Eli made a wooden box in the shape of a rectangular prism. The box has a length of 5 inches, a width of 3 1/2 inches, and a height of 7 inches.
Part A. Eli wants to paint the entire box green and give the box to his dad as a gift. What is the total area that he will paint? Explain how you found your answer.
Part B. Can the box hold 200 cubic inches of packing peanuts? Explain how you know.

BE FAST!!!

Answer: 7.8

Step-by-step explanation: Identify the triangle as a 45-45-90 triangle.

Recognize that the sides of a 45-45-90 triangle are in a ratio of 1:1:√2.

Find the length of the hypotenuse of the triangle. In this case, the hypotenuse is 11 units.

Divide the length of the hypotenuse by √2 to find the length of the side opposite the 45-degree angle. In this case, the length of side x is 11/√2 = 7.77 units.

Round the length of side x to the nearest tenth. In this case, the length of side x is 7.8 units.

Answer:

= 10.4

Step-by-step explanation:

Here given is the right-angled triangle

For angle: = 60º

Perpendicular: = 9

Hypotenuse: =

Now using the trigonometry formula:

  = /

sin 60º = 9/

3√2 = 9/

= 18/3√

= 10.4(rounded to the nearest tenth)

Therefore required length is = 10.4

The total area covered by the roll of wrapping paper is 3.6 square meters.

To calculate the total area covered by the wrapping paper, we need to find the surface area of each cube and then multiply it by the number of cubes.

The formula for the surface area of a cube is:

Surface Area = 6 * (side length)^2

Given that the length of each side of the cube is 20 cm (which is equal to 0.2 meters), we can substitute this value into the formula:

Surface Area = 6 * (0.2)^2

Surface Area = 6 * 0.04

Surface Area = 0.24 square meters

Now, we know that 15 cubes can be covered by the roll of wrapping paper. Therefore, the total area covered by the wrapping paper is:

Total Area = Surface Area * Number of Cubes

Total Area = 0.24 * 15

Total Area = 3.6 square meters

Therefore, the total area covered by the roll of wrapping paper is 3.6 square meters.

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Answer:

[tex]\frac{6}{x+1}[/tex]

Step-by-step explanation:

I learned this like a month ago so I have notes abt it if you don't understand how it works. Just lmk if you need them

Answer:

                                                                      250

                                                                     /       \

                                                   126            124

                                                           \        /     \

                 102                      24                87       57

                /     \                 /     \       /     \

             100     6          22     2          40     17

            /     /   \       /     /   \       /     /   \

         95     0     5      22     0      20     0      37

The frequency tree shows that 126 people arrived late, and 102 of them travelled by train. This means that 24 people arrived late and travelled by bus. There were a total of 250 people who attended the conference, so 124 people arrived on time. Of the people who arrived on time, 87 travelled by bus and 57 travelled by train.

Answer:

Step-by-step explanation:

Answer:

8[tex]\sqrt[3]{2}[/tex]

Step-by-step explanation:

The cube root of -2 to the power of 10 is;

(-2)^10=2^10

2^10=(2^3)*(2^3)*(2^3)*2

You can factor out 2^3=8 of the cube root

So you get 8 times the cube root of 2

Step by Step Solution/ just copy and paste but if this is a test, the answer is 2.000

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

                    2*y-(4*x-5)=0

STEP

1

:Equation of a Straight Line

1.1     Solve   2y-4x+5  = 0

Tiger recognizes that we have here an equation of a straight line. Such an equation is usually written y=mx+b ("y=mx+c" in the UK).

"y=mx+b" is the formula of a straight line drawn on Cartesian coordinate system in which "y" is the vertical axis and "x" the horizontal axis.

