Derive expressions for the means and variances of the following linear combinations in terms of the means and covariances of the random variables X1, X2, and X3. (a) X1 - 2X2 (b) X1 + 2X2 - 3 (C) 3X1 - 4X2 if X1 and X, are independent (So, 012 = 0).

Answer:    

   False

   True

   False

   True

   False

   False

Step-by-step explanation:

From the plot, we can see that curve B is taller and more narrow than curve A, and it is shifted to the right relative to curve A. This tells us that curve B has a larger mean and smaller standard deviation than curve A. Therefore, statement 2 is true, and statements 1, 3, 5, and 6 are false. Finally, since curve A is more spread out than curve B, it has a larger standard deviation. Therefore, statement 4 is true.

Equivalent fractions are defined as fractions that are equal to the same value, regardless of their numerators and denominators.

Equivalent fractions can be defined as fractions that may have different numerators and denominators but represent the same value. For example, 9/12 and 6/8 are equivalent fractions because both simplify to 3/4. 1/2, 2/4, 3/6 and 4/8 are equivalent fractions. Let's see how their values ​​are equal. We will represent each of these fractions with a shaded circle.

It can be seen that, seen as a whole, the hatched parts in all the figures represent the same parts.

Equivalent fractions can be written by multiplying or dividing the numerator and denominator by the same number. This is why these fractions reduce to the same number when they are simplified.

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a) The constant k is 5.427 x 10^−12 and its natural logarithm is -26.68.

b) The mean salary of the given model by using the probability density function is approximately $270.86.

a) The cumulative distribution function of the given random variable is provided as follows:

F(x) = {1−kx^−3 if x>44000, and 0 otherwise

The cumulative distribution function is given as

F(x) = 1−kx^−3 if x>44000 and F(x) = 0, if x≤44000i)

We need to check the value of the cumulative distribution function at 44000

We have, F(44000) = 0

0 = 1−k(44000)^−3

⇒ 1 = k(44000)^−3

⇒ k = 1/(44000)^−3

⇒ 5.427 x 10^−12

Taking the natural logarithm of k, we have ln(k) = −28.68 (approx.)

Hence, the constant k is 5.427 x 10^−12 and its natural logarithm to three decimal places is -28.68

b) The probability density function is given as,

f(x) = F'(x) = 3kx^−4, for x>44000 and f(x) = 0, otherwise

The mean or expected value of the random variable is given as

E(X) = ∫[−∞,∞]xf(x)dx

= ∫[44000,∞]x(3kx^−4)dx

= 3k∫[44000,∞]x^−3dx

= 3k[(−1/2)x^−2] [∞,44000]

= (3k/2)(44000)^−2

= 270.86 (approx.)

Therefore, the mean salary given by the model is $270.86 (approx.)

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The wave is polarized parallel to the y-axis, and the magnetic field lines are parallel to the x-axis. Here option D is the correct answer.

The oscillating electric dipole along the z-axis creates an electromagnetic wave with electric and magnetic fields perpendicular to each other and to the direction of wave propagation. At a position on the y-axis far from the origin, the electric field will be parallel to the y-axis.

The polarization of the wave refers to the orientation of the electric field vector. Since the electric field is parallel to the y-axis, the wave is polarized parallel to the y-axis.

According to the right-hand rule, the direction of the magnetic field lines will be perpendicular to both the electric field and the direction of wave propagation, which is along the z-axis. Therefore, the magnetic field lines will be parallel to the x-axis.

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The dimensions of the poster should be 15 in × 32 in so that the least amount of poster is used.

