In this circumstance, the sample consists of 1,200 inhabitants living within a ten-mile radius of the movie theater that were selected for random deliberation by the overseer.
What is a sample?Samples are frequently utilized to gain information concerning a larger population through the study of a single set of individuals or objects. The aim of selecting a sample is to inspect the populace by delving into a representative, relatively small group.
Surveys, polls, and experiments often utilize samples to make evidence-based inferences regarding the target population. For exact and dependable results, an instance should be randomly chosen, accurately mirroring those present in the whole population so as to reduce prejudice and fully optimize the evaluation.
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Romero Company has a target capital structure that consists of $3.3 million of debt capital, $3.5 million of preferred stock financing, and $4.3 million of common equity. The corresponding weights of its debt, preferred stock, and common equity financing that should be used to compute its weighted cost of capital (rounded to the nearest wo decimal places) are:
The weights of the debt, preferred stock, and common equity financing are 28.6%, 30.4%, and 41.0%, respectively.
To calculate the weighted cost of capital (WACC), the proportion of each component of capital structure is needed. The weight of each component of the capital structure is determined by dividing the market value of the component by the total market value of all the components of the capital structure.
In this case, the total market value of the company's capital structure is the sum of the market value of debt, preferred stock, and common equity.
The weights for each component are calculated as follows:
Weight of debt = Market value of debt / Total market value of capital structure
= $3.3 million / ($3.3 million + $3.5 million + $4.3 million)
= 0.286 or 28.6%
Weight of preferred stock = Market value of preferred stock / Total market value of capital structure
= $3.5 million / ($3.3 million + $3.5 million + $4.3 million)
= 0.304 or 30.4%
Weight of common equity = Market value of common equity / Total market value of capital structure
= $4.3 million / ($3.3 million + $3.5 million + $4.3 million)
= 0.410 or 41.0%
These weights can be used to calculate the weighted cost of capital for Romero Company.
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1. Ashenge Private Limited Company is about to start production of new products. Before the start of the new production, it cost the company $200,000 to construct the factory building. Once the construction is over, the cost per unit of production is estimated to be Birr 20. Upon selling, the company will incur a 20% commission expense. Moreover, the price per unit of products is decided to be Birr 50.
Required:
a) Construct the total cost equation in terms of quantity.
b) Determine the break-even quantity and break-even revenue.
The total cost equation is 200,000 + 40n and the break-even revenue is 20,000.
Given that a company is starting a new production, it cost the company $200,000 to construct the factory building.
The cost per unit of production is estimated to be Birr 20.
The company will incur a 20% commission expense.
The price per unit of products is decided to be Birr 50.
We need to find the total cost equation in terms of quantity and determine the break-even quantity.
a) The fixed cost of the company is $200,000, and 40 per unit sell,
Therefore for n units the total cost =
200,000 + 40n
b) BEQ = FC / P−VC
= 200,000 / 50-40
= 20,000
Hence the total cost equation is 200,000 + 40n and the break-even revenue is 20,000.
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3. A room is 17 feet by 16 feet. Carpet for the room costs
$101 per square yard.
How much will it cost to carpet the room?
Question 1
Answer: First, let's convert the room's dimensions from feet to yards, since the carpet cost is given per square yard:
17 feet = 5.67 yards (rounded to two decimal places)
16 feet = 5.33 yards (rounded to two decimal places)
Next, we can calculate the area of the room in square yards by multiplying these values:
Area = 5.67 yards × 5.33 yards = 30.23 square yards (rounded to two decimal places)
Finally, we can multiply the area by the cost per square yard to get the total cost:
Total cost = 30.23 square yards × $101/square yard = $3,056.23 (rounded to two decimal places)
Therefore, it will cost $3,056.23 to carpet the room.
please help me
What degree of rotation about the origin will cause the triangle below to map
onto itself?
Factor out the Greatest Common Factor (GCF): 64d³ - 24d²
The factored form of 64d³ - 24d² is 8d²(8d³ - 3).
