a landscape architect wishes to enclose a rectangular garden on one side by a brick wall costing $40/ft and on the other three sides by a metal fence costing $20/ft. if the area of the garden is 142 square feet, find the dimensions of the garden that minimize the cost.

The required future value of the annuity is $127,336.80.

Jones Company borrowed money that must be paid back in 12 years. To ensure that the debt is repaid by the end of the 12th year, the corporation invests $8,000 at the end of each year at a rate of 5% compounded yearly.

Compute the future value of the annuity as follows:

Future value = Annuity - FVIFA

FVIFA is taken from the table, and substitutes the value of the annuity in the above formula

Future value = $8,000 × 15.9171

Apply the multiplication operation, and we get

Future value = $127,336.80

Therefore, the required future value of the annuity is $127,336.80.

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As proportional relationship, the amount decreasing at a rate milligrams per hour expression P(t) = 500 + e⁻⁰²ˣ

Proportional relationship:

In math, the relationships between two variables where their ratios are equivalent is known as proportional relationship.

Given,

Here we have the rate at which the= drug leaves the bloodstream proportional to the amount of the drug bloodstream: The amount of the drug in the bloodstream can be modeled by K; where constant and- time; hours At time 500 milligrams of the drug was administered. At the moment when the amount of the drug in the bloodstream 50 milligrams, the amount decreasing at a rate milligrams per hour.

Here we need to find the expression.

While we looking into the given question, we have identified the following details,

=> Bloodstream = 500 milligrams

Here they state that the bloodstream 50 milligrams, the amount decreasing at a rate milligrams per hour.

So, the expression for this proportional relationship is written as,

=> P(t) = 500 + e⁻⁰²ˣ

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The translation rule that maps A(-4, -2), B(-2, 6) and C (4, 4) to A' (-2, -2) B' (0, -10) and C' (6, -8) is

(x + 2, y + 4)

The transformation rule is solved by comparing the both preimage and image transformations as follows

preimage  image

A(-4, -2)   A' (-2, -2)

B(-2, 6)     B' (0, -10)

C (4, 4)     C' (6, -8)

x direction

-4 + x = -2, x = -2 + 4 = 2

-2 + x = 0, x = 0 + 2 = 2

4 + x = 6, x = 6 - 4 = 2

y direction reflection on the x axis leads to change of sign

preimage  image

A(-4, -2)   A' (-2, 2)

B(-2, 6)     B' (0, 10)

C (4, 4)     C' (6, 8)

-2 + y = 2, y = 2 + 2 = 4

6 + y = 10, y = 10 - 6 = 4

4 + y = 8, y = 8 - 4 = 4

The transformation rule is (x + 2, y + 4)

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The Future value of an annuity due of $200 each quarter for 2 1 2 years at 13%, compounded quarterly is $10263.734 ..

The future value of an annuity is the value of a group of regular payments at some point in the future. It assumes a particular rate of return, or discount rate. The higher the discount rate, the greater the annuity's future value.

P = PMT× ((1+r)ⁿ −1)/r

where:

P---> Future value of an annuity stream

PMT---->Dollar amount of each annuity payment

r -->Interest rate (also known as discount rate)

n--->Number of periods in which payments will be

We have given that

Present value for an Annuity = $200

compounded rate , r = 13%

but compounded quarterly, then, r = 13%/4

= 0.13/4 = 0.325

Number of years , n = 2 + 1/2 = 5/2

then change into quarterly, n = 5/2 × 4 = 10

Future value formula ,

F.V = PMT ( (1+i)ⁿ - 1)/r

=> Future value = 200((1+0.325)^10/0.325)

=> F.V = 10263.734

Hence, the future value of an annuity is $10263.734..

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Average one hour 45 minutes time is taken to read A Chirstmas Carol Novel.

There is total five chapters in this novel. In the ed of of beginning, Scrooge has completely transformed into a charitable, altruistic man. A chirstmas Carol is at a time when the British were investigating and reassessing past Christmas

traditions and place is Washington.