The dimensions of the rectangular poster are 15 in × 32 in so that the least amount of poster is used.A rectangular poster is given that is to contain 450 square inches of print. The margins at the top and bottom of the poster are 2 inches, and the margins on the left and right are 1 inch. Let us suppose the width of the poster is x in and the length of the poster is y in. Also, we need to find the least amount of poster used.Therefore, the dimensions of the poster be x in × y in. The printable area of the poster is given as 450 sq in. Hence, the area of the poster minus the area of the margins should be 450 sq in. Therefore,x × y = (x - 2) (y - 4) + 450x × y = xy - 2x - 4y + 8 + 450xy - xy - 2x + 4y = 8 + 450(y - 4)x = (450(y - 4) - 8) / (y - 1)x = (450y - 1808) / (y - 1)Now we need to calculate the dimensions of the rectangular poster. We need to find the value of x and y. Substituting the value of x in the first equation we get,y = (450 / (x - 2)) + 4We also know that x > 2 and y > 4. We need to minimize the amount of poster used. Hence we need to minimize x × y. The dimensions of the rectangular poster are 15 in × 32 in so that the least amount of poster is used.Therefore, the dimensions of the poster should be 15 in × 32 in so that the least amount of poster is used.

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The chance that a randomly selected individual found to have a positive result actually has the disease is called the Positive Predictive Value (PPV). What is the chance that a randomly selected individual found to have a positive result actually has the disease?

The probability that a randomly chosen individual with a positive test result really has the disease is referred to as the Positive Predictive Value (PPV). It reflects how well the test can detect disease in those who have it. In statistics, the PPV is calculated as follows:

PPV = True Positives / (True Positives + False Positives) x 100

In addition, the PPV is influenced by a variety of factors, including the disease's prevalence, the sensitivity and specificity of the test, and the prevalence of the disease in the population.

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The selling price of laptop after VAT (15 percent) is Rs 4830.

To determine the quantity or percentage of something in terms of 100, use the percentage formula. Percent simply means one in a hundred. Using the percentage formula, a number between 0 and 1 can be expressed.

A number that is expressed as a fraction of hundred is what it is.

it is mostly used to compare and determine ratios and is represented by the symbol %.

We are given that:-

so the amount after VAT = 4200+4200*15%

= 4200+4200+0.15

= 4200+630= 4830.

therefore, the selling price of laptop after VAT is Rs 4830.

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As a result, Jerome has 728 tracks that aren't from his country among the 1,040 music he has downloaded to his Spotify account.

A mathematical relationship called proportionality asserts that two values are related in such a way that if one quantity rises or falls, the other quantity rises or falls by a fixed amount. The proportionality constant, also known as this constant factor, is typically represented by the letter "k".

given

The remaining 70% of Jerome's 1,040 songs are not country songs if only 30% of them are.

We can use the following calculation to get the proportion of non-country songs:

70% of 1,040 = 0.7 x 1,040 = 728

As a result, Jerome has 728 tracks that aren't from his country among the 1,040 music he has downloaded to his Spotify account.

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Answer:

37

Step-by-step explanation:

we know that:

C=?

c=17

b=26

a=14

using the law of cosine:

[tex]a^{2} +b^{2} -2ab Cosc=c^{2}[/tex]

[tex]14^{2} +26^{2} -2(14)(26)Cosc=17^{2} \\872-728Cosc=289\\-728Cosc=-583\\Cosc=\frac{-583}{-728} \\C=36.791\\C=37[/tex]

The shortest possible distance between Alan and Ryan is 11,250 miles, and the longest possible distance is 12,000 miles

Distance is a numerical measurement of how far apart two objects or points are. It is a scalar quantity, meaning that it has magnitude but no direction. Distance is usually measured in units such as meters, kilometers, miles, or feet, depending on the system of measurement used.

Sound is a type of physical energy that is produced by vibrating objects and travels through a medium, such as air, water, or solids, as a series of pressure waves. When an object vibrates, it creates a disturbance in the surrounding medium that causes molecules to move back and forth, creating areas of high and low pressure that propagate outward from the source of the sound.

In the given question,

Let d be the distance between Alan and Ryan in miles. Then, the time it takes for sound to travel this distance is given by d/768. Therefore, we have:

d/768 = 45 - 30 = 15

Solving for d, we get:

d = 15 x 768 = 11520

So the distance between Alan and Ryan is 11520 miles.

