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We can graph a reciprocal function using the function’s table of values and transforming the graph of y=1/x

A new function called the reciprocal function is produced when the reciprocal function is found. These functions have intriguing characteristics and distinctive graphs. We also represent these patterns using reciprocal functions when two expressions are inversely proportional. A constant on the numerator and an algebraic expression in the denominator makes up reciprocal functions.

How to find the reciprocal of a function?

By dividing 1 by the provided number, we can find the reciprocal of a given number. Similar reasoning is used to get a function's reciprocal: we divide 1 by the function's expression.

We can graph a reciprocal function using the function’s table of values and transforming the graph of y=1/x

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Answer:

26 R 1

Step-by-step explanation:

The fractions found in the 2/n table in the Rhind Mathematical Papyrus.

2/7 = (m n 2 ) 1 n (m n 2 )

= (2 7 2 ) 1 7 (2 7 2 )

= (14 2 ) 1 7 (14 2 )

= 7 1 7 + 7 1 14

2/35 = (m n 2 ) 1 n (m n 2 )

= (2 35 2 ) 1 35 (2 35 2 )

= (70 2 ) 1 35 (70 2 )

= 35 1 35 + 35 1 70

2/91 = (m n 2 ) 1 n (m n 2 )

= (2 91 2 ) 1 91 (2 91 2 )

= (182 2 ) 1 91 (182 2 )

= 91 1 91 + 91 1 182

Using the identity (m n 2 ) 1 n (m n 2 ) we can decompose the fractions 2/7, 2/35, and 2/91 into unit fractions. For 2/7, we obtain the decomposition 7 1 7 + 7 1 14, for 2/35 the decomposition 35 1 35 + 35 1 70, and for 2/91 the decomposition 91 1 91 + 91 1 182. This matches the fractions found in the 2/n table in the Rhind Mathematical Papyrus.

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Answer:3/2

Step-by-step explanation: just did the test

As all sides have grown by 2/3 times, The scale factor is  2/3. Thus, option A is correct.

In its simplest form, a scale factor is the proportion between the model measurement and the actual measurement. The scale factor, as opposed to a scale ratio, does not contrast various measurement units. A model car that is scaled at one-twentieth of its real-world counterpart is said to be that size. The car is also 20 times bigger than the model, according to this statement.

16 feet is the length of a fence. The fence is depicted as being 4 inches tall on a map. Write a ratio comparing the two quantities before attempting to calculate the scale factor of the drawing to the actual fence.

Given triangle side are 6, 6, 8 and scaled triangle is 9,9,12

The corresponding sides are

6/9, 6/9, 8/12

When you simply, we get

2/3, 2/3, 2/3

As all sides have grown by 2/3 times, The scale factor is  2/3. Thus, option A is correct.

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Answer:

$1.5 per book

Step-by-step explanation:

Since y=1.5x, the rate of change is 1.5/1. Rate of change: y/x. Hence, the rate of change is 1.5/1 since y=1.5 and x=1.

1.5 / 1 = 1.5

Hence, the rate of change is 1.5.

But what's 1.5 represent?

1.5 is the number of dollars earned per book sold.

Hence, the rate of change is $1.5 per book.

Percentage is a concept used to express a fraction as a part of 100. It is typically expressed as a fraction with a denominator of 100 and is written as a number followed by the percent sign (%). For example, the fraction 3/20 can be expressed as 15%, which means 15 out of every 100. Percentage is a useful concept when comparing two or more values, as it provides a way to measure the relative size of each value. For example, if one group of people has 25% of the total number of votes, this means that they have more votes than the other groups, whose percentages are lower.

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Complete question:

A total of 28% of Americans smoke cigarettes, 7% smoke cigars and 5% smoke both cigarettes and cigars

The area covered by the wallpaper will be 164.25 square feet.

We know the perimeter of any 2D figure is the sum of the lengths of all the sides except the circle and the area of a rectangle is the product of its length and width.

We know the area of a rectangle is (length×width).

Given, A wallpaper measures 9 feet by 18 1/4 feet.

Therefore, The area of the wallpaper will be,

= (9×73/4) square feet.

= 164.25 square feet.

