2 $4.2 - Optimization At a price of $6 per ticket, a musical theater group can fill every seat in the theater which has a capacity of 1700. For every additional dollar charged, the number of peo- ple attending decreases by 85. The total revenue the group will make can be computed by multiplying the ticket price per seat by the number of seats that are occupied. What is the ticket price that maximizes revenue?
Answers
The ticket price that maximizes revenue is 6 + 7 = 13.
Let x be the additional dollar charged and y be the number of people
attending the musical theater group at the ticket price of 6+x.
Then we can write:
y = 1700 - 85x
This is because for every additional dollar charged, 85 fewer people
attend the theater.
The total revenue the group will make is the product of the ticket price per seat and the number of seats occupied, which is:
Revenue = (6+x)y
Substituting the expression for y, we get:
Revenue = (6+x)(1700 - 85x)
Expanding the brackets, we get:
Revenue = \(10200 - 510x + 1700x - 85x^2\)
Simplifying, we get:
Revenue = \(-85x^2 + 1190x + 10200\)
This is a quadratic function of x, and the revenue is maximized at the
vertex of the parabola. The x-coordinate of the vertex can be found using
the formula:
x = -b/2a
where a = -85 and b = 1190. Substituting these values, we get:
x = -1190/(2× (-85)) = 7
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Related Questions
Break your message into groups of three letters, using a dash (-) to represent a space. Create a column matrix for the groups, using the correspondence:a -> 1b -> 2...z -> 26space -> 27Now create a 3x3 matrix (M) that has an inverse. Encode your message by multiplying by M, following example 7. This will give you a series of 3x1 column matrices.
Answers
First we need to decide a message:
"Irene has a party"
Then we need to break the message and replace every letter with a number
Ire ; ne- ; has ; -a- ; par ; ty-
becomes...
IRE = [9;18;5]
NE- = [14;5;27]
HAS = [8;1;19]
-A- = [27;1;27]
PAR = [16;1;18]
TY- = [20;25;27]
Please, take into account that [a;b;c] is writen as:
\(\begin{bmatrix}{} & a{} & {} \\ {} & b{} & \\ {} & c & \end{bmatrix}\)Now, we need to select a 3x3 matriz that has an inverse
\(\begin{gathered} M=\begin{pmatrix}1 & 1 & -3 \\ -2 & 1 & 0 \\ 0 & 0 & 3\end{pmatrix} \\ M^{-1}=\begin{pmatrix}\frac{1}{3} & -\frac{1}{3} & \frac{1}{3} \\ \frac{2}{3} & \frac{1}{3} & \frac{2}{3} \\ 0 & 0 & \frac{1}{3}\end{pmatrix} \end{gathered}\)Matrix M has an inverse M^-1
Now, we need to mutiply each column matrix by M
IRE = [9;18;5]
\(\begin{gathered} \begin{pmatrix}1 & 1 & -3 \\ -2 & 1 & 0 \\ 0 & 0 & 3\end{pmatrix}\times\begin{pmatrix}9 \\ 18 \\ 5\end{pmatrix} \\ =\begin{pmatrix}1\cdot\: 9+1\cdot\: 18+\mleft(-3\mright)\cdot\: 5 \\ \mleft(-2\mright)\cdot\: 9+1\cdot\: 18+0\cdot\: 5 \\ 0\cdot\: 9+0\cdot\: 18+3\cdot\: 5\end{pmatrix} \\ =\begin{pmatrix}12 \\ 0 \\ 15\end{pmatrix} \end{gathered}\)NE- = [14;5;27]
