The 147 heights of males from a data set of body measurements vary from a low of 152.0 cm to a high of 192.5 cm. Use the range rule of thumb to estimate the standard deviations and compare
the result to the standard deviation of 12.22 cm calculated using the 147 heights. What does the result suggest about the accuracy of estimates of s found using the range rule of thumb? Assume the
estimate is accurate if it is within 1.7 cm.

Answer:

9.968

Step-by-step explanation:

[tex]c^2=a^2+b^2 -2ab*cos(C)[/tex]

and more generally, a side squared of a triangle is equal to the other two sides squared then added, minus double the product of the other two sides and the cosine of the opposite angle, generally denoted as the capital letter of the side. (c is the side, C is the opposite angle)

in this case the other two sides are 7 and 10, so we can say that a=7, b=10 if  it helps understand this a bit more, but "a" and "b" really just represent the other two sides.

the opposite angle is: [tex]\frac{5\pi}{13}[/tex] and the unknown is "a", but we can just express it as "c" for the sake of simplicity. Now plugging in all the known values we get the following equation:

[tex]c^2=7^2+10^2-2(7)(10)cos(\frac{5\pi}{13})\\\\c^2=49+100-140cos(\frac{5\pi}{13})\\\\c^2=149-140cos(\frac{5\pi}{13})[/tex]

Now from here we can just use a calculator to approximate the cosine, but make sure it's in radian mode! otherwise your answer may be incorrect as degrees are different than radians.

[tex]c^2=149-140(0.3546)\\\\c^2=149-49.64468\\\\c^2=99.355315814\\\\c=\sqrt{99.355315814}\\\\c=9.96771367035\\\\c\approx 9.968[/tex]

So the side is approximately 9.968 units in length.

Answer:

Cost $50.63

Step-by-step explanation:

To calculate the cost, we need to find out how many gallons of gasoline the car will consume in 450 miles. We can use the formula:

Gallons = Total miles / Miles per gallon

Gallons = 450 miles / 24 miles per gallon

Gallons = 18.75

Next, we multiply the number of gallons by the cost per gallon to get the total cost:

Total cost = Gallons * Cost per gallon

Total cost = 18.75 gallons * $2.70 per gallon

Total cost = $50.63

So, it will cost $50.63 to drive 450 miles when gasoline costs $2.70 per gallon and your car gets 24 miles per gallon.

Answer:

Step-by-step explanation:

Here's a step-by-step explanation of the reflections:

Point R is located at (1, 1) on the coordinate plane.

Reflection over the y-axis: This reflection changes the sign of the x-coordinate. In other words, if the point (x, y) is reflected over the y-axis, the reflected point will be ( -x, y). So, for point R at (1, 1), the reflection over the y-axis creates R' at (-1, 1).

Reflection over the x-axis: This reflection changes the sign of the y-coordinate. In other words, if the point (x, y) is reflected over the x-axis, the reflected point will be (x, -y). So, for point R' at (-1, 1), the reflection over the x-axis creates R'' at (-1, -1).

So the final location of R'' is at the ordered pair (-1, -1).

Given that there are 26 red cards in the deck of 52 cards, the probability of obtaining a red card on any given draw is 26/52 = 1/2.

The probability of the complimentary event—the probability that no red cards are drawn in the first three draws—can be used to determine the likelihood that a red card will be pulled at least once by the third draw.

Particular that there are 26 non-red (black) cards in the 52-card deck, there is a 50% chance that no red cards will be drawn on any given draw.

As a result, the likelihood that none of the three draws will result in a red card is:

(1/2) x (1/2) x (1/2) = 1/8

The likelihood of drawing a red card at least once by the third draw is the counterpart of this probability.

1 - 1/8 = 7/8

Therefore, by the third draw, there is a 7/8 chance of drawing a red card at least once, or 0.88 rounded to two decimal places.

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Answer:

D

Step-by-step explanation:

why the panic ? you only need to compare the tiles with the actual terms in the equations and add them up.

x²

-x²

-x -x

x x x x (clearly that means 4x)

-1 -1 -1

1 1

so, we see it is D.

