An artist has been commissioned to make a stained glass window in the shape of a regular octagon. The octagon must fit inside a 10 in square space. Determine the length of each side of the octagon. Round to the nearest hundredth of an inch.

Answer:

14.2 feet

Step-by-step explanation:

Use the Pythagorean Theorem to solve both parts.

Part 1.

35 is the hypotenuse and 21 is a leg.

[tex]a^{2} +b^{2} =c^{2} \\a^{2} +21^{2} =35^2\\a^2 + 441 = 1225\\a^2 +441-441=1225-441\\a^2 =784\\\sqrt{a^2} =\sqrt{784} \\a = 28 feet[/tex]

28 feet represents how far the base of the ladder is from the house.

Part 2.

Now move the ladder 4 feet farther from the house. 28 + 4 = 32 ft.

Now you have a leg that is 32 feet and the hypotenuse is still 35 feet. Solve for the other leg.

[tex]a^{2} +b^{2} =c^{2} \\a^{2} +32^{2} =35^2\\a^2 + 1024 = 1225\\a^2 +1024-1024=1225-1024\\a^2 =201\\\sqrt{a^2} =\sqrt{201} \\a = 14.177 feet[/tex]

Round to the nearest tenth and you have 14.2 feet

By using the method of interest, principle is 2777.7.

An expense associated with borrowing money or other assets is interest. The principal is the amount borrowed, and the interest is calculated as a percentage of the principal for a specific period of time. The expense of borrowing money is interest. It equates to a fee or additional charge the borrower pays the lender for the loaned amount, and is sometimes stated as a percentage. When you make a payment on a loan with simple interest, the money first goes toward the interest for that month and the rest is applied to the principal. S.I. = P R T, where P = Principal, R = Rate of Interest in% per annum, and T = Time, typically calculated as the number of years, is the formula used to compute simple interest.

Given that,

S.I= PTR

Simple interest= 50

Time= 9/12= 0.75

Rate of interest= 2.4

Principle amount=?

S.I= PTR

50= P x 0.75 x 2.4

50= P x 1.8

P = 50X1.8

P= 2777.7

Therefore, principle is 2777.7

To know more about interest visit:

https://brainly.com/question/13324776

#SPJ9

The area of the shaded portion of the diagram is 9.12 mm²

The triangle is inside the semi circle.

The shaded region of the semi circle is outside the triangle.

Therefore,

area of the shaded region = area of the semi circle - area of triangle

Therefore,

area of the semi circle = 1 / 2 πr²

where

Hence,

r = 4 mm

area of the semi circle = 1 / 2 × 3.14 × 4²

area of the semi circle = 50.24 / 2

area of the semi circle = 25.12 mm²

area of the triangle = 1 / 2 bh

where

Hence,

b = 8mm

h = 4mm

area of the triangle = 1 / 2 × 8 × 4

area of the triangle = 32 / 2

area of the triangle = 16 mm²

Therefore,

area of the shaded region = 25.12 - 16

area of the shaded region = 9.12 mm²

learn more on area here: https://brainly.com/question/23425959

#SPJ1

The probability mass function for this is given by the table that is attached below.

Probability is defined as the proper fraction which signifies the likelihood of an event to occur.

Total number of possible arrangements of 6 people are 6! = 720

Here X can take value 0, 1, 2, 3, or4.

For the probability function : When X= 0 , it means there is no child between mother and father. Taking mother and father as one , number of possible arrangements of 5 people are 5!.

And mother and father can arranged themselves is 2! ways. So for X=0, possible ways are 5! *2 = 240.

Therefore the require probability at X=0 is given by:

P(X=0) = 240 /720 = 0.3333

For the probability function : When X = 1 , then there is one child between mother and father. Number of ways of selecting one child is C(4,1) = 4.

Mother and father can be arrange themselves in 2 ways so possible number of arrangements are 4 * 2 * 4! = 192

Therefore the require probability at X=1 is given by:

P(X=1) = 192 /720 = 0.2667

For the probability function :When X=2 , then there are two children between mother and father. Number of ways of selecting two children is C(4,2) = 6.