\(\begin{gathered} \begin{pmatrix}1 & 1 & -3 \\ -2 & 1 & 0 \\ 0 & 0 & 3\end{pmatrix}\begin{pmatrix}14 \\ 5 \\ 27\end{pmatrix} \\ =\begin{pmatrix}1\cdot\: 14+1\cdot\: 5+\mleft(-3\mright)\cdot\: 27 \\ \mleft(-2\mright)\cdot\: 14+1\cdot\: 5+0\cdot\: 27 \\ 0\cdot\: 14+0\cdot\: 5+3\cdot\: 27\end{pmatrix} \\ =\begin{pmatrix}-62 \\ -23 \\ 81\end{pmatrix} \end{gathered}\)HAS = [8;1;19]
\(\begin{gathered} \begin{pmatrix}1 & 1 & -3 \\ -2 & 1 & 0 \\ 0 & 0 & 3\end{pmatrix}\begin{pmatrix}8 \\ 1 \\ 19\end{pmatrix} \\ =\begin{pmatrix}1\cdot\: 8+1\cdot\: 1+\mleft(-3\mright)\cdot\: 19 \\ \mleft(-2\mright)\cdot\: 8+1\cdot\: 1+0\cdot\: 19 \\ 0\cdot\: 8+0\cdot\: 1+3\cdot\: 19\end{pmatrix} \\ =\begin{pmatrix}-48 \\ -15 \\ 57\end{pmatrix} \end{gathered}\)-A- = [27;1;27]
\(\begin{gathered} \begin{pmatrix}1 & 1 & -3 \\ -2 & 1 & 0 \\ 0 & 0 & 3\end{pmatrix}\begin{pmatrix}27 \\ 1 \\ 27\end{pmatrix} \\ =\begin{pmatrix}1\cdot\: 27+1\cdot\: 1+\mleft(-3\mright)\cdot\: 27 \\ \mleft(-2\mright)\cdot\: 27+1\cdot\: 1+0\cdot\: 27 \\ 0\cdot\: 27+0\cdot\: 1+3\cdot\: 27\end{pmatrix} \\ =\begin{pmatrix}-53 \\ -53 \\ 81\end{pmatrix} \end{gathered}\)PAR = [16;1;18]
\(\begin{gathered} \begin{pmatrix}1 & 1 & -3 \\ -2 & 1 & 0 \\ 0 & 0 & 3\end{pmatrix}\begin{pmatrix}16 \\ 1 \\ 18\end{pmatrix} \\ =\begin{pmatrix}1\cdot\: 16+1\cdot\: 1+\mleft(-3\mright)\cdot\: 18 \\ \mleft(-2\mright)\cdot\: 16+1\cdot\: 1+0\cdot\: 18 \\ 0\cdot\: 16+0\cdot\: 1+3\cdot\: 18\end{pmatrix} \\ =\begin{pmatrix}-37 \\ -31 \\ 54\end{pmatrix} \end{gathered}\)TY- = [20;25;27]
\(\begin{gathered} \begin{pmatrix}1 & 1 & -3 \\ -2 & 1 & 0 \\ 0 & 0 & 3\end{pmatrix}\begin{pmatrix}20 \\ 25 \\ 27\end{pmatrix} \\ =\begin{pmatrix}1\cdot\: 20+1\cdot\: 25+\mleft(-3\mright)\cdot\: 27 \\ \mleft(-2\mright)\cdot\: 20+1\cdot\: 25+0\cdot\: 27 \\ 0\cdot\: 20+0\cdot\: 25+3\cdot\: 27\end{pmatrix} \\ =\begin{pmatrix}-36 \\ -15 \\ 81\end{pmatrix} \end{gathered}\)Now let's write this codes as a string of numbers:
12 0 15 -62 -23 81 -48 -15 57 -53 -53 81 -37 -31 54 -36 -15 81
Can someone please help me I will be forever grateful
Answers
Answer:
5/8
Step-by-step explanation:
1 inches in fraction form would be 8/8 inches, and the button is 3/8 inches, so a 1 inch button is 5/8 inches longer than a 3/8 inch button
Answer:
5/8
Step-by-step explanation:
it takes 5 more inches to get to 1 inch from 3/8
Hope I helped!! If I did please give brainliest because I cant level up without having 2 more ;(
<3 Enjoy,
Dea
True or False: In –6x – 20 = –2x + 4(1 – 3x)
Answers
Given \(-6x-20\)
Proof that it is equal to the \(-2x + 4(1 - 3x)\) or not
\(-2x + 4(1 - 3x)\)
Distribute
\(-2x+ 4-12x\)
\(4-14x\)
Not equal to the \(-6x-20\) \(\neq\) \(4-14x\)
So, it is false
What is Distribute in math?
