Seats for Sale
State's football program has risen to the ranks of the elite with postseason bowl games in each of the past 10 years, including a national championship game. The Bruins (as the fans are called) fill the stadium each game. Season tickets are increasingly difficult to find. In response to the outstanding fan support, State has decided to use its bowl revenues to expand the stadium to 75,000 seats.
The administration is confident that all 75,000 seats can be sold at the normal price of $40 per game ticket; however, Frank Pinto's job, as athletic director, is to get as much revenue out of the stadium expansion as possible. In addition to stadium boxes for wealthy alums, Frank would like to take this opportunity to repurpose existing seats. A certain number of seats (yet to be determined) would be set aside for premium ticket holders who would pay $200 per ticket for the privilege of 50-yard line seats with chair backs and access to indoor concessions. The question is, how many fans would be willing to pay such a premium? If too many seats are designated in the premium sections, they could remain vacant. Too few premium seats would lose potential revenue for the program.
Frank has decided that if the plan has any chance of success, unsold premium seats should not be sold at reduced rates. It would be better to donate them to local charities instead. Gathering data from his cohorts at peer institutions, Frank has put together the following probability distribution of premium ticket holders. The data begin with 1000 tickets since Frank already has requests for 999 tickets from alumni donors. He is asking for your help in performing the analysis.
No. of Premium Tickets Probability
1,000 0.10
5,000 0.30
10,000 0.24
15,000 0.15
20,000 0.10
25,000 0.06
30,000 0.05
a. Using revenue management, determine how many seats should be reserved for premium ticket holders.
b. Considering your answer to part (a) and the possible outcomes listed above, how much total revenue (i.e., regular and premium) can be expected from ticket sales?
c. The administration is unsure about Frank's plan. The VP of finance thinks an expected value of the number of premium seats would produce better results. How would the number of premium seats change using expected value? Considering the possible outcomes, which approach yields the most potential revenue?

The new coordinates after dialting using scale factor are , A ' ( -21, 14 ) ,

B ' ( 28, 14 ) and C ' ( -7, -7 ) .

What is a graph ?

Graph can be defined as the visual representation which is used to represent the data.

The scale factor is k = 7. This tells us to multiply each coordinate, of each point, by the scale factor to get the dilated points.

For example, point A is at (-3, 2) and moves to A ' (-21, 14) after multiplying the x,y coordinates by 7. The same applies for points B and C as well.

The dilation rule can be written as (x, y) -> (7x, 7y)

As a result of the dilation, triangle A'B'C' has sides that are 7 times longer compared to the corresponding sides of triangle ABC.

Example: side AB = 7 units, side A'B' = 49 units

Hence, The new coordinates after dialting using scale factor are , A ' ( -21, 14 ) , B ' ( 28, 14 ) and C ' ( -7, -7 ) .

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Answer: 157.5

Step-by-step explanation:

Answer:

improper fraction

Step-by-step explanation:

A mixed number has a whole number and a fraction.

An improper fraction is a fraction with a numerator bigger than the denominator.

Since 17 > 4 and there is no whole number,  this is an improper fraction.

It can be changed to a mixed number by dividing the numerator by the denominator

17 ÷4 = 4 and there is a remainder of 1.  The remainder goes over the denominator

4  1/4

Answer: It's an improper fraction

Step-by-step explanation: It's an improper fraction because an improper fraction is a fraction where the numerator is greater than the denominator, whereas a proper fraction is the opposite. A mixed number is when there is a whole number and then a regular (proper) fraction beside it. Here's an example:

[tex]5\frac{1}{7}[/tex]

Since 17 is greater than 4, 17/4 is an improper fraction. Now, if you wanted to find 17/4 as a fraction, you would divide the 17 by the 4, so the  whole number (4 in this case) would be the whole number, and the faction would be 1/4

So, [tex]\frac{17}{4}[/tex]= [tex]4\frac{1}{4}[/tex]

To check, you can multiply the 4 by the 4, which is 16, and add the numerator (1) to it, which would be 17/4. I hope this helps.

If a textbook store sold a combined total of 447 sociology and math textbooks in a week. The number of  textbooks of each type  that were sold is: 195 Math textbooks, 138  Sociology textbooks.

Let x represent the number of math textbooks

Let y represent the number of sociology

Altogether bookseller sold 447 math and sociology textbooks

Hence,

x + y = 447

Since the number of sociology textbooks sold was 57 less than the number of math books sold.