In this formula :

y tells us how far up the line goes

x tells us how far along

m is the Slope or Gradient i.e. how steep the line is

b is the Y-intercept i.e. where the line crosses the Y axis

The X and Y intercepts and the Slope are called the line properties. We shall now graph the line  2y-4x+5  = 0 and calculate its properties

Graph of a Straight Line :

Calculate the Y-Intercept :

Notice that when x = 0 the value of y is -5/2 so this line "cuts" the y axis at y=-2.50000

 y-intercept = -5/2  = -2.50000

Calculate the X-Intercept :

When y = 0 the value of x is 5/4 Our line therefore "cuts" the x axis at x= 1.25000

 x-intercept = 5/4  =  1.25000

Calculate the Slope :

Slope is defined as the change in y divided by the change in x. We note that for x=0, the value of y is -2.500 and for x=2.000, the value of y is 1.500. So, for a change of 2.000 in x (The change in x is sometimes referred to as "RUN") we get a change of 1.500 - (-2.500) = 4.000 in y. (The change in y is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)

   Slope     =  4.000/2.000 =  2.000

Geometric figure: Straight Line

 Slope = 4.000/2.000 = 2.000

 x-intercept = 5/4 = 1.25000

 y-intercept = -5/2 = -2.50000

Hello !

1. A quadratic equation results in the form: ax² + bx + c

2. Calculate the discriminant: Δ = b² - 4ac

3. Calculate x with the dicriminant: (-b ± √Δ) / 2a

Example:

3x² + 7x - 2 = 0 is a quadratic equation.

x = (-b ± √(b² - 4ac)) / 2a

= (-7 ± √(7² - 4*3*(-2))) / (2*3)

= (-7 ± √73)/6

To estimate the total distance traveled by the car in those 36 seconds, we can use the trapezium rule to approximate the area under the curve.

From the graph, we can see that the car's speed is constant between 0 and 30 seconds, and then it starts to decrease. Therefore, we can use a single trapezium to estimate the area under the curve for the first part.

The base of the trapezium is 30 seconds, and the height is the average of the speeds at 0 and 30 seconds. Let's denote the speed at 0 seconds as v0 and the speed at 30 seconds as v30.

The distance traveled in the first part can be estimated as:

Distance = 30 * (v0 + v30) / 2

To get a more accurate estimate, we need the specific values of v0 and v30 from the graph. Please provide the corresponding speed values for 0 and 30 seconds, and I can help you calculate the estimated distance.

The z-score corresponding to a sample mean capacity for 20 tanks of 8550 is 2.238.

To find the z-score corresponding to a sample mean capacity for 20 tanks of 8550, we need to use the formula for the z-score:

z = (x - μ) / (σ / √n)

Where:

x = sample mean capacity

μ = population mean capacity

σ = population standard deviation

n = sample size

Given:

x = 8550, μ = 8544, σ = 12 and n = 20

Substituting these values into the formula:

z = (8550 - 8544) / (12 / √20)

z = 6 / (12 / √20)

z = 6 / (12 / 4.472)

z = 6 / 2.683

z = 2.238

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Answer:

-----------------------

Taking the inverse tangent (arctan) of the given ratio 7/9.

Use a calculator or trigonometric table to find:

The approximate value of θ is 37.9°.

(a) The joint probability distribution of X and Y is 3/70.

(b) The value of P[(X,Y) € A), where A is the region that is given is 3/35.

(a) To find the probabilities, we consider the total number of ways to select 4 fruits out of 8:

Total number of ways to select 4 fruits out of 8 = C(8, 4) = 70

The probabilities for each combination of X and Y are as follows:

P(X = 0, Y = 0) = C(3, 0) * C(2, 0) * C(3, 4) / 70

P(X = 0, Y = 0) = 1 / 70

P(X = 0, Y = 1) = C(3, 0) * C(2, 1) * C(3, 3) / 70

P(X = 0, Y = 1)  = 2 / 70

P(X = 1, Y = 0) = C(3, 1) * C(2, 0) * C(3, 3) / 70

P(X = 1, Y = 0) = 3 / 70

P(X = 1, Y = 1) = C(3, 1) * C(2, 1) * C(3, 2) / 70

P(X = 1, Y = 1) = 18 / 70

P(X = 2, Y = 0) = C(3, 2) * C(2, 0) * C(3, 2) / 70

P(X = 2, Y = 0) = 9 / 70

P(X = 2, Y = 1) = C(3, 2) * C(2, 1) * C(3, 1) / 70

P(X = 2, Y = 1) = 18 / 70

P(X = 3, Y = 0) = C(3, 3) * C(2, 0) * C(3, 1) / 70

P(X = 3, Y = 0) = 3 / 70

The joint probability distribution of X and Y is as follows:

X\Y  0   1

0 1/70  2/70

1 3/70 18/70

2 9/70 18/70

3 3/70 0

(b) P[(X,Y) ∈ A], where A is given by ((a + v) | a + y < 2):

From the joint probability distribution table, we can see that the combinations (0, 0), (0, 1), and (1, 0) satisfy this condition.