To "distribute" anything is to divide it up or to give someone a piece of it.
What does the mathematical distributive property mean then?
The distributive property is the distributive law of multiplication over operations in fundamental arithmetic, such as addition and subtraction.
Distributive property: What Is It?
This property states that multiplying the total of two or more addends by a number will provide the same outcome as multiplying each addend by the number separately and then adding the results together.
In other words, an expression of the type A (B + C) can be resolved as A (B + C) = AB + AC in accordance with the distributive property.
This characteristic also holds for subtraction.
A(B-C) = AB-AC
This demonstrates that the other two operands share operand A.
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find the common difference in the linear sequence sequence 69,53,47,30
Answers
someone plssssssss help me with thisss
Answers
Answer:
yes it does match
Step-by-step explanation:
the graph has the coordinates (-2,1),(-1,2),(0,3),(1,4) all on it.
help me solve this:
16-x=x
Answers
Answer:
8
Step-by-step explanation:
16 - x = x
16 = x + x
16 = 2x
16 ÷ 2 = x
8 = x
What is the measure of U? A. 66 B. Cannot be determined C. 74 D. 70
Answers
Answer: B. Cannot be determined
Step-by-step explanation:
Answer:70
Step-by-step explanation:
Mateo is doing an experiment for Physics class. He drops a bouncy ball off a
balcony from a height of 12 meters. The ball's next bounce is always 75% of
the height of the previous bounce. Let n = bounce number. Before the ball is
dropped, n = 0, because the ball has not yet bounced. Which explicit formula
represents the height of the ball after n bounces?
Answers
Answer:
Max. height following bounce # n is 12(¾)n because each prior height is multiplied by three fourths.
Step-by-step explanation: it jus is
how many places can you put the lens to form a well-focused image of the candle flame on the wall?
Answers
The number of places you put the lens to form a well-focused image of the candle flame on the wall is either we have to move the screen towards the lens or the lens towards the screen.
Here we have given that the lens to form a well-focused image of the candle flame on the wall.
As we all know that if the candle is further from the wall than the focal length of the lens, then there are two places which will result in an image. Here we have know that one of them is just beyond the focal length from the wall.
Here we have given the other is that same distance from the candle.
Then the position near the wall will yield a small image.
Here the position near the candle will produce a large image.
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Which graph represents the function f(x)=4⋅3X
Answers
Answer:
D.
Step-by-step explanation:
help me please thanks
Answers
Answer:
\(y = \dfrac{-12}{x} = -\dfrac{12}{x}\)
Step-by-step explanation:
An inverse variation equation is represented by
\(y = \dfrac{k}{x}\)
where k is a constant
Let's take a couple of values from the table to determine the value for k
At x = -2, y = 4 ==> 4 = k/-3 or k = -12
At x = 1/2, y = -24 ==> -24 = k/(1/2); k = -24 x 1/2 = -12
So we have determined that the relationship in the table is an inversely proportionate relationship
The equation is
\(y = \dfrac{-12}{x} = -\dfrac{12}{x}\)
which we can also rewrite as
\(yx = -12 \;or\; xy = -12\)
For the linear regression y = ẞ1 + ẞ2x + e, assuming that the sum of squared errors (SSE) takes the following form:
SSE = 382 +681 +382 + 18ẞ1ẞ2
Derive the partial derivatives of SSE with respect to B1 and B2 and solve the optimal values of these parameters.
a. B₁ = B1
b. B₂ =
Answers
The optimal values of these parameters are:
a. β₁ = 0
b. β₂ = 0
The linear regression y = β1 + β2x + e, assuming that the sum of squared errors (SSE) takes the following form:
SSE = 382 + 681 + 382 + 18β1β2
Derive the partial derivatives of SSE with respect to β1 and β2 and solve the optimal values of these parameters.
Given that SSE = 382 + 681 + 382 + 18β1β2 ∂SSE/∂β1 = 0 ∂SSE/∂β2 = 0
Now, we need to find the partial derivative of SSE with respect to β1.