If we take the lower bound of 750 miles per hour, we can calculate the minimum distance between Alan and Ryan as follows:

d/750 = 15

d = 15 x 750 = 11250

Therefore, the minimum distance between Alan and Ryan is 11250 miles.

If we take the upper bound of 800 miles per hour, we can calculate the maximum distance between Alan and Ryan as follows:

d/800 = 15

d = 15 x 800 = 12000

Therefore, the maximum distance between Alan and Ryan is 12000 miles.

Therefore, the shortest possible distance between Alan and Ryan is 11,250 miles, and the longest possible distance is 12,000 miles.

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the equivalent closed form for the original rate function is

.[tex]S π/t 4tan (t) dt  = -4 ln |cos (t)| + C.[/tex]

a. [tex]S π / π /4 5t+4 / t² + 1 dt[/tex]We can write this rate function as a sum of two functions by expanding the denominator:

[tex]S π / π /4 5t+4 / (t² + 1) dt  = S π / π /4 5t+4 / (t² + 1) (t+1/t - 1/t) dt  = S π / π /4 5t+4 (t+1 - 1/t²) dt  = S π / π /4 5t+4 (t+1) dt - S π / π /4 5t+4 (1/t²) dt[/tex]

Now, integrating the two functions gives us the closed form:

[tex]S π / π /4 5t+4 (t+1) dt = 5/2 (t² + 2t + 2) + CS π / π /4 5t+4 (1/t²) dt = -5/2 (t + 1/t) + C[/tex]

Therefore, the equivalent closed form for the original rate function isS π / π /4 5t+4 / t² + 1 dt  = 5/2 (t² + 2t + 2) - 5/2 (t + 1/t) + C.

b. S π/t 4tan (t) dt
We can use a trig identity to change the form of this rate function:

S π/t 4tan (t) dt  = S π/t 4 (sin (t) / cos (t)) dt  = 4/cos (t) S π/t sin (t) dt

Integrating the rate function gives us the closed form:

S π/t 4tan (t) dt  = 4/cos (t) S π/t sin (t) dt = -4 ln |cos (t)| + C.

Therefore, the equivalent closed form for the original rate function is:

S π/t 4tan (t) dt  = -4 ln |cos (t)| + C.

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Combining these, we have[tex]$6 \times 6 = \boxed{36}$[/tex] different arrangements of the numbers [tex]${}1,$ ${}2,$ ${}3,$ ${}4,$ ${}5,$ $6$[/tex] in a row where the sum of any adjacent numbers is even.

Products intended for exporting after processing into goods or processed products are referred to as "basic products," as are goods planned for export after processing. Samples 1 - 3 Samples 2 - 3.

We may start by noting that at minimum one of the neighboring numbers must be even for the sum of both numbers to be even. This means that a even numbers (2, 4, 6) as well as the odd numbers (1, 3, 5) should be arranged in the appropriate positions.

Let's start by thinking about the even positions. The second, fourth, and sixth places are the only even positions. We can choose any variant of the 3 even numbers to occupy these spots, giving us[tex]$3! = 6$[/tex] ways.

Let's now think about the unusual positions. The first, third, and fifth positions are the only ones that are odd. We have an additional [tex]$3! = 6$[/tex]ways to fill these spots by using any combination of the 3 odd numbers.

Consider the odd locations now. The first, third, and fifth places are the three odd positions. We have an additional[tex]$3! = 6$[/tex]ways by using any permutation of the three odd numbers to fill these positions.

Together, this give us [tex]$6 \times 6[/tex] = [tex]\boxed{36}$[/tex] different ways to arrange the numbers [tex]${}1,$ ${}2,$ ${}3,$ ${}4,$ ${}5,$ $6$[/tex]in a row so that the sum of any two adjacent numbers is even.

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0, 2%, 2 1/2 The values are ordered from smallest to largest, with 0 being the smallest, followed by 2%, and then 2 1/2.

0 is the smallest value because it represents nothing. It is the absence of a quantity, and therefore, it is always the smallest value.