P[(X, Y) ∈ A] = P[(0, 0)] + P[(0, 1)] + P[(1, 0)] = 1/70 + 2/70 + 3/70

P[(X, Y) ∈ A] = 6/70 or 3/35

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Based on the paired difference test conducted at a significance level of α = 0.05, there is sufficient evidence to reject the null hypothesis and conclude that there is a significant difference between the two sets of paired data.

In this paired difference experiment, we have the following data: D₁ = 6, D₂ = 10, D₃ = -3, D₄ = 5, D₅ = 7.

Our objective is to determine if there is a significant difference between the two sets of paired data.

To begin the paired difference test, we state the null hypothesis (H₀) and the alternative hypothesis (H₁).

The null hypothesis assumes that the mean difference between the paired data is equal to zero (µd = 0), while the alternative hypothesis suggests that the mean difference is not equal to zero (µd ≠ 0).

Next, we calculate the mean difference (¯d) by summing the differences and dividing by the number of pairs.

In this case, ¯d = (6 + 10 - 3 + 5 + 7) / 5 = 5.

To assess the variability in the data, we calculate the standard deviation of the differences (sᵈ).

This involves computing the sum of squared differences (SSᵈ) by squaring each difference and summing them.

Dividing SSᵈ by the number of pairs minus 1 (n-1), we then take the square root to obtain sᵈ.

With the mean difference (¯d) and standard deviation (sᵈ) calculated, we can determine the test statistic (t) using the formula t = ¯d / (sᵈ / √n), where n is the number of pairs.

Substituting the values, we compute the test statistic.

Next, we identify the degrees of freedom (df) for the test, which is equal to the number of pairs minus 1 (n-1).

Using the significance level α = 0.05, we consult a t-table or use statistical software to find the critical value for the rejection region.

By comparing the absolute value of the test statistic (t) to the critical value, we make a decision to either reject the null hypothesis if t falls within the rejection region or fail to reject the null hypothesis if it does not.

Finally, we state the final conclusion based on our decision.

If we reject the null hypothesis, we conclude that there is a significant difference between the two sets of paired data.

On the other hand, if we fail to reject the null hypothesis, we conclude that there is insufficient evidence to suggest a significant difference.

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The complete question may be like:

A paired difference experiment produced the following results: D₁ = 6, D₂ = 10, D₃ = -3, D₄ = 5, D₅ = 7. Conduct a paired difference test to determine if there is a significant difference between the two sets of paired data. Use a significance level of α = 0.05.

Context: The paired difference experiment involves measuring a variable of interest on two related subjects or under two different conditions. The goal is to determine if there is a significant difference between the two sets of measurements.

12/13 is the value of cosA is  in the triangle ABC

ABC is a right angle triangle

Angle B has a angle of 90 degrees

We know that the cosine function is a ratio of adjacent side and hypotenuse

The adjacent side of angle A is AB which we have to find

hypotenuse is 26

Cos A =AB/26

Let us find AB by using pythagoras theorem

10²+AB²=26²

100+AB²=676

Subtract 100 from both sides

AB²=576

Take square root on both sides

AB=√576

=24

Now plug in this value in cosA

CosA = 24/26

=12/13

Hence, the value of cosA is 12/13 in the triangle ABC

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[tex]~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \pounds 2496\\ P=\textit{original amount deposited}\dotfill & \pounds1600\\ r=rate\to 8\%\to \frac{8}{100}\dotfill &0.08\\ t=years \end{cases} \\\\\\ 2496 = 1600[1+(0.08)(t)]\implies \cfrac{2496}{1600}=1+0.08t\implies \cfrac{39}{25}=1+0.08t \\\\\\ \cfrac{39}{25}-1=0.08t \implies \cfrac{14}{25}=0.08t\implies \cfrac{14}{25(0.08)}=t\implies 7=t[/tex]

Turn me into a superhero

The given numerical data should be ordered from least to greatest as follows;

-11, -9, -8, -7, -2, 4, 5, 6, |-11|.