Answer:

Step-by-step explanation:

The equation that represents the town's population after 4 years can be found using the formula:

P = P0 * (1 - r)^t

Where P is the population after t years, P0 is the initial population (4.11 x 10^4), r is the annual shrink rate as a decimal (9.6% as 0.096), and t is the number of years (4).

P = 4.11 x 10^4 * (1 - 0.096)^4

P = 4.11 x 10^4 * 0.6994^4

P = 4.11 x 10^4 * 0.4139

P = 1.70 x 10^4

So the town's population after 4 years is 1.70 x 10^4.

Answer:

Let P(t) be the population of the town after t years. We know that P(0) = 4.11 x 10^4. Then, the rate of change of the population is given by -0.096P(t), so we can write the differential equation:

dP/dt = -0.096P(t)

To find the population after 4 years, we need to solve this differential equation with the initial condition P(0) = 4.11 x 10^4. We can do this by separating variables and integrating both sides:

∫(dP/P) = -0.096 ∫dt

ln|P(t)| = -0.096t + C

where C is a constant of integration that can be found using the initial condition. Solving for P(t), we get:

P(t) = Ce^(-0.096t)

where C = e^(ln|P(0)|) = e^(ln|4.11 x 10^4|) = 4.11 x 10^4

Substituting in t = 4, we get:

P(4) = 4.11 x 10^4 e^(-0.096 × 4) = 4.11 x 10^4 e^(-0.384)

So, the equation representing the town's population after 4 years is:

P(t) = 4.11 x 10^4 e^(-0.096t)

The mean of the data is given by the equation M = 679.3846 and the standard deviation σ = 34.1535

The standard deviation refers to a measurement of the data dispersion from the mean. A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed.

Standard Deviation is calculated by

Each number's deviation from the mean must be determined, and then squared.

Next, add up all of these values.

Divide the result by the quantity of numbers.

Then calculate its square root.

σ = √ ( 1/N ) ( ∑₁ⁿ ( x₁ - μ )²

Given data ,

Let the data be represented as Set A

Now , the value of set A is

Set A = { 688 , 711 , 625 ,701 , 688 , 667 , 694, 630, 547, 703, 688, 697, 703, 656, 677, 700, 702, 688, 691, 664, 688, 679, 708, 699, 667, 703 }

The mean of the sample data = Sum of all the values / number of values

The mean M = 17664 / 26

The mean M = 679.3846

Now , the standard deviation is calculated by

σ = √ ( 1/N ) ( ∑₁ⁿ ( x₁ - μ )²

Substituting the values in the equation , we get

The standard deviation σ = √ ( 30328.153846154 / 26 )

The standard deviation σ = √ ( 1166.4674556213 )

The standard deviation σ = 34.1535

Hence , the standard deviation is 34.1535

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The logarithm is the inverse function to exponentiation. That means the logarithm of a number x to the base b is the exponent to which b must be raised, to produce x.

For example, since 1000 = 10³, the logarithm base 10 of 1000 is 3, or log₁₀ = 3

a. log(2^100) = 100 log(2) ≈ 30.103

b. log(100^2) = 2 log(100) = 2 log(10^2) = 2 × 2 = 4

c. log(3.0862.062) = log(3.086) + log(2.062) ≈ 0.488 + 0.316 = 0.804

(Note: The multiplication of 3.086 and 2.062 can be done using a calculator.)

d. log(55^(-3.1)) = -3.1 log(55) ≈ -3.1 × 1.740 = -5.394

e. log(5/1) = log(5) - log(1) ≈ 0.699 - 0 = 0.699

f. log(1/5) = log(1) - log(5) ≈ 0 - 0.699 = -0.699

g. log(1/81^2) = log(1) - 2 log(81) = -2 log(9^2) = -2 × 2 log(9) ≈ -2 × 0.954 = -1.908

(Note: We can use the property that log(a^b) = b log(a) to simplify the expression.)

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Answer:

11xy(121x²-y²)

Step-by-step explanation:

When factorizing, you should always look for what each term has in common.

