A 160-foot tall antenna has 4 guy-wires connected to the top of the antenna, and each guy-wire is anchored to the ground. A side-view of this scenario is shown. One of the guy-wires forms an angle ofα=0.33radians with the antenna and the opposing guy-wire forms an angle ofβ=0.38radians with the antenna.

The main idea that ties all the details together is that there are various types of desserts that are made from fruit or fruit juice, and they are enjoyed by many people.

The paragraph is about different types of desserts that are made from fruit or fruit juice. The details in the paragraph mention three specific desserts: pies filled with peaches, apples, or blueberries; cobbler, which is a baked fruit dessert topped with pieces of a crust; and sherbet, which is a cold treat made of fruit or fruit juice that is often enjoyed in the summer.

Despite their differences in preparation and presentation, all of these desserts have one thing in common: they are made using fruit or fruit juice. The paragraph suggests that fruit-based desserts are popular among many people and can be enjoyed in a variety of forms.

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The pick-up rate in this scenario would be 80%. This is calculated by dividing the number of rooms occupied (160) by the number of rooms reserved (200), and then multiplying by 100 to get a percentage. So, (160/200) x 100 = 80%. This means that 80% of the reserved rooms were ultimately occupied.

It's important to note that a pick-up rate of 80% is generally considered to be a good result in the hospitality industry. It indicates that the hotel was able to accurately predict the number of rooms that would be needed by the groups, and that the groups themselves followed through on their reservations. A lower pick-up rate could suggest that the hotel overestimated demand, or that some of the groups cancelled their bookings at the last minute. On the other hand, a higher pick-up rate could indicate that the hotel was too conservative in its initial estimates, or that some of the groups requested additional rooms after the initial reservation was made. Ultimately, the pick-up rate is a useful metric for assessing the accuracy of a hotel's forecasting and planning processes.

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Step-by-step explanation:

TOTAL ( 360 degree) circumference is pi * d        d = 2r = 6ft

   you want 180 degrees of this

        180 / 360      *    pi* 6 = 1/2 * 6 pi = 3 pi  ft

You can attend 4,941 different combinations of plays at the theater.

To find the different combinations of plays that you can attend, we need to use the combination formula. Since you want to attend at least 3 plays, we can calculate the combinations for attending 3, 4, 5, 6, 7, 8, 9, 10, 11, and 12 plays.

For attending 3 plays, the number of combinations is 220.
For attending 4 plays, the number of combinations is 495.
For attending 5 plays, the number of combinations is 792.
For attending 6 plays, the number of combinations is 924.
For attending 7 plays, the number of combinations is 792.
For attending 8 plays, the number of combinations is 495.
For attending 9 plays, the number of combinations is 220.
For attending 10, 11, or 12 plays, there is only one combination each.

Therefore, the total number of different combinations of plays that you can attend is:

220 + 495 + 792 + 924 + 792 + 495 + 220 + 1 + 1 + 1 = 4,941

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Answer:

(ax+1) = ( ax+89) -12 +1

Step-by-step explanation

add all of it up then subtract by 12 add 1 theres your answer

Answer:

don't say that

Step-by-step explanation:

I am l o

The width of the counter is 3 meters or 9/3 meters as a fraction considering the condition that its value in meters is a number such that its power squared added to its power to the fourth will give 90.

Let's represent the width of the counter in meters as "x". As per the given condition, we can form the equation:

x² + [tex]x^4[/tex] = 90

Simplifying the equation, we get:

[tex]x^4[/tex] + x² - 90 = 0

Now, we can factor the equation as:

(x² - 9)(x² + 10) = 0

So, the possible values of "x" are:

x² = 9 or x² = -10

Since the width of the counter cannot be negative, we can ignore the second solution. Therefore, we have:

x² = 9

x = ±√9

x = ±3

Since the width of the counter cannot be negative, the only possible solution is:

x = 3

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The question is -

In the entrance hall, there is a counter for the sale of tickets, the chief architect will ask one of your assistants to determine how wide it is with the following conditions: its value in meters is a number such that its power squared added to its power to the fourth will give 90. Does the counter have to measure the width?