The average reader will spend 1 hour 4 minutes reading this book at 250 WPM (words per minute). A Christmas Carol is set in London during the Victorian era. The events of the story take place on Christmas Eve at Ebenezer's Scrooge home, where various events are shown by three visiting spirits. Charles Dickens wrote A Christmas Carol at a time when he was very critical of his writing and the world around him.

Dickens wrote A Christmas Carol at a time when the British were investigating and reassessing past Christmas traditions, including carols, and more recent practices such as Christmas cards and Christmas trees. He was influenced by his own adolescent experiences and by other writers' Christmas stories, such as Washington in his Irving and Douglas in his Jerold.

The book is divided into his five chapters, which Dickens entitled "Staves".

By the end of the novel, Scrooge has completely transformed into a charitable, altruistic man, rather than a misanthrope. This concept becomes apparent when you say, "I'm light as a feather, happy as an angel, and so baby." Scrooge changed his attitude and behavior.

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The amount must Lance Industries pay into the fund each period is $2,054.49

Define Sinking Funds

A fund set aside to cover a certain future expense is known as a sinking fund. The sinking fund can be thought of as an annuity if equal contributions are made on a regular basis; its value will rise until it is sufficient to pay the future expense.

Given,

Lance Industries borrowed = $130,000

Time = 18 years

Interest rate = 6%

The future value is,

FVₙ =PMT( (1+i/m)ⁿ - 1 ) / (i/m) )

PMT = payment fund semiannually.

i = 6% or 0.06

m = 2  (semiannually will be 2 times per year)

n = 18 * 2 = 36 periods

FV₃₆ = $130,000

Now, plug in the values in formula

FVₙ =PMT( (1+i/m)ⁿ - 1 ) / (i/m) )

130,000 = PMT ( (1 + 0.06/2)³⁶ - 1 ) / (0.06/2) )

130,000 = PMT ( (1.03)³⁶ - 1 ) / (0.03) )

PMT = 130,000 * ( 0.03 / (1.03)³⁶ - 1 ) )

        = $2,054.49

Hence, the amount must Lance Industries pay into the fund each period is $2,054.49.

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Qualifications for members of house of representatives and senate

r ;- Be a resident of the state from which they are elected, be at least 25 years old, and have been citizens for at least 7 years.

s ;- Be a resident of the State from which he or she is elected, at least 30 years old, and a citizen for at least 9 years.

Given,

The House of Representatives is the lower body of the United States Congress, and the United States Senate is its upper chamber. The United States' national bicameral legislature is made up of them all. Washington DC

Then,

Qualification for a member of the house of representatives, r ;-

Be a resident of the state from which they are elected, be at least 25 years old, and have been citizens for at least 7 years.

Qualification for a senator, s ;-

Be a resident of the State from which he or she is elected, at least 30 years old, and a citizen for at least 9 years.

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The differential treatment of individuals or groups without reference to behavior, qualifications, or other legal factors, resulting in a difference in outcome, is known as discrimination. Discrimination can occur based on various factors such as race, gender, age, religion, disability, or nationality.

There are different forms of discrimination, including: 1. Direct discrimination: This occurs when someone is treated less favorably because of a specific characteristic or attribute. For example, if an employer refuses to hire someone solely based on their gender, it would be considered direct discrimination. 2. Indirect discrimination: This happens when a seemingly neutral policy, criterion, or practice puts individuals with a particular characteristic at a disadvantage. For instance, if a job requires a height requirement that disproportionately affects a certain racial group, it would be considered indirect discrimination.

3. Systemic discrimination: This refers to discrimination that is built into the structures, policies, and practices of an organization or society. It may be unintentional but still leads to unequal outcomes. An example is when certain communities consistently receive lower funding for education compared to others, leading to systemic disadvantages for students in those areas.

Discrimination can have negative impacts on individuals and society as a whole, perpetuating inequality and hindering social progress. It is important to promote equality, fairness, and inclusivity to create a just and equitable society.