First, let's look at the coefficients (numbers) in each term: 1331 and 11. Both are divisible by 11, so let's factorize out 11:

1331x³y-11y³x

11(121x³y-y³x)

Looking at the terms in the bracket, we see they both have 'x's in common (121x³y has three x's multiplied in and y³x has one). Let's factorize out this x:

11(121x³y-y³x)

11x(121x²y-y³)

We can also see both terms in the brackets have 'y's in common (121x²y has one y and y³ has three multiplied in). Let's factorize out this y:

11x(121x²y-y³)

11xy(121x²-y²)

Since there is nothing in common left between the terms, we can say the expression is fully factorized!

Answer:

Step-by-step explanation:

To find the perimeter of a right-angled triangle when only the length of the hypotenuse is known, you'll need to use the Pythagorean theorem. Here's a step-by-step explanation:

Step 1: Understand the Pythagorean theorem

The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b):

c^2 = a^2 + b^2

Step 2: Substitute the known length of the hypotenuse

Let's say the length of the hypotenuse is "h". Substitute "h" for "c" in the Pythagorean theorem:

h^2 = a^2 + b^2

Step 3: Solve for one of the unknown sides

To find the perimeter of the triangle, we need to know the lengths of both sides "a" and "b". To do this, we need to solve for one of the unknown sides. Let's solve for "a".

Square root both sides of the equation:

√(h^2) = √(a^2 + b^2)

h = √(a^2 + b^2)

Square both sides of the equation:

h^2 = a^2 + b^2

Step 4: Use the Pythagorean theorem to find the other unknown side

Now that we have an expression for "a", we can use the Pythagorean theorem again to find "b":

h^2 = a^2 + b^2

Substitute the expression for "a" that we found in Step 3 into the equation:

h^2 = (√(a^2 + b^2))^2 + b^2

h^2 = a^2 + b^2 + b^2

h^2 = 2 * b^2 + a^2

h^2 - a^2 = 2 * b^2

b^2 = (h^2 - a^2) / 2

Take the square root of both sides:

b = √((h^2 - a^2) / 2)

Step 5: Calculate the perimeter

The perimeter of the triangle is the sum of the lengths of all three sides, so we can now calculate the perimeter using the lengths of "a" and "b" that we found in Steps 3 and 4:

P = a + b + h

Step 6: Conclusion

Therefore, the perimeter of the right-angled triangle can be found by first using the Pythagorean theorem to find the lengths of two of the sides, and then adding up the lengths of all three sides to find the perimeter.

The measure of angle 1 is given as follows:

m < 1 = 42º.

To obtain the measure of angle 1 in the kite, we must consider that the consecutive angles are complementary, that is, the sum of their measures is of 90º.

Relative to angle 1, we have that:

m < 4 + m < 1 = 90º.

For the bottom left triangle, the internal angle measures are given as follows:

Considering that the sum of the measures of the internal angles of a triangle is of 180º, the measure of angle 4 is obtained as follows:

m < 4 + 42 + 90 = 180

m < 4 = 58º.

Then the measure of angle 1 is obtained as follows:

m < 1 = 90 - 58

m < 1 = 42º.

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Answer:3.25

Step-by-step explanation:

Divide 325/100=3.25

This curve symbolizes the curve of indifference. Those combinations of quantities that the customer considers to be of equal value are connected by a curve on a graph whose axes reflect amounts of two commodities.

It dislikes all product combinations that offer the same level of enjoyment to the consumer. Because each combination provides the same level of enjoyment, the buyer Favours them all equally. The indifference curve therefore gets its name.

An indifference curve is a graphic representation of a collection of products that give consumers comparable levels of satisfaction, leading to their indifference. A consumer or person is indifferent between the two products at every point on the indifference curve because they provide the same kind of benefit.

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Answer:

Step-by-step explanation:

Step 1: Define each variable

Let's define some variables to make the calculations easier:

t1 = the median monthly rent in 1990, which is $447

t2 = the median monthly rent in 2002, which is $658

Δ = the change in median monthly rent, which is t2 - t1

Step 2: Calculate the change in median monthly rent

Δ = t2 - t1 = $658 - $447 = $211

This means that the median monthly rent increased by $211 from 1990 to 2002.