The volume of pyramid A is twice the volume of pyramid B. If the height of pyramid B increases to twice that of pyramid A, the new volume of pyramid B is equal to the volume of pyramid A.

In Mathematics and Geometry, the volume of a pyramid can be calculated by using the following formula:

Volume = 1/3 × b × h

Where:

Volume of pyramid A = (10 × 20 × h)/3 = 200h/3

Volume of pyramid B = (10 × 10 × h)/3 = 100h/3

Since the heights of the two (2) pyramids are equal, we would substitute them as follows;

Volume of pyramid A = (200 × 3 × Volume of pyramid B)/(100 × 3)

Volume of pyramid A = 2 × Volume B

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Complete Question;

The base of pyramid A is a rectangle with a length of 10 meters and a width of 20 meters. The base of pyramid B is a square with 10-meter sides. The heights of the pyramids are the same.

The volume of pyramid A is ____ the volume of pyramid B. If the height of pyramid B increases to twice that of pyramid A, the new volume of pyramid B is ______the volume of pyramid A.

The numbers from the set {1, 2, 3, 4} that are part of the solution to the inequality 7x + 6 > 20 are:  {3, 4}

There are different Inequalities such as:

Greater than

Less than

Greater than or equal to

Less than or equal to

Now, we are given the inequality as:

7x + 6 > 20

Subtract 6 from both sides to get:

7x > 14

Divide both sides by 7 to get:

x > 2

Thus, the set of solutions is: (3, 4)

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The standard error of the mean is approximately 62.23 (rounded to two decimal places).

The probability that the sample mean will be more than 10 hours (1830 hours) is approximately 0.4364 (rounded to four decimal places).

I understand that you need help calculating the standard error of the mean and the probability that the sample mean will be more than 10 hours. Let's address each part separately:

a. To calculate the standard error of the mean, we will use the formula:

Standard Error (SE) = (population standard deviation) / sqrt(sample size)

In this case, the population standard deviation is 440 hours, and the sample size is 50 adults. Plugging these values into the formula:

SE = 440 / sqrt(50) ≈ 62.23



b. To find the probability that the sample mean will be more than 10 hours, we will first calculate the z-score for a sample mean of 1830 hours (1820 + 10 hours):

z = (sample mean - population mean) / standard error
z = (1830 - 1820) / 62.23 ≈ 0.16

Now, we can use the z-score to find the probability by looking up the area to the right of this value in a standard normal distribution table or using a calculator. For a z-score of 0.16, the area to the right is approximately 0.4364.

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To solve this problem, we need to first find the prime factorization of each integer from 1 to 30. We can then count the number of times the prime factor 3 appears in each of these prime factorizations.

The prime factorization of 1 is 1, which does not contain the prime factor 3. The prime factorization of 2 is 2, which also does not contain the prime factor 3. The prime factorization of 3 is 3, which contains one factor of 3. Continuing in this way, we find that the prime factorization of each integer from 1 to 30 contains a certain number of factors of 3.

To find the greatest integer k for which 3k is a factor of p, we need to find the maximum value of k such that there are at least k factors of 3 in the prime factorization of p. We can do this by counting the number of factors of 3 in each prime factorization and finding the minimum value of these counts.

The prime factorization of p is:

p = 1 × 2 × 3 × ... × 30

To find the number of factors of 3 in this product, we can count the number of times the prime factor 3 appears in each of the factors being multiplied together. For example, the factor 9 contains two factors of 3, and the factor 27 contains three factors of 3.