2% is larger than 0 because it represents a percentage of a whole. Percentages are fractions out of 100, so 2% means 2 out of 100. It is larger than 0, but smaller than 2 1/2.

2 1/2 is the largest value because it represents a whole number and a fraction. It is larger than 2%, because 2 1/2 is equal to 250 out of 10,000 or 25 out of 1,000, which is a larger quantity than 2 out of 100.

Understanding the relative size of different values is an important skill in many areas, including mathematics, science, and finance. Being able to order values from smallest to largest helps us make sense of data and information, and it allows us to make informed decisions based on the relative size of different quantities. It is important to learn how to do this accurately and efficiently in order to be successful in these fields.

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Answer: -109

Step-by-step explanation:

Concept : First take note of what operations are in play and how they relate to y. In this case, -10 is being multiplied to y and then 19 is subtracted from the product of -10 and y.

Steps:

Plug 9 in for y (parentheses just mean multiply):

-10(9)-19

Simplify using correct order of operations:

-90-19

-109

Hope this helps :)

The explicit formula for the arithmetic sequence 12, 5, -2, -9,..is a(n) = -7n + 19.

To find the explicit formula for this arithmetic sequence, we first need to determine the common difference, which is the amount by which each term differs from the previous term.

d = 5 - 12 = -7

d = -2 - 5 = -7

d = -9 - (-2) = -7

Since the common difference is -7, we can use the formula for an arithmetic sequence:

a(n) = a (1) + (n - 1) d

where a(n) is the nth term of the sequence, a (1) is the first term, n is the term number, and d is the common difference.

Plugging in the given values, we get:

a(n) = 12 + (n - 1) (-7)

Simplifying, we get:

a(n) = -7n + 19

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The explicit formula for the arithmetic sequence will be f(n) = 19 -7n.

f(n) = a + (n - 1) d,

where an is the first term and is the explicit formula for an arithmetic series.

d = Common Difference

n = number of terms

The provided arithmetic series is = 12, 5, -2, -9.

First term: a = 12.

Common variation: d= 5-12= 7

[Difference between any two words that follow one another.]

When a = 12 and d = -7 are entered into equation (1), we obtain

f(n) = 12 + (n - 1) ( - 7 )

Thus, the explicit formula for the above arithmetic sequence is

f(n) = 12 = (n - 1). ( - 7 )

If we continue to solve it, we obtain

f(n) = 12 - 7n + 7

f(n) = 19 - 7n

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Answer: 36.8

Step-by-step explanation:

First convert 7/19 to a decimal.

7/19 = 0.368421...

Then to convert a decimal a percent by multiplying by 100

0.3684... x 100 = 36.8

Step-by-step explanation:

the law of sine is

a/sin(A) = b/sin(B) = c/sin(C)

a, b, c are the sides. A, B, C are the corresponding opposing angles.

you fill in what you know and then solve for what you don't know. these are just regular equations. you multiply or divide or add or subtract the same things on both sides and try to get the missing side isolated on one side of an equation.

Answer: £43.50

Step-by-step explanation:

each ticket from samuel is £12 if erica is spending £2.50 more per ticket that is £14.50 per ticket. £14.50 x 3 = £43.50

a) If the number 646 from the ordered list changes to 639, c) the median stays the same.

b) a) If the number 646 from the ordered list changes to 639, a) the mean decreases by 1.

The median is the middle value in an ordered list (descending or ascending).

The mean refers to the average value.

The mean or average is computed as the quotient of the division of the total data value by the total number of items in the data set.

The ordered numbers of trading cards owned by 7 middle-school students = 360, 373, 402, 499, 548, 644, 646

The total value (sum) = 3,472

The number of cards = 7

The median = 499

The mean = 496 (3,472/7)

If the number 646 changes too 639:

The total value (sum) = 3,465

The median = 499

The mean = 495 (3,465/7)

Difference in mean = 1 (496 - 495)

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The answer to the question is 334 kittens.