Mother and father can arrange themselves in 2 ways, children between mother and father can arranged themselves in 2 ways so possible number of arrangements are 6 * 2 * 2* 3! = 144

Therefore the require probability at X=2 is given by:

P(X=2) = 144 /720 = 0.2

For the probability function : When X=3 , then there are three children between mother and father. Number of ways of selecting three children is C(4,3) = 4.

Mother and father can arrange themselves in 2 ways, children between mother and father can arranged themselves in 3! ways so possible number of arrangements are 4 * 2 * 3!* 2! = 96

Therefore the require probability at X=3 is given by:

P(X=3) = 96 /720 = 0.1333

For the probability function: When X=4 , then there are 4 children between mother and father. Number of ways of selecting 4 children is C(4,4) = 1.

Mother and father can arranged themselves in 2 ways, children between mother and father can arranged themselves in 4! ways so possible number of arrangements are 1 * 2 * 4! = 48

Therefore the require probability at X=0 is given by:

P(X=4) = 48 /720 = 0.0667

Hence the probability mass function can be represented by a table below.

To learn more about probability visit:

https://brainly.com/question/14210034

#SPJ1

Given:

The formula is

Required:

Make h the subject of the formula.

Explanation:

We will put formula in terms of h as:

Answer:

Hence, above is the answer.

Answer: 32

Step-by-step explanation:

You need to take -112 and subtract it by -80 to get 32

Hope this helped! :)

Answer:

Step-by-step explanation:

A) 5x+3x

5x+3x

= 8x

B) 9s-3s+4s

9s-3s+4s

6s+4s

=10s

A polynomial of degree 4 in factored form with zeros 1, -4, 0, and 6 is

f(x) = x(x - 1)(x + 4)(x - 6).

Given:

x₁ = 1

x₂ = -4

x₃ = 0

x₄ = 6

Utilize the fact that x - b is a factor of the polynomial if b is a root.

Simply take each zero, modify its sign, and add an x in front of it to obtain the four factors.

The polynomial is,

f(x) = (x - x₁)(x - x₂)(x - x₃)(x - x₄)

f(x) =  (x - 1)(x - (-4))(x - 0)(x - 6)

     = (x - 1)(x + 4(x)(x - 6)

Therefore,a 4 degree polynomial in factored form with zeros 1, -4, 0,and 6 is x(x - 1)(x + 4)(x - 6).

To learn more about polynomials visit:

https://brainly.com/question/2284746

#SPJ9

Answer:

  C. It is not proportional. y/x ratios are not equivalent

Step-by-step explanation:

Given a rental charge of $25 for the first hour and $20 for each additional hour, you want to know if the charges are proportional to the time.

In this situation, if the relationship were proportional, the charge per hour (constant of proportionality) would be the same for every hour. Here, the first hour costs more, so the hourly charge is not constant.

Here, we have, for x=hours, y=dollars, ...

  (1, 25)   ⇒   y/x = 25

  (2, 45)   ⇒   y/x = 22.5

  (3, 65)   ⇒   y/x ≈ 21.67

The y/x values are not constant (because the charge per hour is not constant). The relationship is not proportional.

<95141404393>

[tex]11.9375\%[/tex] is the cost of equity using the capital asset pricing model if the risk free rate is 4.5%, the beta is 1.75 and the equity risk premium is 4.25%.

In the given question we have to find the cost of equity using the capital asset pricing model if the risk free rate is 4.5%, the beta is 1.75 and the equity risk premium is 4.25%.

Firstly we learn about terms used in this question,

The return needed by either a business or an individual to justify an investment in equity is known as the cost of equity.

The relationship between systemic risk, or the general dangers of investing, and expected return for assets, particularly equities, is described by the Capital Asset Pricing Model.

