nearest cent.
Set up a proportion and use cross multiplication to solve. 100 is 250% of?
Answer:
[tex]40[/tex]
Step-by-step explanation:
Let
x-------> the number
[tex]\frac{x}{100\%}=\frac{100}{250\%}[/tex]
[tex]x*250\%=100*100\%\\ \\x=10,000/250\\ \\x= 40[/tex]
What is the solution for 2(4r+6)=2/3(12r+18)
Please help me! And can you explain how you got that answer please?
Which transformations will produce similar, but not congruent, figures?
Triangle PQR is reflected across the x-axis and then rotated 90° clockwise to form triangle P"Q"R" .
Triangle PQR is reflected across the y-axis and then dilated by a scale factor of 6 to form triangle P"Q"R" .
Triangle PQR is rotated 180° counterclockwise and then translated 11 units left to form triangle P"Q"R" .
Triangle PQR is rotated 90° clockwise and then reflected across the y-axis to form triangle P"Q"R" .
Nick’s house is 4.28 miles from school. if nick’s average stride length is 3.1 feet, how many strides will it take him to walk to school?
determine if x+2 is a factor of p(x) = x4 + 3x3 +4x2 -8
I've forgotten how to work out these kind of problems...could someone explain please? Will give brainiest. (Picture attached)
A cylinder has a height of 6 meters and a diameter that is 6 times the measure of the height
Which shows the correct word and expanded forms for the decimal? 3.28
a. three and twenty-eight thousandths 3 + 0.2 + 0.08
b. three and twenty-eight thousandths 3 + 0.02 + 0.008
c. three and twenty-eight hundredths 3 + 0.2 + 0.8
d. three and twenty-eight hundredths 3 + 0.2 + 0.08?
A rectangular park, with dimensions of 1500ft x 2000ft has a diagonal walking path that goes from corner to corner. How long is the walking path?
a cone with a mass of 6 g has a radius measuring 5 cm and a height of 2 cm . what is its density?
You make a large bowl of salad to share with your friends. Your brother eats 1/3 of it before they come over
For items 14 and 15 use the following functions
f(x)=5x+1
g(x)=3x-4
14. Evaluate f(2), g(2), (f o g) (2), and (g o f)(2).
15. Write the composite functions h(x)=g(f (x)) and k(x)=f(g(x)).
The new shanghai restaurant offers a choice of five appetizers, two choices of soups, and eleven choices of entrees for its lunch special. how many different complete lunches can be ordered from the restaurant's lunch special menu?
Final answer:
Using the Multiplication Principle, a customer can choose from 110 different complete lunch combinations by selecting one of each option (appetizer, soup, and entrée) from the menu at the New Shanghai restaurant.
Explanation:
To determine the total number of different complete lunches that can be ordered from the restaurant's lunch special menu, we apply The Multiplication Principle of counting. The principle states that if one event can occur in m ways and another independent event can occur in n ways, then the total number of ways both events can occur together is the product of m and n. In the context of ordering a lunch, each choice (appetizer, soup, and entrée) represents an independent event.
For appetizers, there are 5 choices.
For soups, there are 2 choices.
For entrées, there are 11 choices.
Following the Multiplication Principle, the total number of different complete lunches is calculated as follows:
5 appetizers × 2 soups × 11 entrées = 110 different complete lunches.
Therefore, customers have the opportunity to choose from 110 unique complete lunch combinations at the New Shanghai restaurant.
Mitch refuses to dine at a certain restaurant because he recalls reading two or three negative reviews of its service on a popular website. Mitch is falling prey to:
In this situation, we can actually see that Mitch was simply basing her taste on the information that is readily available to her. She does not even consider whether those reviews are legit or reliable. Mitch is falling into what we call as:
“the availability heuristic”
Mitch is falling prey to the bandwagon effect, where he avoids dining at a restaurant based on a few negative reviews he read online. The bandwagon effect is a cognitive bias that leads us to adopt beliefs or behaviors because we think everyone else is doing the same.
Explanation:Mitch is falling prey to the bandwagon effect. The bandwagon effect is when someone adopts a certain belief or behavior because they believe that everyone else is doing it too. In this case, Mitch refuses to dine at a certain restaurant because of negative reviews he read on a popular website, assuming that those reviews reflect the majority opinion.
The bandwagon effect is a cognitive bias that can influence our decision-making process. It is important to be aware of this bias and make decisions based on objective information rather than simply following the crowd.
Learn more about Bandwagon Effect here:https://brainly.com/question/34612602
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Please answer this question!