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The Maclaurin Series of xe²ˣ: x + 2x² + 2x³+ 4/3x⁴+ 2/3x⁵ +....

Given that,

f(x) = xe^2x

Taylor series of function f(x) at a is defined as:

f(x) = f(a) + f'(a)/1!/(x-a) +f''(a)/2! (x-a)² +....

Maclaurin series of Function F(x) is a Taylor series of Function f(x) at: a=0

f(x) = f(0) + f'(0)/1! /(x) +f''(0)/2!/ (x)² +....

Apply the Maclaurin Formula

= 0 +d/dx (xe²ˣ)(0)/1! x + d²/dx² (xe²ˣ)(0)/2! x² +....

Evaluate the derivatives :

= 0 + 1/1! x + 4/2! x² + 12/3! x³ + ...

Refine :

= x + 2x² + 2x³+ 4/3x⁴+ 2/3x⁵ +....

So, the Maclaurin series for f(x) = xe^2x is  x + 2x² + 2x³+ 4/3x⁴+ 2/3x⁵ +....

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The 500 sample size and 95% confidence level will both tend to increase the width of the confidence interval.

In this question, we have been given  the combinations of sample size and confidence level.

We need to select a combinations of sample size and confidence level that will give the widest interval.

We know that the confidence level is typically set in the range of 99% to 80%. The 95% confidence interval will be wider than the 90% interval and which will be wider than the 80% interval.

As we know increasing the confidence will increase the margin of error which results in a wider interval.

But increasing the sample size decreases the width of confidence intervals, as it decreases the standard error.

This means, for the widest interval we need to select a high confidence interval and small sample size.

Therefore, the sample size = 500 and the confidence interval = 95% will give the widest interval.

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175/26 large tiles can she stick to the ground.

Two or more expressions with an Equal sign is called as Equation.

Given,

A cement mix calls for 2 cups of water and [tex]1\frac{1}{4}[/tex] pounds of mix to make five large tiles stick to the ground,

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

2+5/4

13/4

Which means 13/4 is needed for 5 large tiles.

Yolanda has plenty of water but only [tex]4\frac{3}{8}[/tex] pounds of mix

We need to find how many large tiles can she stick to the ground.

Let x be the number of tiles.

[tex]4\frac{3}{8}[/tex] =35/8

So

(13/4)/5=(35/8)/x

Apply cross multiplication

13/4x=35/8×5

13/4x=175/8

x=175/8×4/13

x=700/104=350/52=175/26

Hence, 175/26 large tiles can she stick to the ground.

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Indefinite integral using integration by parts from x2 ln(x) dx is

[tex]\frac{1}{3}[/tex] [tex]X^{3\\}[/tex] (ln(x) - [tex]\frac{1}{3}[/tex]) + C

The given choice of u and dv

∫ [tex]x^{2} ln(x) dx[/tex]

we can use the formula

∫ u dv = uv - ∫ v du

Then split the component

u =  [tex]ln(x)[/tex]     du = [tex]\frac{1}{x}[/tex][tex]dx[/tex]

dv = [tex]x^{2}[/tex]         v = [tex]\frac{1}{3}x^{3}[/tex]

∫ u dv = uv - ∫ v du

∫ [tex]x^{2} ln(x) dx[/tex]   =  ln(x) [tex]\frac{1}{3}x^{3}[/tex] - ∫ [tex]\frac{1}{3}x^{3}[/tex] [tex]\frac{1}{x}[/tex] dx

                    = [tex]\frac{1}{3}x^{3}[/tex] ln(x) - [tex]\frac{1}{3}[/tex] ∫ [tex]x^{3}[/tex] [tex]\frac{1}{x}[/tex] dx

                    = [tex]\frac{1}{3}x^{3}[/tex] ln(x) - [tex]\frac{1}{3}[/tex] ∫ [tex]x^{3} . x^{-1}[/tex] dx