Define greatest common factorThe greatest common factor (GCF), also known as the greatest common divisor (GCD), is the largest positive integer that divides two or more numbers without leaving a remainder. In other words, it is the largest number that divides evenly into two or more given numbers. For example, the GCF of 12 and 18 is 6, since 6 is the largest number that divides both 12 and 18 without leaving a remainder.
The greatest common factor (GCF) of the given terms is 8d². We can factor it out by dividing each term by 8d²:
64d³/8d² - 24d²/8d²
Simplifying the fractions:
8d³ - 3
Therefore, the factored form of 64d³ - 24d² is 8d²(8d³ - 3).
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A pair of dice are tossed twice. Find the probability that the first roll is a total of at least 5 and the second roll is a total of at least 4.
The probability that the first roll is a total of at least 5 and the second roll is a total of at least 4 is 0.764 or 76.4%.
What is the probability?The probability is the chance that an expected event occurs out of many possible events.
For two independent events happening, we use the rule of multiplication of independent events based on dice probabilities.
The event that the first roll is a total of at least 5 = A
In the event that the second roll is a total of at least 4 = B
The number of faces on each die, n = 6
The probability of event A = ³⁰/₆ = ⁵/₆
The probability of event B = ³³/₃₆ = ¹¹/₁₂
Multiplying the two probabilities, P(A) and P(B) = ⁵/₆ × ¹¹/₁₂
= ⁵⁵/₇₂ = 0.764
Thus, there is a ⁵⁵/₇₂ or 0.764 chance that the first roll is at least 5 and the second roll is at least 4.
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Suppose that the function h is defined as follows.
The graph of the piecewise function is given by the image presented at the end of the answer.
What is a piece-wise function?A piece-wise function is a function that has different definitions, depending on the input of the function.
All the five definitions of the function in this problem are constant, hence the graph will be composed by horizontal lines.
The definitions are given as follows:
y = -3 between x = -2.5 and x = -1.5.y = -2 between x = -1.5 and x = -0.5.y = -1 between x = -0.5 and x = 0.5.y = 0 between x = 0.5 and x = 1.5.y = 1 between x = 1.5 and x = 2.5.More can be learned about piece-wise functions at brainly.com/question/19358926
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Question 2 (1 point)
Thomas's football team lost 3 yards in their first drive while Derrek's
football team gained 5 yards in their first drive. The first drives for each
team can be compared on a number line, where 0 represents the line
of scrimmage for each play.
Select the correct numbers for Derrek and Thomas' football teams.
Oa Derrek's Team has-5
Ob Thomas' Team has +3
OcThomas' Team has -3
Od Derrek's Team has +5
The correct numbers for Derrek and Thomas' football teams are :
c. Thomas' Team has -3d. Derrek's Team has +5How to find the numbers ?According to the information given, Thomas's football team lost 3 yards in their first drive, which means they moved backward 3 yards from the line of scrimmage. This can be represented as -3 on the number line.
On the other hand, Derrek's football team gained 5 yards in their first drive, which means they moved forward 5 yards from the line of scrimmage. This can be represented as +5 on the number line.
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In QA, if m/DBG= 32° and mGFE = 149°, find mDG.
A. mDG = 62°
B. mDG=85°
C. mDG = 107°
D. mDG = 117°
E
Mark this and return
The tangent secant exterior angle measure theorem indicates that the measure of the arc DG, m[tex]\widehat{DG}[/tex] is 85°, the correct option is the option B.
B. m[tex]\widehat{DG}[/tex] = 85°
What is the tangent secant exterior angle measure theorem?The tangent secant exterior angles theorem states that if two secant or tangent or a secant and tangent intersect on the exterior to a circle, the measure of the angle formed is half the difference of the arcs they intercept.
The possible options in the question indicates that the possible drawing in the consists of a tangent and a secant, with the angle m∠DBG, being external to the circle.