ABCD is a rectangle. The length of BD is 8 units and m
What is the length of AC and m
Find the area and perimeter of each composite figure use 3.14 for pi round your answer to the nearest 10th
Find the surface area and volume of each figure use 3.14 for pi round your answer to nearest 10th
I have examples if needed
1. Perimeter is 3 + 3 +3 +4 +5 = 18 feet
Area = 3*3 = 9, 1/2*3*4 = 6, 9 + 6 =15 square feet
2. perimeter = 2.5 +2.5+ 2.5+2.5+0.5+0.5 = 11 meters
Area = 3*.5 = 1.5, 3*2=6, 6+1.5 = 7.5 square meters
3. perimeter = 3.14*2*3 = 18.84 +8 = 26.8 inches
Area = 6*4 = 24 + 3.14*3^2 = 28.26 = 28.26 +24 = 52.3 inches
4. surface area = 2*π*6*20+2*π*6^2= 980.2 yards
Volume = π*6^2*20 = 2261.9 cubic yards
5.surface area = 2*(9*7+2*2+2*9) = 190 cm
Volume = 2*7*9 = 126 cubic cm
6. surface area = 2*(11*11+11*11+11*11) = 726 mm
Volume = 11 *11*11 = 1331 cubic cm
1. Area = 15 square feet
2. Area = 5.5 square meters
3. Area = 52.26 square inches
4. Surface area = 312π square yards, Volume = 720π cubic yards
5. Surface area = 127 square cm, Volume = 126 cubic cm
6. Surface area = 726 square mm, Volume = 1331 cubic mm
let's go through each problem step by step with proper calculations:
**Problem 1:**
Given:
Perimeter = 3 + 3 + 3 + 4 + 5 = 18 feet
Area calculations:
- For the triangle: Area = 1/2 × base × height = 1/2 × 3 × 4 = 6 square feet
- For the rectangle: Area = length × width = 3 × 3 = 9 square feet
Total Area = 6 + 9 = 15 square feet
**Problem 2:**
Given:
Perimeter = 2.5 + 2.5 + 2.5 + 2.5 + 0.5 + 0.5 = 11 meters
Area calculations:
- For the triangle: Area = 1/2 × base × height = 1/2 × 0.5 × 2 = 0.5 square meters
- For the rectangle: Area = length × width = 2.5 × 2 = 5 square meters
Total Area = 0.5 + 5 = 5.5 square meters
**Problem 3:**
Given:
Perimeter = 3.14 × 2 × 3 + 8 = 18.84 + 8 = 26.84 inches
Area calculations:
- For the rectangle: Area = length × width = 6 × 4 = 24 square inches
- For the circle: Area = π × radius² = 3.14 × 3² = 28.26 square inches
Total Area = 24 + 28.26 = 52.26 square inches
**Problem 4:**
Given:
Surface area calculations:
- For the cylinder:
- Lateral Surface Area = 2 × π × radius × height = 2 × π × 6 × 20 = 240π square yards
- Top and bottom circles: Area = 2 × π × 6² = 72π square yards
Total Surface Area = 240π + 72π = 312π square yards
Volume calculations:
- Volume = π × radius² × height = π × 6² × 20 = 720π cubic yards
**Problem 5:**
Given:
Surface area calculations:
- For the rectangular box:
- Front and back: 9 × 7 = 63 square cm
- Sides: 2 × (2 × 9) = 36 square cm
- Top and bottom: 2 × (2 × 7) = 28 square cm
Total Surface Area = 63 + 36 + 28 = 127 square cm
Volume calculations:
- Volume = length × width × height = 9 × 7 × 2 = 126 cubic cm
**Problem 6:**
Given:
Surface area calculations:
- For the cube:
- All faces are identical: 6 × (11 × 11) = 726 square mm
Volume calculations:
- Volume = side³ = 11³ = 1331 cubic mm
If you randomly choose a letter in the word "mathematics", find the probability that you choose an "a".
A quadrilateral whose opposite sides are parallel and congruent and whose opposite angles are congruent is a ____. a. trapezoid c. kite b. heptagon d. parallelogram.
PLZ ANSWER ASAP!!
Help me with the first one please
HELP PLEASE!!! 15pts!!
Dominic is a landscape architect and is designing a garden with an area of up to 500 square feet. He will use two types of plants: zinnias and petunias. Each zinnia plant requires 1.6 square feet of ground and each petunia plant requires 1.8 square feet of ground. Each zinnia plant costs $4 and each petunia plant costs $3, and the architect must spend no more than $600.
Let z represent the number of zinnia plants and p represent the number of petunia plants.
Three of the constraints for this situation are z≥0 , p≥0 , and 1.6z+1.8p≤500 .
What is the other constraint for this situation?
Enter your answer in the boxes.
__ z + __ p ≤ __
The third constraint was based on the total area that the garden can only take. Now the last constraint must be based on the total cost that should be spend in order to make a 500 square feet of garden, that is:
4 z + 3 p ≤ 600
How long is the minute hand on a clock whose tip travels 15 cm from 1:15 to 1:30 to the nearest tenth?
Answer:
The length of minute hand is 9.5 cm
Step-by-step explanation:
We are given the minute hand move from 1:15 to 1:30
Time for 1:30 to 1:30 = 15 minutes
Tip of minute hand move 15 cm in 15 minutes.
In 60 minutes = 360°
In 1 minute = 6°
In 15 minutes = 90°
Formula: [tex]\theta=\dfrac{L}{r}[/tex]
[tex]\theta=90^\circ[/tex]
Now we change [tex]\theta=90^\circ[/tex] into radian
[tex]Radian=\dfrac{\pi}{180^\circ}\times 90^\circ=\dfrac{\pi}{2}[/tex]
L=15 cm
R = Length of minute hand.
[tex]\dfrac{\pi}{2}=\dfrac{15}{R}[/tex]
[tex]R=\dfrac{30}{\pi}\approx 9.5[/tex]
Hence, The length of minute hand is 9.5 cm
Bill ate 1/4 pound of trail mix on his first break during a hiking trip. On his second break, he ate 1/6 pound. How many pounds of trail mix did he eat during both breaks? Explain.
Which type of triangle has one angle with a measurement greater than 90°? A. Obtuse B. Acute C. Isosceles D. Right