                    = [tex]\frac{1}{3}x^{3}[/tex] ln(x) - [tex]\frac{1}{3}[/tex] ∫ [tex]x^{2}[/tex] dx     ----> ∫ [tex]x^{2}[/tex] dx = [tex]\frac{1}{3} x^{3} + C[/tex]

                    =  [tex]\frac{1}{3}x^{3}[/tex] ln(x) - [tex]\frac{1}{3}[/tex] [tex]\frac{1}{3} x^{3} + C[/tex]

                    = [tex]\frac{1}{3} x^{3} ( ln(x) - \frac{1}{3} ) + C[/tex]

Therefore Indefinite integral using integration by parts

∫ [tex]x^{2} ln(x) dx[/tex]  is  [tex]\frac{1}{3} x^{3} ( ln(x) - \frac{1}{3} ) + C[/tex]

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The required simplified value of the x is given as 5.

Given that,
In triangle DEF, if m∠D = (2x)°, m∠E = (2x − 4)°, and m∠F = (x + 9)°.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

here,
for the triangle sum of the interior angles is equal to 180°.
∠D + ∠E + ∠F = 180
2x + 2x - 4 + x + 9 = 180
5x  + 5 = 180
5x = 175
x = 35

Thus, the required simplified value of the x is given as 5.

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When you are doing a survey of the time it takes for a person to run 100m, the unit that you would you use is seconds.

A unit of measurement is a definite magnitude of a quantity that is defined and adopted by convention or law and is used as a standard for measuring the same type of quantity. Any other such quantity can be expressed as a multiple of the unit of measurement. A length, for example, is a physical quantity.

A unit is any standard that is used to compare measurements. Unit conversions allow measurements of a property to be converted from one unit to another, such as centimeters to inches.

In this case, time is measured in seconds.

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Answer:

25!

in this type of questions you need to find 10 makers ( it's means you need to find numbers which has 2 or 5 in their prime factors) obviously there is a bunch of numbers which has 2 in their prime factors.

so we need to find multiples of 5. But you should be aware that some numbers have more than one prime factors of 5 e.g. 25 .

ok let's go back to the question.

starting from 1 , we've got 5, 10 , 15 ,20 &25(5²)

so the answer is 25!

Answer:

4.358

Step-by-step explanation:

sqrt(19) = 4.358

Using the law of cosines, the measure of the angles are  

α ≈ 127°

β ≈ 28°

γ ≈ 25°

From the question, we are to solve the triangle.

To solve the triangle, we will determine the value of the unknown angles.

Using the law of cosines, we can write that

cosα  = (b² + c² - a²)/2bc

From the given information,

a = 34

b = 20

c = 18

Thus,

cosα  = (20² + 18² - 34²)/2(20)(18)

cosα = -432/720

cosα = -0.6

α = cos⁻¹(-0.6)

α = 126.8699°

α ≈ 127°

Calculating angle β

cosβ  = (a² + c² - b²)/2ac

cosβ = (34² + 18² - 20²)/2(34)(18)

cosβ = 1080/1224

β = cos⁻¹(1080/1224)

β = 28.0724°

β ≈ 28°

To determine angle γ

α + β + γ = 180° (Sum of angles in a triangle)

127° + 28° + γ = 180°

155 ° + γ = 180°

γ = 180° - 155°

γ ≈ 25°

Hence,

α ≈ 127°

β ≈ 28°

γ ≈ 25°

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As per the concept of linear regression, the equation of the data is y ​= 133.1807 − 6.3096x.

The term linear regression means to determine the character and strength of the association between a dependent variable and a series of other independent variables.

Here we have given that mathematics and statistics teacher rex boggs, from Australia, weighed the bar of soap in his shower stall before showering in the morning. And the data on day and soap weight (in grams) appear in the table.

Here we need to find the linear regression equation that represents the given situation.

Based on the concept of linear regression, we know the the general formula for the regression is written as,

=> y = a + bx

FRom the given data, we have identified the value of the functions as,

a = 133.1807

b = -6.3096

r² = 0.9962

r = -0.9981

When we apply these values on the formula, then we get the equation as,

Then it implies the regression line is,

=> ŷ = a + bx = 133.18076.3096x

here a represents the day and y represents the weight in grams.