Given that a cat gave birth to 333 kittens who each had a different mass between 147 g and 159 g. Then the cat gave birth to a 4th kitten with a mass of 57 g.

First of all, we will find out the range of the mass of kittens. The range is given as follows;Range = Maximum Value - Minimum Value Range = 159 g - 147 g Range = 12 g

Now, the cat gave birth to a 4th kitten with a mass of 57 g, we can say that the minimum value of kitten's mass is 57 g.So, the maximum value of kitten's mass can be calculated as follows;Maximum Value = 57 g + Range Maximum Value = 57 g + 12 g Maximum Value = 69 g Now, we can say that all kittens with a mass of 69 g or less would be born because the minimum value of kitten's mass is 57 g and the range of mass is 12 g.

Therefore, the answer to the question is 334 kittens.

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The probability the length of the display will exceed 154 inches is 0.1292

The probability that the length of the display shelf given to each bar of soap will exceed 154 inches when there are 50 bars of soap is 0.0062 or 0.62%. This is because the mean is 3 inches and the standard deviation is 0.5 inches, which means that the length of the display will have a normal distribution.

We can calculate this probability by using the following formula:

P(x > 154) = P (x > 154 - 50 × 3/√(50×0.5)) = P(Z > 1.13) = 1 - P(Z < 1.13) = 1 - 0.870 = 0.1292

The probability the length of the display will exceed 154 inches is 0.1292.

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Answer: 24000 g

Step-by-step explanation:

multiply together:

4 bags * 6 kg = 24 kg total

convert:

1 kg = 1000 g

24 kg * (1000 g / 1 kg) = 24000 g

To calculate the total mass of the box in grams, we need to first calculate the total mass of the 4 bags of sugar in kilograms, and then convert that to grams.

The mass of one bag of sugar is 6 kilograms.

The total mass of all 4 bags is:

4 bags x 6 kilograms/bag = 24 kilograms

To convert 24 kilograms to grams, we multiply by the conversion factor of 1000 grams/kilogram:

24 kilograms x 1000 grams/kilogram = 24,000 grams

Therefore, the total mass of the box, including all 4 bags of sugar, is 24,000 grams.

The correct answer is B) 24,000 grams.

Check the picture below.

so if we just set h = 0, we'll get the "t" when that happened

[tex]\stackrel{h}{0}=-16t^2+29t+6\implies 0=-(16t^2-29t-6)\implies 0= 16t^2-29t-6 \\\\\\ 0=(t-2)(16t+3)\implies t= \begin{cases} ~~ ~ 2 ~~ \checkmark\\ -\frac{3}{16} ~~ \bigotimes \end{cases}[/tex]

now, let's notice that we get two valid values for "t", however the negative doesn't apply in this case, because we can't quite have negative seconds for the object in motion.

Answer:

2

Step-by-step explanation:

h(t) = -16t² + 29t + 6

h(2) = -16 * 2² + 29 * 2 + 6

h(2) = 0

t = 2 second's

The probability of randomly selecting a doctor who is either a General Practitioner or under the age of 40 from a small hospital is 9/19, given 6 out of 19 are General Practitioners, 5 out of 19 are under 40, and 2 are both.

To find the probability of randomly selecting a doctor who is either a General Practitioner or under the age of 40, we need to add the probabilities of these two events and subtract the probability of selecting a doctor who is both a General Practitioner and under the age of 40, since we don't want to count that case twice:

P(General Practitioner or under 40) = P(General Practitioner) + P(Under 40) - P(General Practitioner and under 40)

we know 6 out of 19 doctors are General Practitioners, 5 out of 19 doctors are under the age of 40, 2 doctors are both General Practitioners and under the age of 40.

Therefore:

P(General Practitioner) = 6/19

P(Under 40) = 5/19

P(General Practitioner and under 40) = 2/19

Substituting these values into the formula:

P(General Practitioner or under 40) = 6/19 + 5/19 - 2/19

= 9/19

Therefore, the probability of randomly selecting a doctor who is either a General Practitioner or under the age of 40 is 9/19.