Step 3: Divide the change by the original amount

To find the percentage increase, we need to divide the change by the original amount and multiply by 100:

Δ / t1 * 100 = ($211 / $447) * 100 = 47.2%

This means that the median monthly rent increased by 47.2% from 1990 to 2002.

Step 4: Round to the nearest tenth of a percent

The final answer is 47.2%, rounded to the nearest tenth of a percent.

The percent increase in the median monthly rent prices from 1990 to 2002 was 47.2%.

The function type of the graph with asymptotes, x = 2, and y = 0  is a rational polynomial, where the degree of the numerator is less than the degree of the denominator, and (x - 2) is a factor of the denominator, which is a function of the form;

[tex]f(x) = \frac{1}{(x - 2)}[/tex]

An asymptote is a line to which the output value of a function approaches as the input value becomes very large approaches infinity.

The function type represented by the graph is a polynomial function that has an horizontal asymptote of y = 0, and a vertical asymptote of x = 2

A function has a vertical asymptote at the location at which the denominator approaches zero.

The vertical asymptote of x = 2 , indicates that the denominator approaches zero when x = 2, therefore, (x - 2) is a factor of the denominator

A function has an horizontal asymptote which is the value the function approaches as the input value approaches infinity.

Therefore, the horizontal asymptote of y = 0, indicates that the the degree of the numerator is less than the degree of the denominator

The function type in the question is therefore;

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Answer:

41 inches

Step-by-step explanation:

to find the perimeter of any shape, add the length of all the sides together

The numerical value of x in the given right triangle is 20.14.

The figure in the image is right-triangle.

To find the value of x, we use trigonometric ratio.

Sine = Opposite / Hypotenuse

Plug in the values and solve for x.

sin( 32° ) = x / 38

x = sin( 32° ) × 38

x = 0.529919 × 38

x = 20.14

Therefore, the value of x is 20.14.

Option C) 20.14 is the correct answer.

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A student would have to score approximately 0.84 standard deviations above the mean to be publicly recognized.

The dispersion of asset prices from their average price, or market volatility, can be calculated with the use of standard deviation. A large standard deviation indicates a dangerous investment when prices move erratically. Low standard deviation indicates stable prices, which lowers the risk associated with investments.

The remaining 79 percent of pupils are not recognised if just the top 21% of students receive public recognition. Since a normal distribution is assumed, the conventional normal distribution and its corresponding z-scores can be used to provide the solution.

The percentage of scores that are higher than a certain z-score is shown by the area under the standard normal distribution to its right. Finding the z-score that represents the top 21% of scores is equivalent to locating the z-score that represents the bottom 79% of scores. By using a calculator or a table of the ordinary normal distribution, we can determine that the z-score for the bottom 79 percent of scores is roughly 0.84.

In order to be officially acknowledged, a student would need to get a score that is roughly 0.84 standard deviations above the mean.

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Answer:

2.016, 2.16, 2.1682, 2.2

How to put anything from least to greatest?

The decimals that you have put are the following:

2.16

2.1682

2.2

2.016

How to do it:

If you look at the decimals the last one, 2.016 does not have a 1 or a 2 instead it has a 0 so that would be a our first decimal in the least to greatest form.

We can also include the third one 2.2 is the only one that has a 2 so now we know that 2.2 will go last.

Lets compare the first and second ones which are 2.16 and 2.1682 and I think we obviously know that the answer is 2.1682 because it is greater then 2.16.

So now here are the decimals from least to greatest:

2.016, 2.16, 2.1682, 2.2

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Answer:

784 R 13

Hope this helps!

Step-by-step explanation:

The number of times it is not land on the blue color sector is 7-1 = 6

A probability is defined as the ratio to the number of required outcomes to the total number of outcomes of an event.

The spinner is divided into 7 sectors, in which each sector is equal in size.

Among 7 sectors two of of them are blue in color.

We have to calculate that how many times the spinner not landing on the blue color sector.