∂SSE/∂β1 = 0 + 0 + 0 + 18β2 ⇒ 18β2 = 0 ⇒ β2 = 0
Therefore, we obtain the optimal value of β2 as 0.
Now, we need to find the partial derivative of SSE with respect to β2. ∂SSE/∂β2 = 0 + 0 + 0 + 18β1 ⇒ 18β1 = 0 ⇒ β1 = 0
Therefore, we obtain the optimal value of β1 as 0. Hence, the partial derivative of SSE with respect to β1 is 18β2 and the partial derivative of SSE with respect to β2 is 18β1.
Thus, the optimal values of β1 and β2 are 0 and 0, respectively.
Therefore, the answers are: a. β₁ = 0 b. β₂ = 0
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What calculator is used for pre-calculus?
Answers
A scientific calculator is typically used for pre-calculus.
This type of calculator is designed to handle more advanced mathematical functions, such as trigonometry, logarithms, and exponents, which are commonly used in pre-calculus.
It is important to have a scientific calculator for pre-calculus because it allows you to easily solve more complex equations and perform calculations quickly and accurately.
Additionally, many scientific calculators have graphing capabilities, which can be useful for visualizing equations and understanding how they behave. Overall, a scientific calculator is an essential tool for pre-calculus and can help you succeed in the course.
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The continuous-time LTI system has an input signal x(t) and impulse response h(t) given as x() = −() + ( − 4) and ℎ() = −(+1)( + 1).
i. Sketch the signals x(t) and h(t).
ii. Using convolution integral, determine and sketch the output signal y(t).
Answers
(i)The impulse response h(t) is a quadratic function that opens downward and has roots at t = -1. (ii)Therefore, by evaluating the convolution integral with the given input signal x(t) and impulse response h(t), we can determine the output signal y(t) and sketch its graph based on the obtained expression.
i. To sketch the signals x(t) and h(t), we can analyze their mathematical expressions. The input signal x(t) is a linear function with negative slope from t = 0 to t = 4, and it is zero for t > 4. The impulse response h(t) is a quadratic function that opens downward and has roots at t = -1. We can plot the graphs of x(t) and h(t) based on these characteristics.
ii. To determine the output signal y(t), we can use the convolution integral, which is given by the expression:
y(t) = ∫[x(τ)h(t-τ)] dτ
In this case, we substitute the expressions for x(t) and h(t) into the convolution integral. By performing the convolution integral calculation, we obtain the expression for y(t) as a function of t.
To sketch the output signal y(t), we can plot the graph of y(t) based on the obtained expression. The shape of the output signal will depend on the specific values of t and the coefficients in the expressions for x(t) and h(t).
Therefore, by evaluating the convolution integral with the given input signal x(t) and impulse response h(t), we can determine the output signal y(t) and sketch its graph based on the obtained expression.
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The ______________ provides a single measure for a certain population, also called the average.
Answers
The arithmetic mean provides a single measure for a certain population, also called the average.
The sum of a set of numbers divided by the total number of numbers in the set is known as the arithmetic mean or arithmetic average in mathematics and statistics.
The ratio of the total number of observations divided by the sum of all the given observations is known as the arithmetic mean. For instance, if the data set contains 5 observations, it is possible to get the arithmetic mean by adding all 5 of the given observations and dividing by 5.
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Tom's recipe requires 8 cups of sugar to make 40 sugar cookies. How many
sugar cookies will 120 cups of sugar make? *
Answers
1 cup/ 5 cookies
x 120
—————————
120 cups makes 600 sugar cookies
I’m sad
act scores are normally distributed and from 2015 to 2017, the mean was 20.9 with a standard deviation of 5.6. to get accepted into u of m, you need at least a 31. what is the z-score you need to get accepted? enter your answer rounded to the nearest hundredth. question 3 options:
Answers
To find the z-score needed to get accepted into the University of Michigan (U of M) with an ACT score of at least 31, we can use the mean and standard deviation of the ACT scores distribution from 2015 to 2017.
The mean is 20.9, and the standard deviation is 5.6.
The z-score measures how many standard deviations an individual's ACT score is above or below the mean. We can calculate the z-score using the formula: z = (x - μ) / σ, where x is the ACT score, μ is the mean, and σ is the standard deviation.