So:

y = x - 57

Substitute for y in the equation

x + y = 447

x + (x - 57) = 447

2x - 57 = 447

Combine like terms

2x = 447 -57

2x = 390

Divide both side by 2x

x = 390/2

x = 195 (Math textbooks)

y = x - 57

y = 195 -57

y = 138 ( Sociology textbooks)

Therefore 195 and 138 textbooks were sold.

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Answer: The solution of the equation is x = 48. The equation is 20 = x - 28.

Step-by-step explanation:

-20 is like having -20 dollars, and you want to know how much you have to add to it to get to 28 dollars. So we add 20 to -28 and we get the number x = 48, so 48 dollars is what we need to add to -20 dollars to get to 28 dollars.

The consecutive numbers are 21 and 22.

Consecutive numbers are numbers that follow each other in order and they have a difference of 1 between every two numbers. 

We shall represent the consecutive numbers with n and (n + 1) so that:

3(n + 1) = 2n + 24 {open bracket}

3n + 3 = 2n + 24

3n - 2n = 24 - 3 {collect like terms}

n = 21

since the lesser number is 21, then the greater number is 21 + 1= 22.

Therefore, the two consecutive numbers such that 3 times the greater number exceeds twice the lesser by 24 are 21 and 22.

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Answer:

Step-by-step explanation:

poop

Answer:

y = 5x - 4

Step-by-step explanation:

1. Parallel have the same slope (equation)

- Standard form of an equation of a line: y=mx + b

m = slope

x = x-coordinate

b = y-intercept

y = y-coordinate

SLOPE = [tex]\frac{y_{2} -y_{1} }{x_{2}-x_{1}}[/tex]

Given that x-2y = 5

and the line has the point:

(-3,-1)

We need to find another point to find the slope

x - 2y = 5

Let's say x = 7 and y = 1

(7, 1)

Now plug it into the slope equation

[tex]\frac{-3-7}{-1-1} = \frac{-10}{-2} = 5[/tex]

Plug the slope into the standard form of an equation of a line

y = 5x + b

Plug in (7,1)

1 = 5 + b

b = -4

The answer is: y = 5x - 4

Hope this helps :)

Have a great day!

Answer: x = 2

Step-by-step explanation:

Multiply each term between the parentheses by 2 1/3.

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{2\frac{1}{3}(2x-3)=2\frac{1}{3} \iff \ 2\frac{1}{3}\times2x+2\frac{1}{3}\times(-3)=2\frac{1}{3} } \end{gathered}$} }[/tex]

We calculate the expression of the multiplication.

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{2\frac{1}{3}\times2x+2\frac{1}{3}\times(-3)=2\frac{1}{3} \iff \ \frac{14x}{3}+2\frac{1}{3}\times(-3)=2\frac{1}{3} } \end{gathered}$} }[/tex]

We calculate the multiplication and division of rational numbers.

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{\frac{14x}{3}+2\frac{1}{3}\times(-3)=2\frac{1}{3} \iff \frac{14x}{3}-7=2\frac{1}{3} } \end{gathered}$} }[/tex]

We convert the mixed fraction to improper.

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{\frac{14x}{3}-7=2\frac{1}{3} \iff \dfrac{14x}{3}-7=\dfrac{7}{3} } \end{gathered}$} }[/tex]

We eliminate the fractions by multiplying by the least common multiple of the denominators of both sides.

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{\dfrac{14x}{3}-7=\dfrac{7}{3} \iff \ 14x-21=7} \end{gathered}$} }[/tex]

We move the constant to the right side and change the direction of the sign.

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{14x-21=7 \iff 14x=7+21=28, and \ remains \ 14x=28} \end{gathered}$} }[/tex]

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{14x=28 \iff \ we \ divided \ x=\frac{28}{14}=x; \Rightarrow x=2. } \end{gathered}$} }[/tex]

Answer:

605

Step-by-step explanation:

11x55=605

The correct statement is- the square root of the __difference__ of a _the polynomial x²_ and 11 → √x² - 11 the __product__ of _-2x_ times a number and reciprocal of  -11 → -2x/11 the sum_ of the __square root__ of two times a number and 11 → √2x + 11.