Counting the number of factors of 3 in each factor from 1 to 30, we get:

1: 0 factors of 3
2: 0 factors of 3
3: 1 factor of 3
4: 0 factors of 3
5: 0 factors of 3
6: 1 factor of 3
7: 0 factors of 3
8: 0 factors of 3
9: 2 factors of 3
10: 1 factor of 3
11: 0 factors of 3
12: 1 factor of 3
13: 0 factors of 3
14: 0 factors of 3
15: 1 factor of 3
16: 0 factors of 3
17: 0 factors of 3
18: 2 factors of 3
19: 0 factors of 3
20: 0 factors of 3
21: 1 factor of 3
22: 0 factors of 3
23: 0 factors of 3
24: 1 factor of 3
25: 0 factors of 3
26: 0 factors of 3
27: 3 factors of 3
28: 0 factors of 3
29: 0 factors of 3
30: 1 factor of 3

The minimum number of factors of 3 among these integers is 1, which occurs for the factors 3, 6, 9, 12, 15, 18, 21, 24, 27, and 30. Therefore, the greatest integer k for which 3k is a factor of p is 10.

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The expression that is equal to f(x) + g(x) is -3x² - 3x - 3

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

f(x) = -3x² + 4x + 4

g(x) =  -7x - 7

The expression that is equal to f(x) + g(x) is represented as

f(x) + g(x) = -3x² + 4x + 4 -7x - 7

When the like terms are evaluated, we have

f(x) + g(x) = -3x² - 3x - 3

Hence, the expression is f(x) + g(x) = -3x² - 3x - 3

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Step-by-step explanation:

if you need to know the formula yourself, then this is actually physics and not just mathematics.

anyway, we assume this happens on the surface of Earth.

so, with Earth's gravity and such the formula for the height of the bullet at a certain time is

h(t) = -16t² + v0×t + staying height =

= -16t² + 1200t + 5

the x-intercept is the time, when the bullet falls back down and hits the ground. in other words. when it's height = 0.

0 = -16t² + 1200t + 5

a quadratic equation

ax² + bx + c = 0

has the genetic solution

x = (-b ± sqrt(b² - 4ac))/(2a)

in our case

x = t

a = -16

b = 1200

c = 5

t = (-1200 ± sqrt(1200² - 4×-16×5))/(2×-16) =

= (-1200 ± sqrt(1,440,000 + 320))/-32 =

= (-1200 ± sqrt(1,440,320))/-32 =

= (-1200 ± sqrt(64×22505))/-32 =

= (-16×75 ± 8×sqrt(22505))/-32 =

= (75/2 ± 1/4 × sqrt(22505))

t1 = 75/2 + 1/4 × 150.0166657... = 75.00416644... seconds

t2 = 75/2 - 1/4 × 150.0166657... = -0.004166435... seconds

after about 75 seconds the bullet will hit the ground (x-intercept).

the t2 solution is the theoretical extension of the flight curve backwards in time (remember, the staying height is 5 ft, but using the shot graph and the corresponding accelerations the bullet would have started 0.004166435... seconds before the shot on the ground, and this is therefore also an x-intercept.

for the vertex (the max. height of the bullet) we need the zero of the first derivation (the extreme point of the function).

h'(t) = -32t + 1200 = 0

32t = 1200

t = 1200/32 = 37.5 seconds

so, after 37.5 seconds the bullet reaches is maximum height, which is

-16×37.5² + 1200×37.5 + 5 = 22,505 ft

so, the vertex is (37.5, 22505).

Answer:

  24.1 square units

Step-by-step explanation:

You want the base area of a prism with height 9 units and volume 216.9 units³.

The formula for the volume of a prism is ...

  V = Bh

where B is the area of the base, and h is the height. Solving for the base area, we have ...

  B = V/h = (216.9 u³)/(9 u) = 24.1 u²

The area of one of the bases is 24.1 square units.

When a cone is sliced in a direction parallel to the base, the resulting cross section is a circle.

A plane parallel to the base will intersect the curved surface of the cone at the same distance from the vertex all the way around, creating a circular shape.

This type of cross section is called a parallel cross section, and it is one of three types of cross sections that can be made when slicing a cone (the others being perpendicular and oblique).