Since we have to find the cost of equity using the capital asset pricing model. So the formula is

Cost of equity = Risk free rate + Beta * Equity Risk Premium

Risk free rate = 4.5%

Beta = 1.75

Equity Risk Premium = 4.25%

Now putting the value in the formula

Cost of equity [tex]=4.5\%+1.75\times4.25\%[/tex]

Simplifying

Cost of equity [tex]=4.5\%+7.4375\%[/tex]

Cost of equity [tex]=11.9375\%[/tex]

Hence, [tex]11.9375\%[/tex] is the cost of equity using the capital asset pricing model if the risk free rate is 4.5%, the beta is 1.75 and the equity risk premium is 4.25%.

To learn more about The cost of equity link is here

https://brainly.com/question/25651634

#SPJ1

1. A fraction whose denominator is 3 more than it's numerator x: x/(x+3)

A. If x =6, then the value of the fraction is 2/3.

B. If the denominator is 8, then the fraction is 5/8.

2. The length of a rectangular garden with an area of 32 square meters and has width w meters: 32/w.

A. The length of the garden if the width 4 meters = 8 meters

B. The width of the garden if the length is 16 meters = 2 meters

3. The rate of a car traveled 240 kilometers in t hours = 240/t km per hour

A. The rate of the car if t= 2.5 hour is 96 km/hour.

B. The rate of the car if the time is doubled is 120/t.

1. Let 'x' be the numerator. Then the denominator is 3 more than its numerator. So the denominator = x +3.

Hence the fraction whose denominator is 3 more than it's numerator x: x/(x+3).

A. If x = 6, then x+3 = 6+3 = 9.

So x/x+3 = 6/9 = 2/3

So the fraction is 2/3

B. Denominator = 8

⇒ x+3 = 8

⇒ x = 8-3 = 5

So the fraction is x/x+3 = 5/8.

2. Area of the rectangular garden = 32 square meters

⇒ length x width = 32

⇒ length x w = 32

⇒ length = 32/w

So the length of a rectangular garden with an area of 32 square meters and has width w meters is 32/w.

A. Width, w = 4 meters

Then, length = 32/w = 32/4 = 8 meters

B. Length = 16 meters

⇒ 32/w = 16

⇒ w = 32/16

⇒ width, w = 2 meters

3. Distance travelled by the car = 240 kilometers

Let 't' be the time taken in hours.

Then, Rate of the car = Distance / Time taken

⇒ Rate of the car in t hours = 240/t kilometers per hour

A. If t = 2.5 hour, then,

Rate of the car = 240/2.5 = 96 kilometers/ hour

B. If the time is doubled, then time = 2t

Rate of the car = 240/2t = 120/t

Learn more about area of rectangle at https://brainly.com/question/2607596

#SPJ1

The number of stocks that went up yesterday given the stocks that went down yesterday is 618.

Ratio is used compare two or values together. It shows the number of times that one value is contained in another value or values. According to the information provided in the question,  the ratio of stocks that go up and the stock that goes down is 6 : 7.

The number of stocks that went up yesterday = (ratio of stocks that went up x number of stocks that went down yesterday) / ratio of stocks that went down yesterday

The number of stocks that went up yesterday =(6 x 721) / 7 = 618

To learn more about ratios, please check: https://brainly.com/question/9194979

#SPJ1

1. Solution of the rational equation [tex]\frac{x}{3} -6=\frac{9}{3}[/tex]   is x = 27

How is the equation solved?

[tex]\frac{x}{3} -6=\frac{9}{3}\\\\\frac{x- 18}{3} =\frac{9}{3}\\\\x= 18+9\\\\x= 27[/tex]

2.The two numbers = 2, 6

How to find the two numbers?

Let the two whole numbers = x, y

Given:

x+ y =8 --- (1)

1/x+1/y = 2/3 ---(2)

Considering (2),

[tex]\frac{1}{x} +\frac{1}{y} =\frac{2}{3}\\\\\frac{x+ y}{x y} =\frac{2}{3}\\\\\text{Applying } (1),\\\\\frac{8}{x(8-x)} =\frac{2}{3}\\\\(8x-x^{2} )2 =24\\\\(8x-x^{2} ) =12\\\\x^{2} -8x+12 =0\\\\(x-6) (x-2)= 0\\\\x= 2, 6[/tex]

Substituting  x in (1)

We have,

When x = 2 ; y= 6

When x = 6 ; y = 2

So, the two numbers = 2, 6

3. The two numbers = 3, 9

How to find the two numbers?