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The arctan integral. 3 5 arctan 1 x d = 5 [ [tex]x[/tex] arctan ( [tex]\frac{1}{x}[/tex] ) dx - ( [tex]-(\frac{1}{2} )[/tex] [1+[tex]x^{2}[/tex]] ; where ([tex]\sqrt{3}[/tex] to 1 )

The basic arctan formula can be given by θ = tan-1(Perpendicular / Base). Here, θ is the angle between the hypotenuse and the base of a right-angled triangle.

The signed area of the region in the plane that is circumscribed by the graph of a specific function between two points on the real line can be used to describe definitive integrals. Areas above the plane's horizontal axis are often positive, whereas those below it are typically negative.

= [tex]\int\limits[/tex] 5 arctan ( [tex]\frac{1}{x}[/tex] ) dx ; where ([tex]\sqrt{3}[/tex] to 1 )

[tex]\int\limits[/tex] 5 arctan ( [tex]\frac{1}{x}[/tex] ) dx = [tex]5\frac{(2\sqrt{3} )ln(2)+2\pi -\sqrt{3} \pi }{4\sqrt{3} }[/tex]

= 5  [tex]\int\limits[/tex] arctan ( [tex]\frac{1}{x}[/tex] ) dx

= 5 [ x arctan ( [tex]\frac{1}{x}[/tex] ) dx - ( [tex]-(\frac{1}{2} )[/tex] [1+[tex]x^{2}[/tex]] ; where ([tex]\sqrt{3}[/tex] to 1 )[tex]x_{123}[/tex]

Therefore,

The arctan integral. 3 5 arctan 1 x d = 5 [ [tex]x[/tex] arctan ( [tex]\frac{1}{x}[/tex] ) dx - ( [tex]-(\frac{1}{2} )[/tex] [1+[tex]x^{2}[/tex]] ; where ([tex]\sqrt{3}[/tex] to 1 )

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The average wage of men is $819 and of women is $657 in 2009

An equation is the equality between two algebraic expressions, which have at least one unknown or variable.

Information about the problem:

To solve this problem we must establish the equations according to the given data and solve the operations:

M = W + 162                    (1)

M + W = 1476                  (2)

We have two equations with two unknowns, substituting the value (M) in the second equation, we have:

M + W = 1476

W + 162 + W = 1476

162 + 2W = 1476

2W = 1476 - 162

2W = 1314

W = 1314/2

W = 657

Substituting (W) into one of the equations (M) we have:

M = W + 162

M = 657 + 162

M = 819

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Answer:

[tex]18 + \sqrt[12]{2} [/tex]

= 34.97056

The graph of the inequality is added as an attachment

From the question, we have the following parameters that can be used in our computation:

x≤ 8

The above expression is an inequality that implies that

The value of x does not exceed 8

Next, we plot the graph

See attachment for the graph of the inequality

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Answer:

C' (-2, -2)

D' (-2, 2)

E' (2, 0)

F' (0, -2)

Step-by-step explanation:

A dilation of factor k about the origin is a transformation that enlarges a figure by a factor of k, while keeping the origin fixed.

It means that each point (x, y) on the pre-image is transformed to a new point (kx, ky) in the dilated figure.

Therefore, the rule for a dilation of 2 about the origin is:

From inspection of the given diagram, the vertices of the pre-image are:

Applying the dilation rule (x, y) → (2x, 2y):

Answer:

Step-by-step explanation:

we will maintain an accurate count of all inventories.

so A is correct.

The probability that vertex b will be the bottom vertex will be 1/16

The ant has four equally likely possibilities for his initial step from the top vertex, each heading to one of the four vertices close to the top vertex.

When the ant reaches vertex A, he has four equally likely next steps, each heading to one of the vertices next to vertex A.

Only one of these possibilities, however, will send him to the bottom vertex: the one that brings him straight to the bottom vertex.

As a result, the ant's chance of reaching the bottom vertex after two steps is 1/4 * 1/4 = 1/16.

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Answer: 45 cents.