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Step-by-step explanation:

of the following is the correct arrangement of the following atoms in order of DECREASING first ionization energy?

O>Te>Se>Po

Po>Te>Se>O

O>Se>Te>Po

Po>Se>Te>O

Option c; The survey results will underestimate support for this political action committee in the entire population because people who respond are less likely to support an organization that asks for money. This is the correct statement about the survey.

What is politics?

Politics is a category of activities that are related to group decision-making or other types of power dynamics between people, such as the allocation of resources or status. Political science is the name of the area of social science that focuses on politics and governance.

Given,

A political action committee sends out a questionnaire to randomly-selected mailing addresses, asking people to rate the importance of a variety of economic and social issues facing the country. at the end of the questionnaire is an (optional) invitation to donate money to the political action committee.

We have to find the correct statement about the survey from the given options;

Because respondents are less inclined to support a group that solicits donations, the survey results will understate public support for this political action committee.

The correct statement about the survey is option c;

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The rate of change of the linear function A is 2, and the one of function B is 4, then the correct option is D.

A general linear function is written as:

y = a*x + b

Where a is the rate of change and b is the y-intercept.

In this case, we know that function A is:

y = 2x + 1

Then the rate of change is 2, and the y-intecept is 1.

We also know that if a line passes through two points (x₁, y₁) and (x₂, y₂), then the rate of change of that line is given by the formula:

a = (y₂ - y₁)/(x₂ - x₁)

In the case of function B we have the table:

x: 1   3  4  6

y: 3   11  15  23

We can use any two points on the table, if we use the first two ones:

(1, 3) and (3, 11) we will get:

a = (11 - 3)/(3 - 1) = 8/2 = 4

The rate of change of function B is 4, then the correct statement is the one in option D.

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Given Statement (a!)b = ab! is false becuase it is not appropriate to represent factorial like this.

What is Factorial?

In mathematics, the term "Factorial" refers to the sum of all positive integers that are less than or equal to a certain positive integer, which is followed by an exclamation point. Thus, factorial seven is denoted by the symbol 7!, which stands for 1*2*3*4*5*6*7. Factorial 0 is equivalent to 1 by definition.

(a!)*b = ab!

this depends on the value of a and b.

I'm not sure if the phrase "ab!" means to multiply a by b and then compute the factorial of the resulting product, as in (ab)!, or to compute the factorial of b first and then multiply this by a, as in a(b!). Either way, the assertion is false.

Given Question is incomplete Complete Question here:

assume that a and b are positive integers. for each statement below, determine whether the statement is true or false, and indicate your answer in the appropriate box  (a!)b = ab!  

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The VO2max test resulted by z score should result in a minimum score of 36 for 84% of college students.

To find the answer, we will use the z-score formula:

z = (x - μ)/σ

We will use the given values for the mean (μ = 44), the standard deviation (σ = 8), and the value we are looking for (x = 36).

z = (36 - 44) / 8

z = -1

We can then look up the percentage of values equal to or below -1 on the standard normal distribution table. This value is 84%. Therefore, we should expect 84% of college students to score at least 36 on the VO2max test.

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Answer:

  e. f(x) --> -∞ as x --> -3^+ and as x --> -3^-

Step-by-step explanation:

You want to know the behavior of f(x)= (x^2 + x - 12)/(x^2 + 6x + 9) near any excluded x-values.

The function can be factored as ...

  [tex]f(x)=\dfrac{x^2+x-12}{x^2+6x+9}=\dfrac{(x+4)(x-3)}{(x+3)^2}[/tex]

The excluded values are values of x where the denominator is zero. The only excluded value is x = -3. (eliminates all answer choices except E)

At either side of x = -3, the sign of the numerator is negative and the sign of the denominator is positive. That makes f(3-) < 0 and f(3+) < 0.

f(x) will never approach +∞, but f(x) approaches -∞ as x nears -3 from either direction.