The tangent secant exterior angle measure theorem indicates that we get;
m∠DBG = (1/2) × (m[tex]\widehat{GFE}[/tex] - m[tex]\widehat{DG}[/tex])
The question indicates; m[tex]\widehat{GFE}[/tex] = 149°
m∠DBG = 32°
Therefore;
32 = (1/2) × (149° - m[tex]\widehat{DG}[/tex])
149° - m[tex]\widehat{DG}[/tex] = 2 × 32° = 64°
m[tex]\widehat{DG}[/tex] = 149° - 64° = 85°
The measure of the arc DG, m[tex]\widehat{DG}[/tex] is 85°
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25 POINTS
Which is the BEST definition of dilation?
A: a transformation that either reduces or enlarges an object in the coordinate plane
B: a transformation that spins an object in the coordinate plane
C: a transformation that either slides or shifts an object in the coordinate plane
D: a transformation that flips an object in the coordinate plane
Answer: A
Step-by-step explanation:
A dilation is not a rigid transformation, which means it has to scale the object into a different measure. So, enlarging or reducing the size of an object is a dilation.
Use the even and odd properties of the following functions to answer the questions:
a) If secθ=-3.1,then sec(-θ)=?
b)If sinθ=0.62,then sin(-θ)=?
Answer:
[tex]sec(-\theta)=-3.1[/tex]
[tex]sin(-\theta)=-0.62[/tex]
Step-by-step explanation:
Part a.
[tex]sec(\theta)[/tex] is related to [tex]cos(\theta)[/tex] through a reciprocal relationship [tex]sec(\theta)=\frac{1}{cos(\theta)}[/tex].
Since [tex]cos(\theta)[/tex] is an even function (reflecting left-right across the y-axis doesn't change the graph), then [tex]sec(\theta)[/tex] is also an even function.
For any input in the domain, even functions produce the same output if the opposite of the input is used. In other words, if "f" is an even function, for all x in the domain of f, [tex]f(x)=f(-x)[/tex].
Thus, for the secant function, if a mystery value "x" is used as an input, and -3.1 is obtained as an output, then if the opposite of x, or -x, is input into the secant function, the output will also be -3.1.
[tex]sec(-\theta)=-3.1[/tex]
Part b.
The [tex]sin(\theta)[/tex] function does not reflect left-right across the y-axis to produce the same graph, so the sine function is not even.
However, the sine function can be rotated 180 degree about the origin, sometimes thought of as reflecting through the origin, to produce the same graph. Visually, this is an "odd" function.
For any input in the domain, if the opposite of the input is used, odd functions produce the opposite of the original output. In other words, if "g" is an odd function, for all x in the domain of g, [tex]-g(x)=g(-x)[/tex].
Thus, for the sine function, if a mystery value "x" is used as an input, and 0.62 is obtained as an output, then if the opposite of x, or -x, is input into the sine function, the output will be the opposite of 0.62, meaning -0.62.
[tex]sin(-\theta)=-0.62[/tex]
The sales of a certain product after an initial release can be found by the equation s=12 sqrt (4t) + 10 , where s represents the total sales (in thousands) and t represents the time in weeks after release. Make a table of values, graph the function and use the graph to estimate the sales 12 weeks after release.
about $586,000
about $586
about $93
about $93,000
The sales 12 weeks after release is $586,000 . Option A is the correct answer.
To create a table of values, we can plug in different values of t and find the corresponding values of s:
t s
0 10
1 19.882
2 26.248
3 31.177
4 35.064
5 38.185
6 40.731
7 42.837
8 44.6
9 46.095
10 47.384
11 48.508
12 49.498
To graph the function, we can plot the values from the table on a coordinate plane. The horizontal axis represents time in weeks, and the vertical axis represents sales in thousands of units. The resulting graph is a curve that starts at (0,10) and increases as t increases.
To estimate the sales 12 weeks after release, we can look at the graph and see that the corresponding value of s is around 49.5 thousand units. Therefore, the answer is about $586,000 (49.5 x 1000 x 12). Option A is the correct answer.
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The length of a rectangle is five times its width.
If the perimeter of the rectangle is 108 cm, find its length and width.
Answer:
Let the width of the rectangle be w. Then the length of the rectangle is 5w.
The perimeter of a rectangle is the sum of all four sides. So, the perimeter of the rectangle is 2w+2(5w)=108 cm.
Simplifying the right side of the equation, we get 12w=108 cm.