Step-by-step explanation: We can find the cost per inch of wire by dividing the total cost by the total length of wire:

75 cents / 15 inches = 5 cents/inch

Now that we know the cost per inch, we can find the cost of 9 inches of wire by multiplying the cost per inch by 9:

5 cents/inch * 9 inches = 45 cents.

Answer:45 cents for 9 inches of wire

Step-by-step explanation:

Per every 5 incheses is 0.25 cents 0.75/15=$0.25 and then taking 0.25/5=$0.05 cents. So 1 inch costs 0.05 cents. So multiply 0.05×9=$0.45 cents. 45 cents

The expressions that equal 36 is:

E) 53 − (2. 5 × 30) − 20

Evaluated the mathematical expressions in each response to see if they equal 36.

A. (14⋅32)2−28 = (448)² - 28 = 14⁴ - 28 = 2016 - 28 = 1988, not equal to 36.

B. 23 + (58−54)2 + 122 = 23 + (4)² + 12 = 23 + 16 + 12 = 51, not equal to 36.

C. 92 − (43 + 32) + 30050 = 9² - (7 + 3) + 30050 = 81 - 10 + 30050 = 30021, not equal to 36.

D. 124 + (82 − 42) − 99 = 124 + (64 - 16) - 99 = 124 + 48 - 99 = 73, not equal to 36.

Thus, only the expressions listed in my previous answer equal 36.

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(x + 1) is not a factor of the  polynomial,

x¹⁴⁵ + 3x⁴⁵ - 4.

An expression that consists of variables, constants, and exponents that is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial.

Given:

We have a polynomial,

x¹⁴⁵ + 3x⁴⁵ - 4.

If (x + 1) is a factor.

Then x = -1 is a zero of polynomial.

Now,

(-1)¹⁴⁵ + 3(-1)⁴⁵ - 4

= -8

Therefore, (x + 1) is not a factor.

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An equation to model the relationship between the number of weeks, x, and the number of site visits, f(x) is 4800 = a(1.5)^x.

He found that before launching the new marketing plan, there were 4,800 visits.

Over the course of the next 5 weeks, the number of site visits increased by a factor of 1.5 each week.

Over the course of the next 5 weeks, initial visitor at x = 0, 4800

Increasing factor = 1.5

Equation of the model is given as:

f(x) = a(b)^x

From the question b = 1.5

Now the equation of model is:

f(x) = a(1.5)^x

At x = 0, f(x) = 4800

Now the equation of the model is:

4800 = a(1.5)^x

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The local extrema is at point (3, -22).

The function is increasing at interval (3, infinity) and decreasing at interval (- infinity, 3).

Now, According to the question:

The  function is :

[tex]f(x)=x^4-4x^3 +5[/tex]

Graphing Functions:

In order to graph a function, we first need to know the characteristics of that given function. On the other hand, we also need to simplify first the given function or rewrite it in general form for easier graphing.

Now, Graphing the function, we have

From the graph, the local extrema is at point (3, -22).

The function is increasing at interval (3, infinity) and decreasing at interval (- infinity, 3).

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After solving the equation the triangle given in question the 63.8°.

A triangle is a three-sided polygon with three angles. It is one of the basic shapes in geometry and is very versatile as it can be used to create many other shapes and structures. Triangles are generally classified by the length of their sides, which can be equal (an equilateral triangle), longer in one side than the other two sides (an isosceles triangle) or different in length on all three sides (a scalene triangle). They can also be classified by their angles, which can be acute (the angles are all less than 90 degrees), right (one angle is exactly 90 degrees) or obtuse (one angle is greater than 90 degrees).

x = 63.8°
Using the Law of Cosines, we can calculate the value of x:
x² = 17² + 9² - 2(17)(9)cos(90°)
x² = 289 + 81 - 306
x² = 64
x = √64
x = 8
Therefore, x = 63.8° (rounded to the nearest tenth).