For that we have to calculate the possible outcome for the blue color sector for 1 spin.

For 1 spin , the number of possible outcomes = 7.

Number of required outcomes = 2.

Probability of number of spins on blue sector for 1 spin = 2/7.

Probability of number of spins on blue sector for 7 spin = 7*(2/7) = 2.

Standard deviation = [tex]\sqrt{\frac{2}{7} *\frac{5}{7} }[/tex]= 0.4518.≅0.452.

Standard error=root(7)*0.452= 1.19≅1.2

Expected value =2-1.2 = 0.8 ≅1

Therefore the expected value is 1.

Number of times it will land on the blue color sector is 1.

Hence, the number of times it is not land on the blue color sector is 7-1 = 6.

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Answer:

4 cups of fruit sorbet.

Step-by-step explanation:

There are 128 cups in 1 gallon. So, 1 gallon of fruit sorbet is equal to 128 cups.

Therefore, each person will receive 128 cups / 32 people = 4 cups of fruit sorbet.

The solution is, each person get 4 cups of fruit sorbet.

Division is the process of splitting a number or an amount into equal parts. Division is one of the four basic operations of arithmetic, the ways that numbers are combined to make new numbers. The other operations are addition, subtraction, and multiplication.

here, we have,

given that,

Hugo is serving fruit sorbet at his party.

He has 1 gallon of fruit sorbet to serve to 32 friends .

now. we get,

There are 128 cups in 1 gallon.

So, 1 gallon of fruit sorbet is equal to 128 cups.

so, we have,

Therefore, each person will receive 128 cups / 32 people = 4 cups of fruit sorbet.

If each person receives the same amount,

then, each person will receive 4 cups of fruit sorbet.

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Answer: 70˚

Step-by-step explanation:

Goal: find the other angles in the triangle and subtract them from 180 to find x:

180 - 105 = 75˚

the other angle is 35˚, (alternate interior angles).

.: x = 180 - 75 - 35 = 70˚

The solution for x in the triangle is x = 51.98 units

Trigonometry is a branch of mathematics dealing with the relationship between the ratios of the sides of a right-angled triangle with its angles.

Using trigonometric ratio:

sin 38° = 32/x  (Sine = opposite/hypotenuse)

x = 32/sin 38°

x = 51.98 units

Therefore, the solution is x = 51.98 units

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Answer:

2787

Step-by-step explanation:

add them all together

Answer:

Step-by-step explanation:

To find the two diameters that separate the top 3% and the bottom 3% of the bolts produced in the machine shop, we need to find the lower and upper bounds of the interval that contains the middle 94% of the data. This can be done using the standard normal distribution and the z-score.

First, we'll find the z-score that corresponds to the lower bound. To do this, we'll use the formula:

z = (x - μ) / σ

where x is the lower bound, μ is the mean of the data (6.48 mm), and σ is the standard deviation of the data (0.06 mm). We want to find the value of x such that the area to the left of x is equal to 3%:

z = (x - 6.48) / 0.06

z = -2.33

Next, we'll use the z-score to find the value of x (the lower bound). We'll use the standard normal distribution table to look up the value of -2.33 and find that it corresponds to a cumulative probability of 0.01. So, the lower bound is such that 1% of the data is less than or equal to this value. To find the value of x, we'll use the formula:

x = μ + zσ

x = 6.48 + (-2.33) * 0.06

x = 6.32

So, the lower bound of the interval that contains the middle 94% of the data is 6.32 millimeters. This is the diameter that separates the bottom 3% of the bolts from the rest.

Next, we'll find the upper bound in a similar way. To do this, we'll use the formula:

z = (x - μ) / σ

where x is the upper bound, μ is the mean of the data (6.48 mm), and σ is the standard deviation of the data (0.06 mm). We want to find the value of x such that the area to the left of x is equal to 97%:

z = (x - 6.48) / 0.06

z = 2.33

Using the standard normal distribution table, we find that the value of 2.33 corresponds to a cumulative probability of 0.99. So, the upper bound is such that 99% of the data is less than or equal to this value. To find the value of x, we'll use the formula:

x = μ + zσ

x = 6.48 + 2.33 * 0.06

x = 6.64

So, the upper bound of the interval that contains the middle 94% of the data is 6.64 millimeters. This is the diameter that separates the top 3% of the bolts from the rest.