In Mathematics, a rational number can be defined a type of number which comprises fractions, integers, terminating or repeating decimals.

In Mathematics, an integer can be defined as a whole number that may either be positive, negative, or zero (0). This ultimately implies that, a positive integer simply refers to a whole number that is greater than or equal to one (1).

Next, we would order or sort the given numerical data from least to greatest as follows;

-11, -9, -8, -7, -2, 4, 5, 6, |-11|.

Note: |-11| is an absolute value that equals to 11.

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To find the subtracted value, we need to calculate the multiplicative inverse of (4/3 - 4/9) and then subtract it from the sum of 7/12 and 7/8.

First, let's find the multiplicative inverse of (4/3 - 4/9):

Multiplicative inverse = 1 / (4/3 - 4/9)

To simplify the expression, we need a common denominator:

Multiplicative inverse = 1 / ((12/9) - (4/9))

= 1 / (8/9)

= 9/8

Now, we need to subtract the multiplicative inverse from the sum of 7/12 and 7/8:

Subtracted value = (7/12 + 7/8) - (9/8)

To perform this calculation, we need a common denominator:

Subtracted value = (7/12 * 2/2 + 7/8 * 3/3) - (9/8)

= (14/24 + 21/24) - (9/8)

= 35/24 - 9/8

To simplify further, we need a common denominator:

Subtracted value = (35/24 * 1/1) - (9/8 * 3/3)

= 35/24 - 27/24

= 8/24

= 1/3

Therefore, subtracting 1/3 from the sum of 7/12 and 7/8 will give you the multiplicative inverse of (4/3 - 4/9).

Answer:

[tex]slope_{UF}[/tex] = - [tex]\frac{1}{4}[/tex]

Step-by-step explanation:

calculate slope m using the slope formula

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

with (x₁, y₁ ) = U (3, - 5 ) and ( x₂, y₂ ) = F (- 1, - 4 )

m = [tex]\frac{-4-(-5)}{-1-3}[/tex] = [tex]\frac{-4+5}{-4}[/tex] = [tex]\frac{1}{-4}[/tex] = - [tex]\frac{1}{4}[/tex]

Answer: To find the area of the region between the graph of y = x^2 + 1 and the x-axis on the interval [2, 4], we can integrate the function f(x) = x^2 + 1 with respect to x over the given interval. The definite integral represents the area under the curve between the specified x-values. Here's how to calculate it using integration:

∫[2,4] (x^2 + 1) dx

To integrate this function, we apply the power rule for integration. The power rule states that the integral of x^n with respect to x is (x^(n+1))/(n+1), where n is any real number except -1.

∫(x^2 + 1) dx = [(x^3)/3 + x] + C

Now, we can evaluate the definite integral over the interval [2, 4]:

[(4^3)/3 + 4] - [(2^3)/3 + 2]

= (64/3 + 4) - (8/3 + 2)

= (64/3 + 12/3) - (8/3 + 6/3)

= (76/3) - (14/3)

= 62/3

Therefore, the area of the region between the graph of y = x^2 + 1 and the x-axis on the interval [2, 4] is 62/3 square units.

Step-by-step explanation:

Answer:

Step-by-step explanation:

x=6/5,−4

Decimal Form:

x=1.2,−4

Mixed Number Form:

x=1  1/5,−4

Based on the information provided, we have an angle labeled as (4x-10)° and another angle labeled as K. It seems like we need to determine the relationship between these angles and find the value of x.

To determine the relationship between the angles, we need more context or information about the specific geometric configuration or properties mentioned in the task card. Without additional information, it is not possible to determine the relationship between (4x-10)° and K.

If you can provide further details or a description of the geometric setup or any additional instructions related to the angle relationship, I'll be glad to help you further.