For the desired ACT score of 31, we can calculate the z-score as follows:
z = (31 - 20.9) / 5.6 ≈ 1.82
Therefore, the z-score needed to get accepted into U of M with an ACT score of at least 31 is approximately 1.82, rounded to the nearest hundredth.
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Calculate using Pythagorean theorem picture above! Will mark brainliest
Answers
c is the hypotenuse, so c = 24.01
b is 20.5
plug into formula:
a^2 + (20.5)^2 = (24.1)^2
simplify and solve:
a^2 + 420.25 = 580.81
a^2 = 160.56
a = 12.671 miles
Two linear equations are shown.
C
654321₁
4
66
y=1/3x+2
y=4/3x-5
What is the solution to the system of equations?
O (7.4)
0 (7.33)
O
0 (8)
O
O (9.7)
Answers
Answer: Option (2)
Step-by-step explanation:
Setting the equations equal to each other,
\(\frac{1}{3}x+2=\frac{4}{3}x-5\\\\7=x\)
If x=7, then \(y=\frac{7}{3}+2=\frac{13}{3}\)
Find the present value of a sequence of annual payments of Rs 25000 each , the first being made at the end of 5th year and the last being paid at the end of 12th year, if money is worth 6%.
Answers
The present value of the sequence of annual payments of Rs 25000 each, the first being made at the end of the 5th year and the last being paid at the end of the 12th year, if money is worth 6% is Rs. 158620.39.
1: We can use the formula to calculate the present value of the annuity:
P = A x [1 - (1+i)^-n] / i
Where
P = Present Value
A = Annuity
i = Interest Raten = Number of payments
2: Calculate the present value of each payment using the formula:
P1 = 25000 / (1.06)⁵
P2 = 25000 / (1.06)⁶
P3 = 25000 / (1.06)⁷
P4 = 25000 / (1.06)⁸
P5 = 25000 / (1.06)⁹
P6 = 25000 / (1.06)¹⁰
P7 = 25000 / (1.06)¹¹
P8 = 25000 / (1.06)¹²
3: Substitute the values into the formula to find the present value:
P = P1 + P2 + P3 + P4 + P5 + P6 + P7 + P8
P = (25000 / (1.06)⁵) + (25000 / (1.06)⁶) + (25000 / (1.06)⁷) + (25000 / (1.06)⁸) + (25000 / (1.06)⁹) + (25000 / (1.06)¹⁰) + (25000 / (1.06)¹¹) + (25000 / (1.06)¹²)
P = 158620.39
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the average stopping distance of a car traveling at 65 mph on dry, level pavement is:_____.
Answers
From the given information provided, the average stopping distance is 316 feet for car travelling at 65mph on dry level pavement.
The average stopping distance of a car traveling at 65 mph on dry, level pavement depends on various factors, such as the condition of the pavement, the condition of the tires, the weight of the car, and the efficiency of the braking system.
However, as a general estimate, the average stopping distance of a car traveling at 65 mph on dry, level pavement is about 316 feet. This includes both the reaction time of the driver and the braking distance of the car. It's important to note that this is an average estimate and actual stopping distance can vary depending on the conditions mentioned above. It's always best to drive at a safe speed and maintain a safe distance from other vehicles to avoid accidents.
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Use the vertex of the function (h, k) and the x-intercepts . g(x) = 2 * (x + 3) ^ 2 - 6
Answers
Answer:
Hope this helps
Step-by-step explanation:
For any two integers a and b, (a + b)2 = a2 + b?
true or false
Answers
Answer:
False.
Step-by-step explanation:
Using the property of distribution, (a + b)² will be a² + b², never a² + b.
No, for any two integers a and b, (a + b)² ≠ a² + b is a false statement.
What is termed as the distributive property of multiplication?Multiplication's distributive property allows you to simplify expressions in which you multiply a number by the a sum or difference. This property states that the product of a sum or difference of two numbers is equal to the sum as well as difference of the products. When you multiply a value by a sum, the distributive property of multiplication over addition is used.For the given two integers a and b,
The given expression
(a + b)² = a² + b (false statement)
The correct statement is-
(a + b)² = (a + b)(a + b)
(a + b)² = a² + b² + 2ab
Thus, no, for any two integers a and b, (a + b)² ≠ a² + b.
