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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 equivalent equation to Paolo's equation is,

w = Start Fraction uppercase P minus 2l Over 2 End Fraction.

What is algebraic operation?

A basic algebraic operation in mathematics is any of the common arithmetic operations, such as addition, subtraction, multiplication, division, raising to a whole number power, and taking roots (fractional power).

Multiplication and division tasks should be completed first from left to right, followed by addition and subtraction tasks from left to right.

Given:

uppercase P = 2 (l + w)

Simplifying this,

uppercase P = 2l + 2w

Subtract 2l from both sides,

uppercase P - 2l = 2l  + 2w - 2l

uppercase P - 2l = 2w

Divide both sides by 2,

(uppercase P - 2l) / 2 = 2w / 2

(uppercase P - 2l) / 2 = w

Hence, the equivalent equation to Paolo's equation is,

w = Start Fraction uppercase P minus 2l Over 2 End Fraction.

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Answer: [tex]10 \frac{2}{3}[/tex]

Step-by-step explanation:

[tex]5 \times \frac{7}{3}=\frac{5 \times 7}{3}=\frac{35}{3}=10 \frac{2}{3}[/tex]

Answer:

600 ml

Step-by-step explanation:

One of the rules of ratio includes sorting ratio in order according to the question. In this case, squash is mentioned first, then water. Hence, the ratio is:

squash:water = 1:6

Use cross multiplication:

1       :       6

100  :        ?

Multiply 100 by 6 then divide it by 1: which basically means 100 * 6 = 600 ml.

If you are unfamiliar with cross multiplication, then simply find out how many times did you have to multiply the 1 in the squash ratio to result to 100, which is 100, then multiply 6 by that answer = 6 * 100.

Hope you understood :)

0.9976 percent of the time, the automobile won't start immediately away.

An example of a continuous probability distribution is the normal distribution, in which the majority of data points cluster in the middle of the range, while the remaining ones taper off symmetrically toward either extreme. The distribution's mean is another name for the center of the range.

Given that,

X = number of morning car starts right away

X          0            1            2             3               4              5

p(x)  0.0024   0.0283   0.1323   0.3087    0.3601    0.1681

So now we are able to find the given probability

p(x ≥ 1) = 1 - p(0)

1 - 0.024 = 0.9976

Here we used complementary rule to find the answer

p(A') = 1 - p(A)

Therefore, the probability that the car does not start right away is 0.9976.

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Answer:

18w^6u^8 = 2 * 3 * 3 * w^6 * u^8

30w^2u^5y^7 = 2 * 3 * 5 * w^2 * u^5 * y^7

The greatest common factor of these two expressions is 2 * 3 * w^2 * u^5

So the greatest common factor of 18w^6u^8 and 30w^2u^5y^7 is

2 * 3 * w^2 * u^5

Answer:

D

Step-by-step explanation:

the midsegment of a trapezoid is half the sum of the parallel sides, that is

midsegment = [tex]\frac{WT+VU}{2}[/tex] = [tex]\frac{17.5+6.1}{2}[/tex] = [tex]\frac{23.6}{2}[/tex] = 11.8

Answer:

  A, C, D

Step-by-step explanation:

You want the angles in the list that have π/3 as the reference angle.

The reference angle is the smallest angle between the angle's terminal side and the x-axis. The cosine and sine of the reference angle have the same magnitude of the cosine and sine of the angle in question.

The attached table shows that 7π/3, 2π/3, and 19π/3 have the same reference angle: π/3.

The total interest paid for the period of three months will be $600 on the loan amount of $550000.

The interest is the charges levied on the amount which we borrow from any bank for a particular period of time.

Here in the question given data is

P= $550000

R=2.0%+2.8%=4.8%

T=1/4 years or three months

So from the simple interest formula

SI = PRT / 100

= 550000 x 4.8 x 1/4 / 100

= 6600

Hence, the total interest paid for the period of three months will be $600 on the loan amount of $550000.