Answer:

[tex]\textsf{e)} \quad f(x) \rightarrow -\infty\;\;\textsf{as}\;\; x \rightarrow -3^+ \;\;\textsf{and as}\;\;x \rightarrow -3^-[/tex]

Step-by-step explanation:

Given function:

[tex]f(x)=\dfrac{x^2+x-12}{x^2+6x+9}[/tex]

Factor the numerator:

[tex]\implies x^2+x-12[/tex]

[tex]\implies x^2+4x-3x-12[/tex]

[tex]\implies x(x+4)-3(x+4)[/tex]

[tex]\implies (x-3)(x+4)[/tex]

Factor the denominator:

[tex]\implies x^2+6x+9[/tex]

[tex]\implies x^2+3x+3x+9[/tex]

[tex]\implies x(x+3)+3(x+3)[/tex]

[tex]\implies (x+3)(x+3)[/tex]

[tex]\implies (x+3)^2[/tex]

Therefore, the rational function is:

[tex]f(x)=\dfrac{(x-3)(x+4)}{(x+3)^2}[/tex]

As the degree of the numerator is equal to the degree of the denominator, there is a horizontal asymptote at y = 1.

A vertical asymptote occurs at the x-value(s) that make the denominator of a rational function zero.

[tex]\implies (x+3)^2=0[/tex]

[tex]\implies x+3=0[/tex]

[tex]\implies x=-3[/tex]

Therefore, there is a vertical asymptote at x = -3.

As there is a vertical asymptote at x = -3, the excluded x-value is x = -3.

As x approaches x = -3 from both sides, the numerator of the rational function approaches -6 and the denominator approaches a very small positive number.  Therefore, the function approaches a very large negative number.

Therefore, the end behaviour of the function as it approaches the excluded value is:

Answer:

27°

Step-by-step explanation:

Let h = highest temperature

h = -15 + 42

h = 27°

Answer:

1.14x = 19.38

$17

Step-by-step explanation:

Let the price before delivery charge = x.

The charge is 14%, so it is 14% of x, or 0.14x.

The original price plus charge is x + 0.14x, or 1.14x.

1.14x = 19.38

x = 19.38/1.14

x = 17

The price is $17

Answer:

(36, 13)

Step-by-step explanation:

to find the midpoint you have the add the x and the y and then divide by two

to find one of the endpoints you just do the opposite

you multiply the midpoint by 2

and then subtract the remaining endpoint from it

(11, -1) --> (22, -2)

now subtract T from it

(36, 13)

that is your answer

The stock yield for the stocks will be 4.8%. The correct option is A.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

To get the stock to yield use this formula - annual dividend / current stock price or share price

Substitute the dividend of $.88 and the closing price of $18.33 to the formula above. Divide and simplify.

Stock yield = .88 / 18.33

Stock yield = 0.0480 x 100

Stock yield = 4.8%

Therefore, the stock yield for the stocks will be 4.8%. The correct option is A.

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The rate at which the volume of the cube is changing is 1200 in³/seconds.

Volume is the space occupied by a solid object.

To calculate the rate at which the volume of the cube is changing, we use the formula below.

Formula:

Where:

From the question,

Given:

If, the volume of a cube is V = L³,

Then,

Substitute these values into equation 1

Hence, the rate at which the volume is changing is 1200 in³/seconds.
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The restrictions for x and y are given as follows:

3. x ∈ W, y ∈ W.

5. x ∈ W, y ∈ W.

To obtain the restrictions, the first step is classifying the variables as either discrete or continuous, as follows:

In this problem, the variables are both resumed as follows:

Number of tickets sold in the Super Bowl.

The possible values are given as follows:

0, 1, 2, ...

Which are countable values, hence discrete, and that also cannot assume negative values, hence they belong to the whole set and not the integer set, thus the restrictions are:

x ∈ W, y ∈ W.

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