In practical terms, this means that if you were to slice a cone-shaped cake or piece of fruit parallel to the base, you would end up with circular slices. This type of slicing can also be useful in engineering and construction, as it can create cylindrical shapes that can be used as columns or supports.

In summary, when a cone is sliced parallel to the base, the resulting cross section is a circle, and this type of slicing can be useful in a variety of applications.

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By using a maclaurin series to obtain the maclaurin series for the given function is  F(x) = x cos(5x) = [tex]1 - 25x^2/2! + 625x^4/4! - 15625x^6/6! + ...[/tex]

To obtain the Maclaurin series for the function f(x) = x cos(5x), we need to write the Maclaurin series for cos(5x). The Maclaurin series for cos(x) is: [tex]cos(x) = 1 - x^2/2! + x^4/4! - x^6/6! + ...[/tex]

Using this formula, we can substitute 5x for x and obtain the Maclaurin series for cos(5x): cos(5x) =[tex]1 - (5x)^2/2! + (5x)^4/4! - (5x)^6/6! + ...[/tex]

[tex]= 1 - 25x^2/2! + 625x^4/4! - 15625x^6/6! + ...[/tex]

We can substitute this series into the original function f(x) = x cos(5x) and obtain its Maclaurin series: f(x) = x cos(5x)

[tex]= x[1 - 25x^2/2! + 625x^4/4! - 15625x^6/6! + ...][/tex]

[tex]= x - 25x^3/2! + 625x^5/4! - 15625x^7/6! + ...[/tex]

This is the Maclaurin series for the function f(x) = x cos(5x). It is obtained by substituting the Maclaurin series for cos(5x) into the original function and simplifying the resulting series. Maclaurin series are useful for approximating functions using polynomials. By truncating the series after a certain number of terms, we can obtain a polynomial that approximates the original function to a certain degree of accuracy. The accuracy of the approximation depends on the number of terms in the series that are used. The more terms we include, the more accurate the approximation will be.

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The reason that there always be an upside down triangle in the Sierpiński triangle is because  of its recursive process or what we call the self-similar nature of all of its pattern.

The pattern of the Sierpiński triangle is seen as a product the result of repeatedly removing certain triangles from an original equilateral triangle. The process involves dividing an equilateral triangle into four smaller triangles by connecting their midpoints during each iteration.

Note that, afterwards the triangle located at the center is eliminated. This procedure is repeated endlessly, where every triangle that remains is split into four smaller triangles, and the middle one is extracted.

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Answer:

Step-by-step explanation:

The p-value in this hypothesis test is 0.3398.

 To find the p-value for this hypothesis test, we will follow these steps:

1. Identify the null hypothesis (H0) and the alternative hypothesis (H1). In this case, H0: p = 0.227 (percentage of asthma in children is the same in both countries) and H1: p < 0.227 (percentage of asthma in children is lower in the other country).

2. Calculate the test statistic. In this case, the test statistic z is given as -0.9559.

3. Find the p-value associated with the test statistic. Since the alternative hypothesis is one-tailed (p < 0.227), we will look up the one-tailed p-value corresponding to the z-score -0.9559 in the standard normal (z) table or using a calculator.

Looking up the z-score in a table or using a calculator, we find that the p-value is approximately 0.1694.

So, in this hypothesis test, the test statistic, z = -0.9559 and the p-value = 0.1694.

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The value of b in the given function is 4.

Since we know that the coefficient of the term is 2, we can plug in the values of a and b into the equation for the axis of symmetry.

We also know that the vertex of the parabola lies on the axis of symmetry, and we can see from the graph that the vertex is at the point.

Since x = -1 and y = 6, this will be;

6 = 2(-1)² + b(-1) + 8

b = 4

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So the probability that a randomly selected song had 501-1,000 plays given that the song was country is 7/12, or approximately 0.583.

To find the probability that a randomly selected song had 501-1,000 plays given that the song was country, we need to use conditional probability.