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The five vectors in the span {v1, v2} are (0 0 0), (3 1 2), (-4 0 1), (-1 1 3) and (7 1 1)

We are given that two vectors

v1 = ( 3 1 2 ) and v2 = ( −4 0 1 )

We have to list five vectors in the span {v1, v2}

Let us choose five sets of weights as:

w = {0, 0}, {1, 0}, {0, 1}, {1, 1}, {1, -1}

So, the five vectors are:

V1 = 0 (v1) + 0 (v2) = (0 0 0)

V2 = 1 (v1) + 0 (v2) = (3 1 2)

V3 = 0 (v1) + 1 (v2) = (-4 0 1)

V4 = 1 (v1) + 1 (v2) = (3-4 1+0 2+1) = (-1 1 3)

V5 = 1 (v1) - 1 (v2) = (3+4 1-0 2-1) = (7 1 1)

Hence, the five vectors in the span {v1, v2} are (0 0 0), (3 1 2), (-4 0 1), (-1 1 3) and (7 1 1)

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Answer:

24 vowels

Step-by-step explanation:

A B C D E F G

  two out of 7 are vowels....you would expect to get 2/7 ths of 84 spins to be vowels

2/7 * 84 = 24 vowels

Suppose X and Y have joint p.d.f. f(x, y) = cxy/(1+x² + y² ) for 0 < x < 1, 0 < y < 1, and whatever constant c makes the nasty mess integrate to 1 is No as well as x and y are not independent

What is variables?

Any qualities, quantity, or number that can be gauged or tallied qualifies as a variable. A data item is another name for a variable. Examples of variables include age, sex, company income and expenses, country of birth, capital expenditures, class grades, eye color, and vehicle kind.

The joint p.d.f of X and Y is f(x, y)

f(x,y) = cxy/ 1+[tex]x^{2}[/tex]+[tex]y^{2}[/tex] for 0 < x < 1 and 0 < y < 1

marginal p.d.f of x = f(x):

f(x) = {1y_of(x,y)dy

= {1y=0 /cxy/ 1+x+[tex]y^{2}[/tex] dy

Cx/2 ( {1y=0 /2y/1+ [tex]x^{2}[/tex] + [tex]y^{2}[/tex] dy)

Take substitute 1+[tex]x^{2}[/tex]+ [tex]y^{2}[/tex] = t⇒2y dy=dt

Lower limit: y = 0⇒t=1+[tex]x^{2}[/tex]

Upper limit: y=1➡t=1+[tex]x^{2}[/tex]+1

F(x) =  cx/2

f 1y= 0 2y

=0 1+2+[tex]y^{2}[/tex]dy)

=Cx/2({1+[tex]x^{2}[/tex]+1dt/t

=1+[tex]x^{2}[/tex]t)

=cx/2(In(t) - ln(1+[tex]x^{2}[/tex])/1[tex]x^{2}[/tex])

=cx/2 (In (1+[tex]x^{2}[/tex]+1))-In(1+[tex]x^{2}[/tex]))

=cx/2 (In (1+[tex]x^{2}[/tex]+1/1+[tex]x^{2}[/tex]))

=Cx (In(1+1/1+[tex]x^{2}[/tex]))

marginal p.d.f of y = f(y):

f(y) = {1x

=0(x,y)dx

= F1x

=0/cxy/ 1+[tex]x^{1}[/tex][tex]y^{2}[/tex]=dx

= cy/2({1x)

=0/2x/1+[tex]y^{2}[/tex]+[tex]x^{2}[/tex]dx}

Take substitute 1 + [tex]y^{2}[/tex] + [tex]x^{2}[/tex] = t 2x dx = dt

Lower limit: x = 0

t = 1 + [tex]y^{2}[/tex]

Upper limit: x =1

=t + [tex]y^{2}[/tex] + 1

F(y)=cy/2({1x=0 2x/1+[tex]y^{2}[/tex]+[tex]x^{2}[/tex]/dx)

=cy({1+[tex]y^{2}[/tex]+1dt/t

=1[tex]y^{2}[/tex]t/)

=Cy/2((In(t))1+[tex]y^{2}[/tex]+1/1+[tex]y^{2}[/tex])

=cy(In(1+[tex]y^{2}[/tex]+1) – In( 1+[tex]y^{2}[/tex]))

=cy(In(1+[tex]y^{2}[/tex]+1/1+[tex]y^{2}[/tex]))

=cy/2(In(1+1/1+y2))

Now we have to check for independence.