The vector shown in component form is (-4, -3)

We have to find the vector which is shown in the component form

To find this vector we have to find the difference of tail and head

Tail has coordinates (1, 2)

Head has coordinates (-3, -1)

We have to subtract  (-3, -1) from (1, 2)

(-3, -1)-(1,2)

We have to do this by subtracting x coordinates and y coordinates

(-3-1, -1-2)

(-4, -3)

Hence, (-4, -3) is the vector shown in component form

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The coordinates of the focus obtained from the vertex form of the equation of the parabola is; (h, v) = (2, -7/4)

The vertex form of the equation of a parabola is; y = a·(x - h)² + k

The points on the parabola are;

(3, -1), and (2, -2)

The vertex of the parabola is; (2, -2)

Therefore, we get;

The vertex form of the equation of a parabola is; y = a·(x - h)² + k

Where;

(h, k) = The coordinates of the vertex, therefore;

y = a·(x - 2)² - 2

y + 2 = a·(x - 2)²

The point (3, -1), indicates that we get;

-1 + 2 = a·(3 - 2)²

(-1 + 2)/((3 - 2)²) = 1 = a

The equation of the parabola in focus form is; (x - h)² = 4·p·(y - k)

Therefore; (x - 2)² = 4·p·(y + k)

We get; (x - 2)² = (y + k)

(x - 2)²/(4·p) = y + k

(4·p) = a = 1

p = 1/4

The y-coordinates of the focus, v = -2 + 1/4 = -1 3/4 = -7/4

The coordinates of the focus, (h, v) is therefore;

(h, v) = (2, -7/4)

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Answer:  it would take the cyclist 8.5 hours to travel 153 miles.

Step-by-step explanation: We can use proportions to solve this problem.

Let's define:

x = the time it would take for the cyclist to travel 153 miles.

Using proportions, we can set up the following equation:

45 miles / 2.5 hours = 153 miles / x

We can then cross-multiply and solve for x:

45 * x = 2.5 * 153

45x = 382.5

x = 382.5 / 45

x = 8.5

The correct answer is $28,100.

To calculate the difference between the costs of the accident and the premiums paid by the car owner, let's break down the expenses step by step:

(1) Annual Premium: The car owner pays an annual premium of $780 for automobile insurance. Over five years, the total premium paid is $780 * 5 = $3,900.

(2) Liability Coverage: The liability coverage provided by the insurance is up to $100,000. However, the other driver is claiming $32,000 in damages. Therefore, the insurance will cover the full amount of $32,000.

(3) Difference in Costs: To find the difference between the costs of the accident and the premiums paid, we subtract the insurance coverage from the total premium paid. In this case, the difference is $32,000 - $3,900 = $28,100.

Therefore, the costs of the accident were $28,100 more expensive than what the car owner paid in premiums.

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Answer:

  D.  62 points

Step-by-step explanation:

You want to know the improvement in credit score needed so that Josua can borrow $150,000 with payments less than $14000 per year.

Josua can afford 12 monthly payments of $14,000/12 = $1166.67. According to the rate table, the monthly payment will be less than this amount if Josua has a credit score of 560 or better. With a score of 560, his payment would be $1157.

To get his score up to 560, he needs to improve it by ...

  560 -498 = 62 . . . . points

He would need to improve his credit by 62 points.

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Answer: C

Step-by-step explanation:

For box and whiskers plot the box is where the majority of the data is.  the whiskers(the lines on both sides will tell you where the range of numbers lie)

The middle line in the box is the median number.

The question is worded oddly where they want least likely to be more than 30 which means which one will have less than 30. (Double negative question)

You want the majority of the data to be less than 30, which is subway.  C

Answer:

True, True, False

Step-by-step explanation:

1. 8 ≥ 5-1 Is correct

2. 8 ≥ 5-4 is correct

3. 8 ≥ 5-(-4) is not correct

Answer:

x = 1 makes the inequality true

x = 4 makes the inequality true

x = -4 makes the inequality false

Step-by-step explanation:

We can determine whether x = 1, x = 4, and x = -4 makes the inequality by plugging in 1, 4, and -4 for x and seeing whether the inequality still holds true:

Step 1:  Plugging in 1 for x:

8 ≥ 5 - 1

8 ≥ 4

Because 8 is greater than 4, x = 1 makes the inequality true.