Let the two whole numbers = x, y

Given:

x- y =6 --- (1)

1/y -1/x = 2/9 ---(2)

Considering (2),

[tex]\frac{x-y}{xy} =\frac{2}{9} \\\\\text{Applying } (1)\\\\\frac{6}{x y} =\frac{2}{9} \\\\x y = 27\\\\(6+y)y = 27\\\\y^{2} +6y-27=0\\\\(y+9) (y-3) = 0\\\\y= 3, -9[/tex]

Since x and y are whole numbers we will have y = 3

When y = 3 ; x=9 (substituting in (1))

So, the two numbers = 9,3

To learn more about solving equations, refer:

https://brainly.com/question/25678139

#SPJ13

Answer: 270

Step-by-step explanation: A tip for multiplying a number with any power of 10 is to just "add" a 0 to the end of the number depending on how many 0's there are in the power of 10.

For example, there is one 0 in 10. So I would just add a 0 to the end of 27 to get 270. If I were to multiply 27 by 100, there are two 0's in 100 so it would be 2700. 27 x 1000 would be 27000.

Hope this helped

The first mistake on the finding on the continuity of the function happened on Step 3, hence option B is correct.

A function f(x) is continuous at x = a if it is defined at x = a, and the lateral limits are equal, that is, if these three conditions are respected:

[tex]\lim_{x \rightarrow a^-} f(x) = \lim_{x \rightarrow a^+} f(x) = f(a)[/tex]

To verify the continuity on this problem, the limit was first found at x = 4. Following the standard procedure, replacing each instance of x by 4, an undetermined value of 0/0 is reached. Thus the correct procedure was undertaken, factoring each polynomial in the numerator and in the denominator, then simplifying the common terms and calculating the limit.

However, to calculate the numeric value of the function at x = 4, the simplification cannot be applied, each instance of 4 needs to be replaced.

Replacing each instance of x by 4, the denominator will be of 0, meaning that the function is not defined at x = 4, hence the first mistake was in Step 3 and option B is correct.

More can be learned about the continuity of a function at https://brainly.com/question/24637240

#SPJ1

Answer:

can i see a ss of the question?

Step-by-step explanation:

Minimum number of gallons pumped after 30 days = 24,192,000 gallons

The minimum amount of water pumped in 1 minute = 1120 gallons

The minimum number of hours used for pumping per day = 12 hours

Number of minutes in 1 hour = 60 minutes

Number of minutes in 12 hours = 12 x 60 = 720 minutes

The minimum amount of water pumped per day = 1120 x 720

The minimum amount of water pumped per day = 806400 gallons

Let the number of days used for pumping be x

Let the total number of gallons pumped x days after pumping begins = y

Since 806400 gallons is pumped per day:

y = 806400x

Minimum number of gallons pumped after 30 days, that is, x = 30

y = 806400 (30)

y = 24,192,000 gallons

Minimum number of gallons pumped after 30 days = 24,192,000 gallons

The equation that represents the possible tables that may be used to seat 200 people at the wedding is 8x + 10y = 200.

The combination will be 10 round tables and 12 rectangular tables; 15 round tables and 8 rectangular tables.

Based on the information, there can be round tables that sit 8 people and rectangular tables that sit 10 people and the total number will be 200.

Therefore, the equation that represents the possible tables is 8x + 10y = 200

where x = number of round table

y = number of rectangular tables

The possible combinations of table types that your sister can use at her wedding reception will be 10 round tables and 12 rectangular tables. This will be:

8x + 10y = 8(10) + 10(12) = 200

Another combination will be 15 round tables and 8 rectangular tables

8x + 10y = 8(15) + 10(8) = 200

Learn more about equations on:

brainly.com/question/2972832

#SPJ1

Answer:

simply divide 12.50 by 5. Therefore each bracelet costs $2.05 : 2$ and 5 cents.