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The new Virgo the Vampire Hunter novel is 540 pages. Skyler has read 145 pages in 5 hours. Ramon has read 124 pages in 4 hours who reads faster, Skyler or Ramon? How long will it take Ramon to read entire book if he continues to read at his current rate?
Answers
Answer:
Ramon, 16 hours
Step-by-step explanation:
Find the x-intercept of the graph of the linear equation Y=-1/2x + 3.
x-intercept =______
Answers
Answer:
if you are doing edg its 6 but if you are not its (6,0)
Step-by-step explanation:
Answer:
6
Step-by-step explanation:
The parallelogram shown below has an area of 72 units?.
h
13
Find the missing height.
Answers
Answer:
area is given base is given so area of parallelogram =b x h
or 72=13 x h
or h =72/13=5.5 units
Answer:12
Step-by-step explanation:
V=IR
In an experiment I and R are both measured correct to 1 decimal place.
When I= 4.0 and R=2.7, find the lower bound for V.
Answers
Answer:
10.75
Step-by-step explanation:
4.0×2.7=10.8
lower bound of 10.8 is 10.75
you're in the wilderness hunting bears. you see a bear and chase it 10 miles south, 10 miles east, and 10 miles north. you wind up at the exact same point that you started. what color is the bear?
Answers
The triangle formed while chasing the bear in the given direction is an equilateral triangle and total distance covered is equal to 30 miles.
Direction while chasing bear are,
South , East , and North.
Distance covered in each direction while chasing = 10 miles.
The triangle formed by the movements of,
10 miles south, 10 miles east, and 10 miles north is an equilateral triangle.
This is because each of the three sides has a length of 10 miles.
And all three angles are 60 degrees.
To find the total distance you covered while chasing the bear,
Add up the lengths of the three sides of the equilateral triangle,
10 miles (south) + 10 miles (east) + 10 miles (north) = 30 miles
Therefore, triangle formed is an equilateral triangle and covered a total distance of 30 miles while chasing the bear.
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The given question is incomplete, I answer the question in general according to my knowledge:
You're in the wilderness hunting bears. you see a bear and chase it 10 miles south, 10 miles east, and 10 miles north. you wind up at the exact same point that you started. What type of triangle get formed and find the total distance you cover while chasing?
Who prepares the questions for grade 7 math worksheets?
Answers
The questions for grade 7 math worksheets are typically prepared by math teachers, curriculum specialists, and educational publishers.
These professionals use their knowledge of math concepts and pedagogy to create questions that are appropriate for the grade level and aligned with educational standards.
Additionally, they may use feedback from students and other teachers to refine the questions and ensure they are effective for teaching and learning. It is important for the questions to be clear, accurate, and challenging in order to help students develop their math skills and prepare for more advanced concepts.
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A fence was installed around the edge of a rectangular garden. The length, 1, of the fence was 5 feet less than 3 times its width, w. The amount of fencing used was 90 feet. Write a system of equations or write an equation using one variable that models this situation. Determine algebraically the dimensions, in feet, of the garden.
Answers
The dimensions of the garden are 12.5 feet by 30.5 feet.
To model this situation, we can use two equations. Let the width of the rectangular garden be w feet and the length be l feet.
Then:We know that the perimeter of the garden is 90 feet because the amount of fencing used was 90 feet.Perimeter = sum of all sides2(l + w) = 90Divide both sides by 22(l + w)/2 = 45l + w = 45Now,
we also know that the length of the fence, 1, was 5 feet less than 3 times the width,
w.l = 3w - 5Substitute this equation for l in the first equation:3w - 5 + w = 45Simplify:4w - 5 = 45
Add 5 to both sides :4w = 50Divide both sides by 4:w = 12.5
Now that we know the width of the garden is 12.5 feet, we can use the equation for l to find the length:l = 3w - 5l = 3(12.5) - 5l = 30.5
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