Step 2:  Plugging in 4 for x:

8 ≥ 5 - 4

8 ≥ 1

Because 8 is also greater than 4, x = 4 also makes the inequality true.

Step 3:  Plugging in -4 for x:

8 ≥ 5 - (-4)

8 ≥ 5 + 4

8 ≥ 9

Because 8 is not less than 9, x = -4 makes the inequality false

The equation of the line that passes through the points (1,6) and (2,7) is y = x + 5.

We can use the point-slope version of the equation, which is: to determine the equation of a line passing through two specified points.

y - y₁ = m(x - x₁)

where (x₁, y₁) are the coordinates of one of the points, m is the slope of the line, and (x, y) are the coordinates of any other point on the line.

Use the points (1,6) and (2,7) to find the equation of the line:

Using (x₁, y₁) = (1,6):

y - 6 = m(x - 1)

Now, substitute the coordinates (2,7) into the equation:

7 - 6 = m(2 - 1)

1 = m

So, the slope of the line is m = 1.

Substitute this value into the equation:

y - 6 = 1(x - 1)

y - 6 = x - 1

y = x + 5

Therefore, the equation of the line that passes through the points (1,6) and (2,7) is y = x + 5.

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Answer:

906.89 in²

Step-by-step explanation:

A regular dodecagon is a specific type of 12-sided polygon where all sides and angles are equal.

The formula for the area of a regular polygon is:

[tex]\boxed{\begin{minipage}{6cm}\underline{Area of a regular polygon}\\\\$A=\dfrac{n\cdot s\cdot a}{2}$\\\\where:\\\phantom{ww}$\bullet$ $n$ is the number of sides.\\ \phantom{ww}$\bullet$ $s$ is the length of one side.\\ \phantom{ww}$\bullet$ $a$ is the apothem.\\\end{minipage}}[/tex]

We know that the number of sides is 12 and that the length of one side is 9 inches, so in order to calculate the area, we first need to find the apothem.

The formula for the apothem of a regular polygon is:

[tex]\boxed{\begin{minipage}{6cm}\underline{Length of apothem}\\\\$a=\dfrac{s}{2 \tan\left(\frac{180^{\circ}}{n}\right)}$\\\\\\where:\\\phantom{ww}$\bullet$ $a$ is the apothem.\\ \phantom{ww}$\bullet$ $s$ is the length of one side.\\ \phantom{ww}$\bullet$ $n$ is the number of sides.\\\end{minipage}}[/tex]

Substitute s = 9 and n = 12 into the apothem formula, and solve for a:

[tex]a=\dfrac{9}{2 \tan\left(\frac{180^{\circ}}{12}\right)}[/tex]

[tex]a=\dfrac{9}{2 \tan\left(15^{\circ}\right)}[/tex]

[tex]a=\dfrac{9}{2 \left(2-\sqrt{3}\right)}[/tex]

[tex]a=\dfrac{9}{4-2\sqrt{3}}[/tex]

[tex]a=\dfrac{9}{4-2\sqrt{3}}\cdot \dfrac{4+2\sqrt{3}}{4+2\sqrt{3}}[/tex]

[tex]a=\dfrac{36+18\sqrt{3}}{4}[/tex]

[tex]a=\dfrac{18+9\sqrt{3}}{2}[/tex]

Now we have calculated the apothem, substitute this along with n = 12 and s = 9 into the area of a polygon formula

[tex]A=\dfrac{n \cdot s \cdot a}{2}[/tex]

[tex]A=\dfrac{12 \cdot 9 \cdot \frac{18+9\sqrt{3}}{2}}{2}[/tex]

[tex]A=\dfrac{108 \cdot \frac{18+9\sqrt{3}}{2}}{2}[/tex]

[tex]A=54 \cdot \dfrac{18+9\sqrt{3}}{2}}[/tex]

[tex]A=27\cdot (18+9\sqrt{3}})[/tex]

[tex]A=486+243\sqrt{3}[/tex]

[tex]A=906.89\; \sf in^2\;(nearest\;hundredth)[/tex]

Therefore, the area of a regular dodecagon with a side length of 9 inches is 906.89 in² (nearest hundredth).

Note: Please see the attached image for confirmation of the area using a graphic calculator.