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The required distance the ship traveled from its starting point to its destination is approximately 44.8 miles.

To solve this problem, we can use the Pythagorean theorem to find the distance the ship traveled from its starting point to its destination.

We can see that the ship traveled 35 miles east and 28 miles south, forming a right triangle. The distance from the starting point to the destination is the hypotenuse of this triangle.

Using the Pythagorean theorem, we can find the length of the hypotenuse:

[tex]$\begin{align*}\text{distance} &= \sqrt{35^2 + 28^2}\&= \sqrt{1225 + 784}\&= \sqrt{2009}\&\approx 44.8 \text{ miles}\end{align*}[/tex]

Therefore, the distance the ship traveled from its starting point to its destination is approximately 44.8 miles.

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The cost of covering the wall with wall paper is 495.

the lengthe of the wall = 11 feet

the width of the wall = 15 feet

so, the area of the wall

A = the length of the wall x the width of the wall

A = 11 x15

A = 165 square foot

then, the total cost is

= 165 x 3

= 495

So, the cost of covering the wall with wall paper is 495.

The surface of a shape's area is measured. You must multiply the length and breadth of a rectangle or square in order to determine its area. A has an area of x time y.

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Answer:

Step-by-step explanation:

using the ratio given, the number of computers could be sold by the company last week is: A. 448 desktops, 168 laptops.

To find the actual numbers of desktop and laptop computers sold, we need to choose a common factor for the ratio 8:3.

Let's assume that the total number of computers sold is 33x (where x is a positive integer). Then, the ratio 8:3 corresponds to 8x desktops and 3x laptops. We can check which of the given options satisfies this condition:

A. 8x = 448, 3x = 168 --> This satisfies the condition, as 8:3 = 448:168

B. 8x = 448, 3x = 165 --> This does not satisfy the condition, as 8:3 is not equal to 448:165

C. 8x = 440, 3x = 168 --> This does not satisfy the condition, as 8:3 is not equal to 440:168

D. 8x = 400, 3x = 165 --> This does not satisfy the condition, as 8:3 is not equal to 400:165

Therefore, the answer is option A: 448 desktops and 168 laptops could be the numbers of computers sold by the company last week.

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The coordinates of R are (-8,-1). To find the coordinates of R, we first need to find the length of PQ.

Using the distance formula, we have:

d(P,Q) = √((x2-x1)² + (y2-y1)²)

= √((-4-(-12))² + (-9-7)²)

= √(8² + (-16)²)

= √(320)

= 8 √(5)

Since PR:QR is 3:5, we can set up the following equation:

d(P,R)/d(R,Q) = 3/5

Let the coordinates of R be (x,y). We can use the midpoint formula to find the coordinates of the midpoint of PQ, which is also the coordinates of the point that divides PQ into two parts in the ratio of 3:5.

Midpoint of PQ = ((-12-4)/2, (7-9)/2) = (-8,-1)

Using the distance formula again, we can find the distance between P and R:

d(P,R) = (3/8) d(P,Q)

= (3/8) (8 √(5))

= 3 √(5)

Now we can use the ratio PR:QR = 3:5 to find the distance between R and Q:

d(R,Q) = (5/3) d(P,R)

= (5/3) (3 √(5))

= 5 √(5)

Finally, we can use the midpoint formula to find the coordinates of R:

x = (-12 + (3/8) (8))/2 = -8

y = (7 + (-1))/2 = 3

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Complete Question:

The coordinates of the endpoints of bar (PQ) are P(-12,7) and Q(-4,-9). Point R is on bar (PQ) and divides it such that PR:QR is 3:5. What are the coordinates of R ?

Step-by-step explanation:

Perimeter:

12m + 10m + 8m + (10 - 8)m + 9m + (12 - 9)m = 44m

or

12m * 2 + 10m * 2 = 44m

Area:

A = 9m * 8m + 12m * (10 - 8)m

A = 72m² + 24m² = 96m²