Using Bayes' theorem, we have:

P(B|A) = P(A|B) * P(B) / P(A)

We can find each of these probabilities from the given information:

P(A) = (7+3)/(7+3) = 1 (since all songs recorded were either country or rock)

P(B) = (7+2)/(7+3+2) = 9/12 (since 9 out of the 12 songs recorded had 501-1,000 plays)

P(A|B) = P(A and B) / P(B) = 7/9 (since out of the 9 songs with 501-1,000 plays, 7 were country)

Therefore,

P(B|A) = (7/9) * (9/12) / 1

P(B|A) = 7/12

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The sample is a three-stage cluster sample

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Answer:

3052.08

Step-by-step explanation:

v = 4/3[tex]\pi r^{3}[/tex]

v = [tex]\frac{4(3.14)9^{3} }{3}[/tex]

v = [tex]\frac{4(3.14)(729)}{3}[/tex]

v = [tex]\frac{9156.24}{3}[/tex]

v = 3052.08

Helping in the name of Jesus.

Answer:

The answer for Volume is 3052.08in³

Step-by-step explanation:

Volume of sphere=4/3pir³

V=4_3×3.14×9³

V=4/3×9×9×9×3.14

V=4×3×9×9×3.14

V=12×81×3.14

V=3052.08in³

Sample Values are estimated from known population is true about sampling in statistics.

In statistics, sampling refers to the process of selecting a subset of individuals or objects from a larger population. The sample is used to estimate or make inferences about the population from which it was drawn. Option A is false because as the sample size increases, the variability generally decreases as the sample better represents the population. Option B is false because sample statistics (such as the sample mean or sample standard deviation) vary from sample to sample and are estimated from the data in the sample. Option C is true because sample values (such as the sample mean or sample proportion) are estimated from the known population values, and this estimation process involves sampling error due to random variability in the sample.

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The equation in slope-intercept form of a line that contains points D and E is y = x.

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical expression:

y - y₁ = m(x - x₁)

Where:

First of all, we would determine the slope of this line;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (4 - 2)/(4 - 2)

Slope (m) = 2/2

Slope (m) = 1.

At data point (2, 2) and a slope of 1, a linear equation for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 2 = 1(x - 2)

y = x - 2 + 2

y = x

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

sphere volume = (4.0 / 3.0) * 3.14159 * sphere radius ** 3

Here's a step-by-step explanation using the terms "radius", "volume", and "division":

1. Given the sphere's radius (sphere radius), we'll use the formula for calculating the volume of a sphere: V = (4.0 / 3.0) * π * r^3, where V is the sphere's volume and r is its radius.

2. Perform floating-point division by using (4.0 / 3.0) instead of (4 / 3). The floating-point division ensures a more accurate result since it retains decimal values.        
   
3. Compute the sphere's volume (sphere volume) using the formula: sphere volume = (4.0 / 3.0) * π * (sphere radius)^3.

4. Assign the calculated value to the sphere volume.      

By following these steps and using the given formula, you can calculate the volume of a sphere with the specified radius.

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The probability that a soccer player who tests positive takes steroids is approximately 0.279 or 27.9%.

To solve this problem, we can use Bayes' theorem:

P(Steroids|Positive) = P(Positive|Steroids) * P(Steroids) / P(Positive)

where:
P(Steroids|Positive) = probability of taking steroids given a positive test result
P(Positive|Steroids) = probability of testing positive given that the player takes steroids (93%)
P(Steroids) = probability of a soccer player taking steroids (5%)
P(Positive) = overall probability of testing positive (calculated below)

To calculate P(Positive), we need to use the law of total probability:

P(Positive) = P(Positive|Steroids) * P(Steroids) + P(Positive|No Steroids) * P(No Steroids)

where:
P(Positive|No Steroids) = probability of testing positive given that the player does not take steroids (12%)
P(No Steroids) = probability of a soccer player not taking steroids (100% - 5% = 95%)

Plugging in the values, we get:

P(Positive) = 0.93 * 0.05 + 0.12 * 0.95 = 0.1165

Now we can calculate P(Steroids|Positive):

P(Steroids|Positive) = 0.93 * 0.05 / 0.1165 = 0.398

Therefore, the probability that a soccer player who tests positive takes steroids is 0.398 (rounded to three decimal places).