Step-by-step explanation:

The cost of each bracelet will be $2.5.

What is Division method?

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications.

For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

Given that;

The cost of 5 bracelets = $12.50

Now,

Since, The cost of 5 bracelets = $12.50

So, The cost of 1 bracelets = $12.50 ÷ 5

                                         = $2.5

Thus, The cost of each bracelet will be $2.5.

Learn more about the divide visit:

https://brainly.com/question/28119824

#SPJ2

1) I'll calculate the hypotenuse

hyp = squared root [(16)^2 + (12)^2]

= squared root [ 256 + 144]

2) the answer is letter C. 5/7

3) calculate the hypotenuse

hyp = squared root [(2^2 + (-3)^2]

= squared root [ 4 + 9]

= squared root [13]

sin 0 = -3/squared root 13

= -3squared root (13) / 13

The answer for number three = letter B

Answer:800

Step-by-step explanation:

x + 4x = 1000

   5x     = 1000

    x     = 1000/5 = 200 dollars.

In geometry, two figures or objects are said to be congruent if their shapes and sizes match, or if one is the mirror image of the other.

Which postulate establishes the congruence of triangles SSS AAS SAS ASA?

According to the Angle-Side-Angle Postulate (ASA), two triangles are congruent if two angles and the included side of one triangle are congruent with two angles and the included side of another triangle.

Congruence exists between one comparable pair of sides.

Detailed explanation:

If two triangles have three matching angles that are congruent,

The following postulates will be required to demonstrate the congruence of the triangles:

1) AAS ( Angle-Angle-Side ) ( Angle-Angle-Side )

2) ASA ( Angle - Side - Angle) ( Angle - Side - Angle)

Since we require at least one pair of congruent sides in both postulates.

Given that two triangles have three congruent corresponding angles, the extra information that will be utilized to prove their congruence is that "they have one pair of congruent corresponding angles."

To learn more about Congruent of a triangle refer to:

https://brainly.com/question/2938476

#SPJ13

Answer:

true

Step-by-step explanation:

the answer of both the smaller squares added is the same as the andwer of the bigger square

Before change

Dimensions: r= 2 ; h=7

Lateral Surface area=  2πrh= 28π sqyd

Total Surface area= 2πr(h+r)=4π(9)= 36π sqyd

After change(trippling radius)

Dimensions: r= 6 (3*2); h=7

Lateral Surface area=  2πrh= 84π sqyd

Total Surface area= 2πr(h+r)=12π(13)= 156π sqyd

What is surface area of a cylinder?

To learn more about surface area of cylinder, refer:

https://brainly.com/question/27440983

#SPJ13

Answer:

g

<

−

7

Step-by-step explanation:

The multiplication of  [tex](9n- \frac{4}{7} z)^{2}[/tex]   [tex]=81n^{2} -\frac{72}{7} nz +\frac{16}{49} z^{2}[/tex]

How is the expression  [tex](9n- \frac{4}{7} z)^{2}[/tex]  solved?

[tex](9n- \frac{4}{7} z)^{2} \\\\=(9n- \frac{4}{7} z) (9n- \frac{4}{7} z)\\\\=81n^{2} -\frac{36}{7} nz -\frac{36}{7} nz +\frac{16}{49} z^{2} \\\\=81n^{2} -\frac{72}{7} nz +\frac{16}{49} z^{2}[/tex]

What is the binomial squares pattern?

To learn more about binomial squares pattern , refer:

https://brainly.com/question/14640524

#SPJ13

a) The total central angle of a circle is 360 degrees.

Therefore, the angle of the shaded area is,

Therefore, the angle of the shaded area is 240 degrees.

b) The percent of the circle shaded is,

Therefore, the percent of the circle shaded is 66.67%.

c) The fraction of the circle shaded is,

Therefore, the fraction of the circle shaded is 2/3.