Dividing both sides of the equation by 12, we get w=9 cm.
Since the width is 9 cm, the length of the rectangle is 5w=5(9)=45 cm.
Therefore, the length of the rectangle is 45 cm and the width is 9 cm.
help please PLEASE !!!!!
Answer:
Positive Association
Complementary Angles
Negative Association
Clusters in Data
Supplementary Angle
Non-linear Association
Step-by-step explanation:
Match the boxes on the left to the answers:
Positive Association
Complementary Angles
Negative Association
Clusters in Data
Supplementary Angle
Non-linear Association
Between 7 am and 11 am the temperature in Antartica increased by 8.4 C. If the temperature at 11 am was -28.3 degrees, what was the temperature at 7 am?
Answer:
the temperature at 7 am was -36.7 degrees.
Step-by-step explanation:
Let's denote the temperature at 7 am by "x". Since the temperature increased by 8.4 C between 7 am and 11 am, we can set up the equation:
x + 8.4 = -28.3
Subtracting 8.4 from both sides, we get:
x = -36.7
Therefore, the temperature at 7 am was -36.7 degrees.
$5850 is invested at 6.5% compounded continuously. How long will it take for the balance to reach $11700? Round your answer to two decimal places.
Answer:10.66 years. Punch again to double check
Step-by-step explanation:
A=Pe^(rt)
11700=5850e^(.065t)
isolate the variable expression
2=e^(.065t) divide by 5850
ln2=lne^(.065t) take the natural log of both sides
ln2=.065t. Bring down the power, lne equals
t is about 10.66 years. Divide ln2 by .065
What's the answer to this problem
The function shows that the chairs and sofas the manufacturer should produce to earn that profit is C. (6, 12) P= 1,260
How to explain the functionThe profit function is P = 50x + 80y.
In order to find the optimal production quantities that will maximize the profit function, we need to determine which vertex yields the highest profit.
From the given vertices, we can see that the profit at (0,0) is 0. The profit at (0,15) is 1,200, and the profit at (6,12) is 1,260.
Therefore, the manufacturer should produce 6 chairs and 12 sofas to earn a profit of 1,260.
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Select all that apply. By making the financially irresponsible decision of maxing out your credit card limit, you might...
A) not have money for an emergency situation.
B) get a very low interest rate when you want to buy a house.
C) not be able to buy the things you need.
D) have enough saved up for retirement.
By making the financially irresponsible decision of maxing out your credit card limit, you might not have money for an emergency situation.
As, There is no foolproof technique to determine how much you can spend in excess of your credit limit, but you can go over it.
When determining the risk of accepting an over-the-limit transaction, card issuers may take into account a number of criteria, including your prior payment history.
Now, maxing out credit card leads to negative results.
So, either not have money for an emergency situation or not be able to buy the things you need.
But we can still spend after maxing out the limit.
Thus, not have money for an emergency situation is correct option.
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A manager of Furniture store has compiled a list of written complaints during the past three months. The complaints were categorized as follows. Type and Frequency Error in billing, Rudeness by store personnel, Late delivery, Questions not answered during telephone inquiry,and Other 42 14 8 6 5 Total 75 Present the above data using pie-chart(put the relative frequencyand the central angle measure toeach categoryon a table)
We can conclude that there is significant evidence that the number of complaints received by Lara music store is different from number of complaints received by music stores in general.
Here, we have,
H0 : μ ≥ 6
H1 : μ < 6
Test statistic :
n = 20
Sample Mean, x = 3
σ = 1.5
Test statistic = (x - μ) ÷ σ/sqrt(n)
Test statistic = (3 - 6) ÷ 1.5/sqrt(20)
Test statistic = - 3 / 0.3354101
Test statistic = −8.944271
Since, sample size is < 30 ;
Obtaining the Critical value using the from T;
Tcritical at 0.05, df = 19 = - 1.729
Tstatistic < Tcritical
−8.944271 < - 1.729
Hence, we reject the Null:
We can conclude that there is significant evidence that the number of complaints received by Lara music store is different from number of complaints received by music stores in general.