To find the probability that a soccer player who tests positive takes steroids, we can use Bayes' Theorem:

P(A|B) = (P(B|A) * P(A)) / P(B)

Here, let A be the event "player takes steroids" and B be the event "player tests positive."

We are given:
- P(B|A) = 0.93 (93% of players taking steroids test positive)
- P(A) = 0.05 (5% of soccer players take steroids)
- P(B|A') = 0.12 (12% of players not taking steroids test positive)

To find P(B), we can use the Law of Total Probability:

P(B) = P(B|A) * P(A) + P(B|A') * P(A')

Since P(A') = 1 - P(A) = 1 - 0.05 = 0.95, we have:

P(B) = (0.93 * 0.05) + (0.12 * 0.95)

Now, we can use Bayes' Theorem to find P(A|B):

P(A|B) = (0.93 * 0.05) / ((0.93 * 0.05) + (0.12 * 0.95))
P(A|B) ≈ 0.279

Therefore, the probability that a soccer player who tests positive takes steroids is approximately 0.279 or 27.9%.

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The reason why some data mining algorithms require that variables are standardized to zero mean and standard deviation of 1.0 is because it helps to normalize the data and make it more comparable across different variables.

Standardizing the data helps to remove the impact of the scale of the variables on the analysis, allowing for more accurate comparisons and correlations between variables. By doing this, it ensures that no one variable has an undue influence on the results of the analysis. Standard deviation is a statistical measure that is used to measure the amount of variability or dispersion in a dataset. When data is standardized, it allows for a more accurate assessment of the relationship between variables and can improve the accuracy of the analysis. Overall, standardizing variables is a crucial step in the data mining process, as it helps to ensure that the results of the analysis are reliable and accurate.

The reason some data mining algorithms require variables to be standardized (or normalized) to a zero mean and a standard deviation of 1.0 is to ensure consistent and comparable scales for all variables involved. Standardizing variables helps in improving the performance and accuracy of the algorithms.

When variables have different scales or units, it can be challenging for algorithms to interpret their relative importance accurately. By transforming variables to have a zero mean and a standard deviation of 1.0, the algorithms can more effectively process and analyze the data. This standardization process is particularly important for distance-based and gradient-based algorithms, where scale differences can significantly impact the results.

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The probability that a randomly selected dorm room has either a refrigerator or a TV (or both) is 0.69, or 69% (rounded to two decimal places).

The probability of a aimlessly  named dorm room having either a refrigerator or a television( or both) is0.69, as calculated from the given data. This implies that  nearly 70 of the dorm apartments have at least one of these amenities. We can also interpret this as saying that having a television or a refrigerator is a  fairly common  circumstance in the dorm apartments on this particular  council lot.

P(R) = 0.38 (38% had refrigerators)

P(T) = 0.52 (52% had TVs)

P(R and T) = 0.21 (21% had both a TV and a refrigerator)

Substituting these values into the equation, we get:

P(R or T) = 0.38 + 0.52 - 0.21

P(R or T) = 0.69

  It's worth noting that having both a television and a refrigerator in a dorm room isn't as common, with only 21 of the apartments having both amenities. This could be due to a number of factors,  similar as space constraints or  particular preference. still, it's still important to fete  that having both amenities can  give  fresh convenience and comfort to the  scholars living in these apartments.

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The calculated value of the area of this figure is 28 sq units

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

The composite figure

The area is the sum of the individual areas

The figure can be divided into two trapezoids

Using the above and the area formulas as a guide, we have the following:

Area = 1/2 * (3 + 5) * 2 + 1/2 * (3 + 7) * 4

Evaluate

Area = 28

Hence, the area is 28 sq units

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