F(x,y)= cxy/1+[tex]x^{2}[/tex]+[tex]x^{2}[/tex] for0<x<1 and 0<y<1

F(x) = cx/2( In(1+1/1+[tex]x^{2}[/tex])) for 0<x<1

F(y)=cy/2(In(1+1/1+[tex]y^{2}[/tex])) for < y <1

=f(x)*f(y)

=c2xy/4 ( In ( 1+1/1+[tex]x^{2}[/tex] ) *In( 1+1/1+[tex]y^{2}[/tex])) #f(x,y)

F(x,y) #f(x)* f(y) for all x and y

=x and y are not independent.

no is correct answer.

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The Coase theorem states that if property rights are well-defined and transaction costs are low, then the allocation of resources will be efficient, regardless of the initial allocation of property rights.

If Winston and Chloe successfully apply the Coase theorem to solve the problem of Winston's loud music externalizing a cost onto Chloe, they may reach a mutually beneficial agreement. This could result in either Winston reducing the volume of his music or compensating Chloe for the cost of the externalization, or a combination of both.

The goal is to reach a solution where the costs and benefits are more efficiently allocated between the two parties.

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The real exponential sequence for f[k]=f[kt] is f[k]=b^k.

What is exponential sequence ?

The exponential function is a mathematical function denoted by f(x)=\exp or e^{x}. Unless otherwise specified, the term generally refers to the positive-valued function of a real variable, although it can be extended to the complex numbers.

The real exponential sequence for f[k]=f[kt] can be shown to be f[k]=b^k by using the definition of exponential functions. If f[k]=f[kt], then f[k]=f[k-1]t and f[k-1]=f[k-2]t, and so on. By substitution, we have:

f[k]=f[k-1]t

f[k-1]=f[k-2]t

f[2]=f[1]t

f[1]=f[0]t

So we can write:

f[k]=f[k-1]t=f[k-2]t^2=...=f[1]t^(k-1)=f[0]t^k

Next, we can define b as f[0] and substitute it into the above equation:

f[k]=b^k

Therefore, the real exponential sequence for f[k]=f[kt] is f[k]=b^k.

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(OCF): OCF = Net Income + Depreciation & Amortization - Changes in Working Capital, (CapEx): CapEx = Investment in Property, Plant & Equipment + Investment in Intangible Assets. therefore, (FCFF): FCFF = OCF - CapEx

The Free Cash Flow to Firm (FCFF) is a measure of a company’s cash flow available for distribution to shareholders and debt holders. To calculate FCFF, the following three steps are taken:

1. Calculate Operating Cash Flow (OCF): OCF is calculated by taking net income, adding back depreciation and amortization, and subtracting any changes in working capital.

2. Calculate Capital Expenditures (CapEx): CapEx includes investments in property, plant, and equipment, as well as any investments in intangible assets.

3. Calculate Free Cash Flow to Firm (FCFF): FCFF is calculated by subtracting CapEx from OCF. This figure represents the cash flow available for distribution to shareholders and debt holders.

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height = 10.74 inches

for steps refer attachment

The volume of a cone = (1/3) πr2h cubic units

Therefore, the volume of a cone = 20.93 cubic units

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The correct values that create ordered pairs that are solutions to the solutions to the equation 3x - 5y = 20 are,

⇒ y₁ = - 1

⇒ x₂  = 10

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

The equation is,

⇒ 3x - 5y = 20

Now, If (5, y₁) is the solution of above equation, then it satisfy the equation.

⇒ 3x - 5y = 20

⇒ 3 × 5 - 5y₁ = 20

⇒ 15 - 5y₁ = 20

⇒ 15 - 20 = 5y₁

⇒ - 5 = 5y₁

⇒ y₁ = - 1

And, If (x₂, 2) is the solution of above equation, then it satisfy the equation.

⇒ 3x₂ - 5y = 20

⇒ 3x₂ - 5×2 = 20

⇒ 3x₂ - 10 = 20

⇒ 3x₂ = 20 + 10

⇒ 3x₂ = 30

⇒ x₂  = 10

Thus, The correct values that create ordered pairs that are solutions to the solutions to the equation are,

⇒ y₁ = - 1

⇒ x₂  = 10

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