Polynomial is made up of two terms, namely Poly (meaning “many”) and Nominal (meaning “terms.”). A polynomial is an expression composed of variables, constants, and exponents, combined using mathematical operations such as addition, subtraction, multiplication, and division (No division operation by a variable). Based on the number of terms present in the expression, it is classified as monomial, binomial, and trinomial. For example P(x) = x2-5x+11

Given here, [tex]\sqrt{x^2-11}[/tex] , This in word phrase can be written the square root of the difference between a square of a number and 11.

-2x/11 can be written as twice the number multiplied by the reciprocal of -11

√2x + 11 can be written as sum of square root of twice the number and 11

Hence, The correct statement is- the square root of the __difference__ of a _the polynomial x²_ and 11 → √x² - 11 the __product__ of _-2x_ times a number and reciprocal of  -11 → -2x/11 the sum_ of the __square root__ of two times a number and 11 → √2x + 11.

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Answer:

the circuit a1 and a3 are parallel to each other

rest of them must be in series

When the function, m ( x)  = x + 1 is graphed, the result is shown attached.

When graphing a function, you need to remember that x is the independent variable. This means that you need to come up with the values of x and then use these values to come up with the corresponding values of y or m (x ) using the function.

Assuming you have values of x which are -3, -2, -1, 0, 1, 2, 3, the values of y would be:

x = - 3:
= x + 1

= - 3 + 1

= -2

x = - 2

= - 2 + 1

= - 1

x = - 1

= - 1 + 1

= 0

x = 0:

= 0 + 1

= 1

x = 1 :

= 1 + 1

= 2

x = 2 :

= 2 + 1

= 3

x = 3 :

= 3 + 1

= 4

The points would then be:
( - 3, - 2) , ( - 2, - 1) , ( - 1 , 0 ) ( 0, 1 ) ( 1, 2 ) ( 2, 3 ) ( 3, 4 )

The graph would be shown as attached.

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Answer:

y = 5/4x - 8

Step-by-step explanation:

first you convert the equation to y = mx + b

then you add the the -8 into the x and the 2 into the y and solve for b

b = -8 and since it is parallel same slope.

hope this helps :)

Son solving the provided question we can say that - the fraction is (2 + 1/x ) / ( 7-1/x ) = 5/13

Any number of equal portions, or fractions, can be used to represent a whole. Fractions in standard English indicate how many units of a certain size there are. 8, 3/4. A whole includes fractions. The ratio of the numerator to the denominator is how numbers are expressed in mathematics. Each of these is an integer in simple fractions. In the numerator or denominator of a complex fraction is a fraction. True fractions have numerators that are less than their denominators. A fraction is a sum that constitutes a portion of a total. By breaking the entire up into smaller bits, you can evaluate it. Half of a full number or item, for instance, is represented as 12.

here, the fraction is

(2 + 1/x ) / ( 7-1/x )

2x+1/7x-1

x = 2

5/13

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Answer:

C, E and F

Step-by-step explanation:

[tex]P(t)=3400e^{0.04t}\implies 68000=3400e^{0.04t}\implies \cfrac{68000}{3400}=e^{0.04t} \\\\\\ 20=e^{0.04t}\implies \log_e(20)=\log_e(e^{0.04t})\implies \log_e(20)=0.04t \\\\\\ \ln(20)=0.04t\implies \cfrac{\ln(20)}{0.04}=t\implies 74.89\approx t[/tex]

that's about 74 years and 325 days more or less.

based on the exponential equation which is really a continuously compounding equation with an initial value of 34000 in 1994, so 74 years later that'd be 1994 + 74 = 2068, then we add the 325 days to that, well, that's pretty much in November in 2069.

Answer:

(a) The central 95% of IQ scores in a standardized test would be found in the interval from 85 to 115. This is because a normal distribution is symmetric around the mean, and 95% of the data falls within two standard deviations of the mean. So, the interval would be mean - 2standard deviation to mean + 2standard deviation i.e. 100 - 215 to 100 + 215 = 85 to 115

(b) About 2.5% of people should have IQ scores above 115. This is because the IQ scores follow a normal distribution and IQ scores above 115 are considered to be in the top 2.5% of the distribution.

(c) About 16% of people should have IQ scores between 70 and 85. This is because the IQ scores follow a normal distribution, and IQ scores between 70 and 85 fall within one standard deviation of the mean (85 is one standard deviation below the mean and 70 is one standard deviation below that)

(d) About 0.1% of people should have IQ scores above 130. This is because IQ scores above 130 are considered to be in the top 0.1% of the distribution.