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Answer:

D. 41 races

Step-by-step explanation:

We can use the equation:

Number of races per year = Total number of races / Number of years

In this case, the total number of races is 287 and the number of years is 7.

Plugging in the values:

Number of races per year = 287 / 7

Number of races per year = 41

So, Laurie won 41 races each year. The answer is D) 41 races

The simultaneous equation 5x + 2y = 9 and x + y = -3 is solved by elimination method as follows

There are various methods of solving simultaneous equation however for this problem we solve with elimination method

The equation is 5x + 2y = 9 and x + y = -3

multiply x + y = -3 by 2

2x + 2y = -6

subtract 2x + 2y = - 6 from 5x + 2y = 9

5x + 2y = 9

2x + 2y = - 6

this will result to 3x = -15

solve for x by dividing by 3

x = -5

substitute x = -5 to x + y = -3

-5 + y = -3

y = -3 + 5

y = 2

hence x = -5 and y = 2

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where’s the answer choices??? the picture?? did you finish the question??

Answer:

Step-by-step explanation:

The average speed for the whole journey will be 62.33 km per hour.

Speed is the rate at which an object's location changes in a particular direction. The distance traveled on relation changes to a particular direction. The distance in relation to the time it took to travel the distance is the speed. It's a scalar quantity.

Since Dwight drives 85 km at an average speed of 120 km/h and then 6 km at 90 km/h without stopping.

The average speed for the whole journey will be:

= (85 + 6) / (85 / 120) + (90 / 120)

= 91 / (0.71 + 0.75)

= 62.33 km per hour.

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Answer:

Step-by-step explanation:

82

The cost of both the shirt and pants each is $10, solved using elimination method.

Let s stand for shirt and p for trousers.

Then we may solve the following equations:

1st Equation:

2s + 3p = 50

2nd Equation:

3s +1p = 40

Our initial aim is to determine the cost of one shirt. To get rid of the pants, we might artificially multiply the second equation by -3. This is what it would look like:

2s + 3p = 50

-3(3s +1p) = -3(40) (40)

———————————————

2s + 3p = 50

-9s - 3p = -120 We can obviously remove the pants (p) now.

—————————————

-7s = -70

Divide both sides by -7 to isolate s, and we get:

s = 10 -> As a result, one shirt costs $10.

Pants = 2(10) + 3p = 50

p = $10

Let us calculate the cost of 5 shirts.

As a result, we will perform 5 x $10 = $50.

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Complete question:

You buy 2 shirts and 3 pairs of pants for $50. Your friend buys 3 shirts and 1 pair of pants for $40. how much does the shirts cost?

Considering the figure the value of angle b is

According to the vertical angle theorem, the opposing angles of two crossing lines must have the same value, or be congruent.

hence angle a = angle y

Then from exterior angle of a triangle theorem: If a triangle's side is created, the outside angle that results is equal to the sum of the two opposite internal angles.

angle b = angle a + 90

= 34 + 90

= 124 degrees

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The ordered pair of coordinates is (0, 28)

To answer to the question given, we have to find the point on the line that goes through the points given in the table when the x-axis represents the month of the year  and the y-axis represents the average temperature for that month.

We can read out this ordered pair from the attached graph

In conclusion, the graph displays the point on that line which is on the y-axis is (0, 28).

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Answer:

2 [tex]\frac{2}{9}[/tex] days

Step-by-step explanation:

Let d = the number of days.