Therefore, the two diameters that separate the top 3% and the bottom 3% of the bolts produced in the machine shop are 6.32 millimeters and 6.64 millimeters, rounded to the nearest hundredth.

The values for the sets are -

A∪B = { 1 , 2 , 4 , 6 , 8 , 9 , 10 , 12 , 14 , 15 , 16 , 17 , 19 , 20 } and n(A∪B) = 14.

A∩B = { 10 , 12 , 14 , 16 } and n(A∩B) = 4

What is sets?

A set is a precisely defined collection or aggregate of all feasible objects with predetermined qualities that are specified in accordance with a precisely defined rule. Elements of sets are the items used to compare sets.

The set S is - S = { 1 , 2 , 3 , ... , 18 , 19 , 20 }

The set A is - A = { 1 , 2 , 4 , 10 , 12 , 14 , 16 }

The set B is - B = { 6 , 8 , 9 , 10 , 12 , 14 , 15 , 16 , 17 , 19 , 20 }

A∪B is the set of elements of S that are part of A or B, or both.

A∪B = { 1 , 2 , 4 , 6 , 8 , 9 , 10 , 12 , 14 , 15 , 16 , 17 , 19 , 20 }

Count the number of elements present in set A∪B.

Therefore, n(A∪B) value is 14.

A∩B is the set of elements of S that are common to A and B.

A∩B = { 10 , 12 , 14 , 16 }

Count the number of elements present in set A∩B.

Therefore, n(A∩B) value is 4.

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Answer: The present value of an annuity due with a monthly payment of $300 at 6% interest compounded monthly for 10 years can be calculated using the formula:

PV = PMT * [ (1 - (1 + r)^-n) / r ] * (1 + r)

where:

PMT = $300 (the monthly payment)

r = 0.06/12 (the monthly interest rate)

n = 10*12 (the number of periods over 10 years, with 12 months in a year)

Plugging in the values into the formula, we get:

PV = $300 * [ (1 - (1 + 0.06/12)^-n) / (0.06/12) ] * (1 + 0.06/12)

PV = $300 * [ (1 - (1 + 0.06/12)^-(10*12)) / (0.06/12) ] * (1 + 0.06/12)

PV = $300 * [ (1 - 1.06^-120) / (0.06/12) ] * (1 + 0.06/12)

PV = $300 * [ (1 - 0.379362539) / (0.06/12) ] * (1 + 0.06/12)

PV = $300 * [ (0.620637561) / (0.06/12) ] * (1 + 0.06/12)

PV = $300 * 10.34300138

PV = $31,029.

So the present value of the annuity due is $31,029. This means that if you were to invest $31,029 today, you would receive a monthly payment of $300 for 10 years at 6% interest compounded monthly.

Step-by-step explanation:

Answer: Let's say there are a total of 100 students at the middle school. Then, 5 parts out of 7 are playing basketball and 2 parts out of 7 are playing soccer. The percent of students playing soccer can be calculated as follows:

(2/7) * 100 = 28.57% (rounded to the nearest percent)

So, approximately 28.57% of the students at the middle school play soccer.

Step-by-step explanation:

The required Length of the DC is 30.47 Units.

A right triangle, also known as a right-angled triangle, right-perpendicular triangle, orthogonal triangle, or formerly rectangled triangle, is a triangle with one right angle, or two perpendicular sides. The foundation of trigonometry is the relationship between the sides and various angles of the right triangle.

We have;

In ΔABD, ∠BAD = 54° and in ΔBDC, ∠BCD = 28°.

Then, In ΔABD

Sin∅ = BD/20

Sin(54°) = BD/20

BD = 0.809(20)

BD = 16.18

in ΔBDC

tan(28°) = BD/DC

DC = BD/tan(28°)

DC = 16.18/0.531

DC = 30.47 Units.

Thus, required Length of the DC is 30.47 Units.

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