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consider the time taken to completion time (in months) for the construction of a particular model of homes: 4.1 3.2 2.8 2.6 3.7 3.1 9.4 2.5 3.5 3.8 Find the mean, median mode, first quartile and third quartile. Find the outlier?
Sum
Mean = (4.1 + 3.2 + 2.8 + 2.6 + 3.7 + 3.1 + 9.4 + 2.5 + 3.5 + 3.8) / 10
Mean = 36.7 / 10
Mean = 3.67
To find the median, we need to put the values in order:
2.5, 2.6, 2.8, 3.1, 3.2, 3.5, 3.7, 3.8, 4.1, 9.4
The middle number is the median, which is 3.35 in this case (3.2+3.5)/2.
To find the mode, we look for the value that appears most often. In this case, there is no mode as no value appears more than once.
To find the first quartile (Q1), we need to find the value that separates the bottom 25% of the data from the top 75%. We can do this by finding the median of the lower half of the data:
2.5, 2.6, 2.8, 3.1, 3.2
The median of this lower half is 2.8, so Q1 = 2.8.
To find the third quartile (Q3), we need to find the value that separates the bottom 75% of the data from the top 25%. We can do this by finding the median of the upper half of the data:
3.7, 3.8, 4.1, 9.4
The median of this upper half is 3.95, so Q3 = 3.95.
To find the outlier, we can use the rule that any value more than 1.5 times the interquartile range (IQR) away from the nearest quartile is considered an outlier. The IQR is the difference between Q3 and Q1:
IQR = Q3 - Q1
IQR = 3.95 - 2.8
IQR = 1.15
1.5 times the IQR is 1.5 * 1.15 = 1.725.
The only value that is more than 1.725 away from either Q1 or Q3 is 9.4. Therefore, 9.4 is the outlier in this data set.
Answer:
Step-by-step explanation:
Mean is the average of the data vales : 38.7 (sum of all values) divided by 10 (the number of values). Mean = 38.7/10 = 3.87
Median is the "middle" number" = put the date in order and find the middle value:
2.5, 2.6, 2.8, 3.1, 3.2, 3.5, 3.7, 3.8, 4.1, 9.4, since there is no middle data value, find the average of the 2 in the middle.
3.2 + 3.5/2 = 6.7 ÷ 2 = 3.35 - median
All values appear once so there is no mode.
First quartile is the middle of the lower set of data = 2.8
Third quartile is the middle of the upper set = 3.8
The outlier is 9.4.
How to calculate the outlier:
First you need the IQR which is the diffence of Q3 - Q1,
so the IQR is 3.8- 2.8 = 1
Outliers are the quartile + or - (1.5)(IQR)
Q1 -(1.5)(1) = 2.8 - 1.5 = 1.3
Q3 - (1.5)(1)= 3.8 + 1.5 =4.5
So anything below 1.3 or above 4.5 is an outlier.
There is one 9.4
Find the length of the third side. If necessary, round to the nearest tenth.
6 and 10
The length of the third side is 8units
What is Pythagoras theorem?Pythagoras theorem states that : the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse.
If a and b are the legs of the triangle and c is the hypotenuse,then
c² = a²+b²
For example , if a = 3 and b = 4 , then
c = √3²+4²
c = √ 9+16
c = √25
c = 5units.
Similarly, c = 10, a= 6, and b is unknown
therefore
10²= 6²+b²
b² = 10²-6²
b² = 100-36
b² = 64
b = √64
b = 8units
therefore the length of the third leg is 8units.
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what does it mean the name of the numbers
help
Answer:
It is called as triangular numbers
Step-by-step explanation:
these numbers can be represented as a triangle of dots
Please solve quickly will give brainlest if correct!!!!!