Step-by-step explanation:

Answer:

a) To determine an equation for the revenue, y, when x packages of batteries are sold, we need to know the price of each package of batteries.

Since the price of a package of batteries is $5.00, the revenue, y, when x packages of batteries are sold is given by y = 5x, where x is the number of packages of batteries sold and y is the revenue in dollars.

b) To find the maximum daily revenue that Rahj can expect from battery sales, we need to find the value of x that maximizes y = 5x.

Given that for every increase of 10¢ in the price A of a package of batteries, sales decrease by 10 packages per day. And the store normally sells 700 packages of batteries per day, at $5.00 per package.

It means that the store will sell a maximum number of batteries when the price is at $5.00

And the maximum daily revenue will be $5 * 700 = $3500.

So the maximum daily revenue that Rahj can expect from battery sales is $3500. And the number of packages of batteries sold when the revenue is at a maximum is 700.

The equation is y = 5x, where x is the number of packages of batteries sold and y is the revenue in dollars.

The zeroes of the equation are the points at which the function crosses the x and y-axis.

The x-intercept is the point at which the function crosses the x-axis. It happens when y = 0. So the x-intercept of this equation is (0,0)

The y-intercept is the point at which the function crosses the y-axis. It happens when x = 0. So the y-intercept of this equation is (0,0)

Step-by-step explanation:

Answer:

what is this i do not know sorry so no 30 points right

Area of figure 1 is 468 cm² and figure 2 is 45 cm².

Area is the entire amount of space occupied by a flat (2-D) surface or an object's form. On a sheet of paper, draw a square using a pencil. It has two dimensions. The area of a form on paper is the area that it occupies.

In these given figure for calculating the area of them we need to divide them into two or more shape like rectangle, triangle or square. For example, I will take Figure 1 and 2

For figure 1

Length of base = 16 + 14 =  30 cm

Length of right rectangle whose side is 14 and 14(smaller one)

Thus, its area = 14 * 14 = 196

Area of left rectangle whose side is 16 and 17 = 16 * 17 = 272

Total area of the figure = 272 + 196 = 468 square cm

For figure 2

If we split them into two shape they will become a square and a triangle

Area of triangle = 1/2 base * height = 1/2 * 6 *3 = 9

Area of square = side * side = 6*6 = 36

Thus, total area = 9 + 36 = 45 square cm

Therefore, Area of these given figures(in unit square) are:

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The quotient of these two expressions is not a finite value.

A quotient is a result obtained by dividing one quantity by another. It is the number that results from dividing one number by another.

Here,

Given : The quotient of

2-√√√8

and

4+√12

is not a finite value.

Explanation:

The square root of 8 is 2, so the first square root is 2, the second one is also 2, the third one is 2 again.

So the expression inside the first square root becomes 8, and the whole first square root becomes 2.

So the final expression would be:

2 - (2) = 0

On the other hand, √12 = √(223) = 2*√3

So the final expression would be:

4+2*√3

Hence, the quotient of these two expressions is not a finite value.

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The cost of a candy bar is equal to $1.61.

In order to write an equation that model this situation, we would assign variables to the cost of candy bars and the cost of soda respectively, and then translate the word problem into algebraic equation as follows:

Next, we would translate the word problem into an algebraic equation based on the fact that three (3) candy bars and one (1) soda costs $5.63 as follows;

3x + y = 5.63   ...equation 1.

Additionally, one candy bar and four sodas cost $4.81 at the same price;

x + 4y = 4.81 ...equation 2.

x + 4(5.63 - 3x) = 4.81

x + 22.52 - 12x = 4.81

11x = 22.52 - 4.81

x = 17.71/11

x = $1.61

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Answer:

Step-by-step explanation:

The quadrilateral's new coordinates will be J(4, 4), K(3, 4), L(1, 1), and M (4,1) when the procedure is applied.

A pair of numbers called coordinates are used to locate a point or a form in a two-dimensional plane. The x-coordinate and the y-coordinate are two numbers that define a point's location on a 2D plane.