[tex]\frac{1}{4}[/tex] d = [tex]\frac{1}{5}[/tex]d = 1

[tex]\frac{5}{20}[/tex] d + [tex]\frac{4}{20}[/tex] d = 1

[tex]\frac{9}{20}[/tex] d = 1  Multiply both sides by [tex]\frac{20}{9}[/tex]

([tex]\frac{20}{9}[/tex])([tex]\frac{9}{20}[/tex]) d = 1([tex]\frac{20}{9}[/tex])

d = [tex]\frac{20}{9}[/tex]   I can break 20 into 9 + 9 + 2

d = [tex]\frac{9}{9}[/tex] + [tex]\frac{9}{9}[/tex] + [tex]\frac{2}{9}[/tex]           [tex]\frac{9}{9}[/tex] = 1

d = 1 + 1 + [tex]\frac{2}{9}[/tex]

d = 2 [tex]\frac{2}{9}[/tex]

Answer:

Let's call the amount his wife paid for her car "x". We know that:

Marc's car = $52,000

Marc's car = 2x - $7,600

We can substitute the first equation into the second equation

52,000= 2x-7600

52,000+7600=2x

59,600=2x

x=29,800

His wife paid $29,800 for her car.

Answer:

$29,800.00

Step-by-step explanation:

52000 = 2x - 7600  Add 7600 to both sides

52000 + 7600 = 2x

59600 = 2x  Divide both sides by 2

29800 = x

Answer: 24/14 or 1 10/14

Step-by-step explanation:

11/14 + 9/14 = 20/14

Add the 11 and nine first.

Then add 20/14 + 4/14 and that = 24/14 or you can turn it into a mixed fraction of 1 10/14.

You're Welcome!

Solution for the given System of linear equation is:

Simultaneous equations, system of equations Two or more equations in algebra must be solved jointly (i.e., the solution must satisfy all the equations in the system). The number of equations must match the number of unknowns for a system to have a singular solution.

There are four methods to solving systems of equations: graphing, substitution, elimination and matrices.

Given,  the system of linear equations on the left with its solution type on the right

For  Y=2x-1 and Y=2x+1

Adding both equation,  we will get y = 4x

Thus, these equations have infinite number of solution

For 2x - y = 7 and 3x + y = 3

Adding these equations

5x = 10

x= 2

Substitute the value in equation 1

y = -3

Thus, solution is (2, - 3)

therefore, the Solution for the given System of linear equation is:

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Complete question:

Answer:

The answer is 32

Step-by-step explanation:

We solve this by first finding the angle 3. To do this we subtract 180 (the sum of a triangle) and the two known angles. 180-15-17 = 148.

So now we know that the 3rd angle is equal to 148. Now to find the angle 4 we subtract angle 3 from 180, because a straight line is equal to to 180 degrees; 180-148=32

Hope that helps

Answer:

27/7

Step-by-step explanation:

First, note that 3 6/7 is a mixed number, also know as mixed fraction. It has a whole number and a proper fraction. The numbers in the mixed fraction are defined as follow:

3 = whole number

6 = numerator

7 = denominator

To convert mixed number 3 6/7 to improper fraction, you follow these steps:

Multiply the whole number by the denominator

3 × 7 = 21

Add the product from Step 1 to the numerator

21 + 6 = 27

Write answer from Step 2 over the denominator

27/7

The mixed number 3 6/7 converted to improper fraction is therefore :

27/7

Answer:

27/7

Step-by-step explanation:

Answer:

Step-by-step explanation:

Approximately 68% of the data points in a dataset are expected to be within one standard deviation of the mean, assuming that the data follows a normal distribution. This is known as the Empirical Rule or the 68-95-99.7 rule. According to this rule, approximately 95% of the data points are expected to be within two standard deviations of the mean, and approximately 99.7% of the data points are expected to be within three standard deviations of the mean.

Please note that this rule applies only to a normal distribution, if the data is not normally distributed, the proportion may be different.

Answer:

Approximately 68% of the data points in a data set are expected to be within one standard deviation of the mean because of the 68-95-99.7 rule.

Step-by-step explanation:

This rule states that approximately 68% of the data points in a normal distribution fall within one standard deviation of the mean, 95% within two standard deviations, and 99.7% within three standard deviations.

Answer:

Step-by-step explanation:

The number of new jobs that would be created would be 1,120,000. This is calculated by multiplying the number of workers (16,000,000) by the projected job growth rate (7%) which equals 1,120,000.