The sum expression [tex][2(4 + \frac9n)^4](\frac9n) + ... + [2(4 + \frac{9n}n)^4](\frac9n)[/tex] using the sigma notation is [tex]\sum\limits^{n}_{i=1} [2(4 + \frac{9i}n)^4](\frac9n)[/tex]
Writing the sum using the sigma notationFrom the question, we have the following parameters that can be used in our computation:
[tex][2(4 + \frac9n)^4](\frac9n) + ... + [2(4 + \frac{9n}n)^4](\frac9n)[/tex]
From the above expression, we can see that the different expression in each term is
9/n
So, we introduce a variable
Assuming the variable is i, the i-th term of the expression would be[tex]t(i) = [2(4 + \frac{9i}n)^4](\frac9n)[/tex]
When represented using the sigma notation, we have
[tex]\sum\limits^{n}_{i=1} [2(4 + \frac{9i}n)^4](\frac9n)[/tex]
Hence, the sum expression using the sigma notation is [tex]\sum\limits^{n}_{i=1} [2(4 + \frac{9i}n)^4](\frac9n)[/tex]
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Solve for the missing side using c =
Answer:
c=12.04
Explanation:
You can use the formula given: c=√a^2+b^2
c=√8^2+9^2=√64+81=√145=12.04
Can you help me answer this question?
Step-by-step explanation:
The constant of proportionality is just the slope of the line
using 0,0 and 3,2 points
slope = (y1-y2 ) / ( x1-x2) = (0-3) / ( 0-2) = 3/2 = constant of proportionality
Need help! I HAVE 30 MIN! will pay for all work shown (ZELLE ONLY) Do all 3 please!
Answer: i gotchu
Step-by-step explanation:
1) Since the base of this function is greater than 1, this means its increasing exponentially (increases from left to right). So as x approaches positive infinity, y approaches positive infinity as well.
Domain (-∞,∞) Range (0,∞)
2) If the base changes to 1/9 the function would decrease. So as x approaches positive infinity, y approaches 0 (Check attached screenshot)
3) The "+5" raises the horizontal asymptote up 5 units. So the new equation for the horizontal asymptote is y=5.
The "x-2" shifts the x values to the right by 2 units.
u dont have to pay me, i literally just learned this like a month ago :)
Brynen is driving to a new job five days this week. He drives 27 miles each way. His car gets 35 miles per gallon of gas. How many gallons of gas will he use driving to and from work this week? Round to the nearest tenth.
The number of gallons of gas Brynen will use in driving to and from work, during the week, obtained using arithmetic operations is 7 5/7 gallons
What are arithmetic operations?Arithmetic operations are operations involving addition, subtraction, multiplication, and division.
The distance Brynen travels each way to his new job = 27 miles
The distance his car gets per gallon of gas = 35 miles
The number of gallons he will use in a week (five days of driving in the week), can therefore, be found by arithmetic operations follows;
The distance Brynen travels = 27 × 2 × 5 = 270 miles
The number of gallons = 270 miles/(35 miles/gallon) = 270/35 = 7 25/35
7 25/35 = 7 5/7
The volume of gas he will use to and from work this week is; 7 5/7 gallons
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Given this unit circle what is the value of x
Answer:
[tex]x=-\dfrac{\sqrt{51}}{10}[/tex]
Step-by-step explanation:
You want the value of x in the third quadrant of a unit circle where y = -7/10.
Pythagorean theoremThe radius of a unit circle is 1, so the Pythagorean theorem tells you the magnitude of the value of x is ...
1² = x² +(7/10)²
x = -√(1 -49/100) = -√(51/100) . . . . . . x < 0 in the third quadrant
x = (-√51)/10
Find the length of the missing side
Step-by-step explanation:
This is a right triangle , so the Pythagorean theorem applies
c^2 = a ^2 + b^2 c is the hypotenuse a and b are the legs
15^2 = 9^2 + x^2
15^2 - 9^2 = X^2
x = 12 ft
find the area of the shaded region
The area of the shaded region is 51.75 in².
From the figure
Radius of semicircle = √25² - 20²
=√625- 400 = 15 inch
Now, Area of Trapezium = 1/02 ( a +b ) h
= 1/2 (17 + 37) x 15
= 1/2 (54) x 15
= 27 x 15
= 405 in²
Then, Area of Shaded region
= Area of Trapezium - Area of semicircle
= (405 - πr²)
= 405 - 353.25
= 51.75 in²
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