Given coordinates of a quadrilateral J(-4, 4), K(-3, 4), L(-1, 1), M(-4,1)

Reflect in the x-axis

Since,

When you reflect a point across the x-axis, the x-coordinate remains the same, but the y-coordinate is taken to be the additive inverse. The reflection of point (x, y) across the x-axis is (x, -y).

thus new coordinates will be,

J(-4, -4), K(-3, -4), L(-1, -1), M(-4,-1)

Rotate 180 degrees about the origin

Since,

When we rotate a figure of 180 degrees about the origin either in the clockwise or counterclockwise direction, each point of the given figure has to be changed from (x, y) to (-x, -y) and graph the rotated figure.

Thus new coordinates will be

J(4, 4), K(3, 4), L(1, 1), M(4,1)

Therefore, After applying the given operation the new coordinates of the quadrilateral will be  J(4, 4), K(3, 4), L(1, 1), and M(4,1).

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The number of quarters Dalton has is 5.

Dalton has $3.05 in dimes and quarters. He has 13 more dimes than quarters. Therefore, the number of quarters he has can be calculated as follows:

Hence, using system of equation,

Therefore,

let

x = number of quarters

y = number of dimes

y = x + 13

0.25x + 0.1y = 3.05

using substitution method,

0.25x + 0.1(x + 13) = 3.05

0.25x + 0.1x + 1.3  = 3.05

0.35x = 3.05 - 1.3

0.35x = 1.75

x = 1.75 / 0.35

x = 5

Therefore,

number of quarters = 5

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The value of the expression - 9(18 - 9 + 12) + 12(- 9 + 18 + 18) is 135.

If a system of equations only contains two linear equations with two variables, the system's equation can be graphed, the graph will have two straight lines, and the intersection point(s) of those lines will be the system's solution.

There are only three matching forms of solution for a given system of equations because there are only three different ways that two straight lines in the plane can graph.

Let, The rectangle be x, the triangle by y, and the star be z.

Therefore,The three linear equations are,

x + 3y + z = 57...(i)

12x + 5y = 234...(ii)

8x - 6x + 3x = 60...(iii)

5x = 60.

x = 12.

Putting the value of x in eqn(ii) we have,

12(12) + 5y = 234.

144 + 5y = 234.

5y = 90.

y = 18.

Now, Putting the value of x and y in eqn(i) we have,

12 + 3(18) + z = 57.

12 + 54 + z = 57.

z = - 9.

So, The value of the expression z(y + z + x) + x(z + y + y) is,

= - 9(18 - 9 + 12) + 12(- 9 + 18 + 18).

= - 9(21) + 12(27).

= - 189 + 324.

= 135.

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Answer:

x=3

Step-by-step explanation: I'm not 100% if this is it because it's been awhile but I believe that you write 2x+2=4x-4 to solve for x since they're both y=mx+b equations. After solving it you would get 3

Answer:

No, Jasmine is not correct. The Lowest Common Multiple (LCM) of two numbers is the smallest number that is a multiple of both numbers. Multiplying the two numbers together is not always the correct method to find the LCM.

For example, the LCM of 5 and 8 is 40, but the product of 5 × 8 = 40 is not the LCM.

A more accurate way of finding the LCM is by using the prime factorization of the numbers. By finding the prime factorization of the two numbers, you can take the highest exponent of each prime factor and multiply them together. The result of that multiplication is the LCM of the two numbers.

In this case, the prime factorization of 5 is 5 and 8 is 2^3. The LCM of 5 and 8 is 2^3*5 = 40. So Jasmine's claim that 5 x 8 = 40 and the LCM of 5 and 8 is 40 is not correct.

Answer:

Step-by-step explanation:

3/ B is a salesperson and C is a programmer.

The correct option is: 2/ B is a programmer, and C is a salesperson

Let's analyze the statements and determine what B and C are:

A mumbled a response that the visitor couldn't hear clearly. We don't have any information from A's response.

B said, "A said that he is a salesperson." Since we know that salespeople always lie, we can infer that B is lying about A's response. Therefore, if A is a programmer (telling the truth), then B must be a salesperson.

C said, "Don't believe B; he is lying!" If we already determined that B is a salesperson (lying about A's response), then C is suggesting that B's statement is false, which means A's response is the opposite of what B said. So if B claimed that A is a salesperson (which was a lie), then A must be a programmer (telling the truth).

Based on the above analysis:

A is a programmer.

B is a salesperson.

C is a programmer.

So, the correct option is: 2/ B is a programmer, and C is a salesperson.

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