The equation that can be used to determine the total cost, given the number of movie tickets, is c = 8. 50 c

The equation that shows the total cost when you buy a certain number of tickets, can only be found after you solve for the ticket price.

The ticket price is :
= Cost of tickets / Number of tickets

= 42. 50 / 8

= $ 8. 50

The equation for the total cost would therefore be:

Total cost = Number of tickets x Cost per ticket

c = f x 8. 50

c = 8. 50 f

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Answer:

Solving by Factoring is a strategy used to solve quadratic equations. This strategy involves factoring the quadratic equation. Factoring is breaking an expression down into smaller expressions that when multiplied together will equal the original expression.

Step-by-step explanation:

To solve a quadratic equation by factoring we must first get the equation into the form ax^2 + bx + c = 0. From here we must use a strategy of factoring known as Reverse FOIL. By using reverse FOIL we will break the equation down into smaller parts. The four steps to use in reverse FOIL are:

1. Find two factors of “ac” (the coefficient of x^2) that when added together equal “b” (the coefficient of x).

2. Multiply the two factors you found in step one to produce “ac.”

3. Group the two terms with the “ac” terms in the equation.

4. Factor the two terms with “bx” in them.

For example, if we have an equation such as 9x^2 + 15x + 4 = 0  we would look for two factors of 4 (ac) that when added together equal 15 (b). The two factors of 4 that when added together equal 15 are -1 and -4. Therefore our equation would become: (9x^2 -1x -4x +4) and we can group the terms like this: (9x^2 -1x)(-4x +4).

The fourth step is to factor the two terms with “bx” in them. In our equation, the two terms with “bx” in them are -1x and -4x. Factoring these terms give us: (9x^2 -1x)(-4x +4) = (3x -1)(3x -4).

The final step is to find the two solutions, or the “x” values, that make the equation equal zero. To find these two x values, just set each factor to zero, and solve the resulting equations. In this example, setting the first factor, (3x - 1) equal to zero, we get x = (1/3); setting the second factor, (3x - 4) equal to zero, we get x = (4/3).

Therefore, the two solutions to 9x^2 + 15x + 4 = 0 are x = (1/3) and x = (4/3).

Using the strategy of Factoring, we have been able to successfully solve the equation 9x^2 + 15x + 4 = 0.

Answer:

  D.  5

Step-by-step explanation:

You want the constant of proportionality in the relation shown by the graph.

A proportional relation has the equation ...

  y = kx . . . . . . . . where k is the constant of proportionality

When x=1, this becomes ...

  y = k

The value of y when x=1 is marked on the graph: y = 5 at that point, so ...

  k = 5

The value of the constant of proportionality is 5.

The exact value of x depends on the context of the problem. Without any additional information, it is impossible to answer this question.

The average of the numbers 11, 20, 13, and 16 is 15

The average may be calculated by dividing the total number of values by the sum of all the numbers. An average of the values in a sample of data may be used to determine a mean. In other words, the arithmetic mean is another name for an average. A mean is a term used to describe the average.

Finding an average helps us understand a general pattern of behavior or trend. For example, knowing Mrs. Mansell's average shopping expenditure helps us understand whether she typically spends a lot or little money, and knowing Keiran's average spelling score helps us understand how proficient he typically is.

In the above question:-

The average of the numbers 11, 20, 13, and 16  is

15

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To divide 3/4 by 1/2 using unit rate proportionality, we can set up a proportion with 3/4 as the numerator and 1/2 as the denominator, and then cross-multiply and solve for the unknown value.

3/4 / 1/2 = X

To solve for X, we can cross-multiply to get:

(3/4) * (2/1) = X * (1/2)

Which simplifies to:

3/2 = X

So 3/4 divided by 1/2 is equal to 3/2.

It's important to note that when dividing fractions, we can also simply invert the divisor and multiply the two fractions, 3/4 * 2/1 = 6/4 =3/2.