The value of the triple integral ∭E 3xy dV does not exist. The integral does not converge because the integrand becomes unbounded as z approaches infinity.
To evaluate the triple integral ∭E 3xy dV, where E lies under the plane z = x + y and above the region in the xy-plane bounded by the curves y = 0, y = 1, and x = 0, we need to set up the integral using appropriate limits of integration.
Let's first consider the region of integration in the xy-plane. It is a rectangle bounded by the lines y = 0, y = 1, and x = 0. Therefore, the limits of integration for x are from 0 to 1, and for y, the limits are from 0 to 1.
Now, let's determine the limits for z. The plane z = x + y intersects the xy-plane at z = 0, and as we move up in the positive z-direction, the plane extends infinitely. Thus, the limits for z can be taken from 0 to infinity.
Now, we can set up the triple integral:
∭E 3xy dV = ∫[0 to 1] ∫[0 to 1] ∫[0 to ∞] 3xy dz dy dx
The innermost integral with respect to z evaluates to z times the integrand:
∭E 3xy dV = ∫[0 to 1] ∫[0 to 1] [3xyz] evaluated from 0 to ∞ dy dx
Simplifying further:
∭E 3xy dV = ∫[0 to 1] ∫[0 to 1] (3xy ∞ - 3xy(0)) dy dx
Since we have ∞ in the integrand, we need to check if the integral converges. In this case, the integral does not converge because the integrand becomes unbounded as z approaches infinity.
Therefore, the value of the triple integral ∭E 3xy dV does not exist.
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Determine the area between the curve y = x² + 3x - 28 and the x-axis, from x = -8 to x=0.
The area between the curve y = x² + 3x - 28 and the x-axis, from x = -8 to x=0 is 64/3 square units.
We want to calculate the integral of the absolute value of the function over the given interval:
Area = ∫[from -8 to 0] |x² + 3x - 28| dx
Since the curve lies below the x-axis between x = -7 and x = 4, we need to split the integral into two parts and change the sign of the function for the interval [-7, 4]
Area = ∫[from -8 to -7] -(x² + 3x - 28) dx + ∫[from -7 to 4] (x² + 3x - 28) dx + ∫[from 4 to 0] -(x² + 3x - 28) dx
We can now integrate each part separately:
Area = -∫[from -8 to -7] (x² + 3x - 28) dx + ∫[from -7 to 4] (x² + 3x - 28) dx - ∫[from 4 to 0] (x² + 3x - 28) dx
Simplifying, we get:
Area = [-1/3 x³ - 3/2 x² + 28x] [from -8 to -7] + [1/3 x³ + 3/2 x² - 28x] [from -7 to 4] - [-1/3 x³ - 3/2 x² + 28x] [from 4 to 0]
Area = [(-1/3(-7)³ - 3/2(-7)² + 28(-7)) - (-1/3(-8)³ - 3/2(-8)² + 28(-8))] + [(1/3(4)³ + 3/2(4)² - 28(4)) - (1/3(-7)³ - 3/2(-7)² + 28(-7))] - [(-1/3(0)³ - 3/2(0)² + 28(0)) - (-1/3(4)³ - 3/2(4)² + 28(4))]
Area = [(343/3 + 147 - 196) - (-512/3 + 96 - 224)] + [(64/3 + 24 - 112) - (-343/3 + 147 - 196)] - [0 - (-64/3 + 24 - 112)]
Area = [(343/3 + 147 - 196) - (-512/3 + 96 - 224)] + [(64/3 + 24 - 112) - (-343/3 + 147 - 196)] - (-64/3 + 24 - 112)
Area = (64/3)
Therefore, the area between the curve y = x² + 3x - 28 and the x-axis from x = -8 to x = 0 is 64/3 square units.
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Fill in the blank using a term found in the vocabulary list. The ratio of the value of a subtotal to the value of the total is called _________________.
Answer:
Relative frequency
Step-by-step explanation:
Can someone help me with this question. Need answer and explanation/work. Thank you. Will make brainliest.
Answer:
y = - 3 x - 5
Step-by-step explanation:
find the negative reciprocal of the slope of the original line use the point slope formula y - y 1 = m ( x - x 1 ) to find the line perpendicular to 3 y = x + 6
hope this helps
Given that a is in Quadrant 2 and cos(a) = give an exact answer for the following: a sin(20) b. cos(2a) c. tan(20) = 2. Given that B is in Quadrant 4 and sin(B) = give an exact answer for the following: a sin(25) = b.cos(2B) c. tan(28) . Decimal approximations are not allowed for this problem, • Enter your answer in exact form. • Use "sqrt()" to represent.
a) In Quadrant 2, a sin(20) is equal to -sin(20).
b) In Quadrant 2, cos(2a) is equal to -cos(2a).
c) In Quadrant 2, tan(20) is equal to -tan(20).
In Quadrant 2, the angle 'a' is between 90 degrees and 180 degrees, or π/2 and π radians. Knowing that cos(a) is a negative value, we can determine the exact values for the given trigonometric expressions.
a) a sin(20) = -sin(20):
The sine function (sin) is positive in Quadrant 1 and negative in Quadrant 2. Therefore, the value of a sin(20) in Quadrant 2 is equal to the negative of sin(20). This means that the answer for a sin(20) is -sin(20).
b) cos(2a) = -cos(2a):
The cosine function (cos) is negative in Quadrant 2. Since we are given that a is in Quadrant 2, the angle 2a will also be in Quadrant 2. Therefore, cos(2a) in Quadrant 2 is equal to the negative of cos(2a). Thus, the answer for cos(2a) is -cos(2a).
c) tan(20) = -tan(20):
The tangent function (tan) is negative in Quadrant 2. Hence, the tangent of any angle in Quadrant 2 will be equal to the negative of its positive counterpart. Consequently, the answer for tan(20) in Quadrant 2 is -tan(20).
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The null hypothesis is that the laptop produced by HP can run on an average 120 minutes without recharge and the standard deviation is 25 minutes. In a sample of 50 laptops, the sample mean is 125 minutes. Test this hypothesis with the alternative hypothesis that average time is not equal to 120 minutes. What is the p-value?
The p-value for testing the hypothesis that the average runtime of HP laptops is not equal to 120 minutes, based on a sample mean of 125 minutes from a sample of 50 laptops, cannot be determined without additional information.
To calculate the p-value, we need the population standard deviation or the t-value associated with the sample mean and the degrees of freedom. The p-value represents the probability of observing a sample mean as extreme or more extreme than the observed sample mean, assuming the null hypothesis is true.
However, since the population standard deviation is not provided in the question, we cannot directly calculate the p-value. Similarly, the degrees of freedom for the t-distribution depend on the sample size and are not given.
To determine the p-value, we would need either the population standard deviation or the t-value associated with the sample mean and the degrees of freedom. With this information, we could look up the p-value from the t-distribution table or use statistical software to obtain the p-value.
Therefore, without the necessary information, the p-value for the hypothesis test cannot be determined.
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If n = 240 and p (p-hat) = 0.55, construct a 90% confidence interval. Give your answers to three decimals кр
The formula for calculating confidence interval is: $\overline{X} \pm Z_{\alpha/2}\frac{σ}{\sqrt{n}}$,
where $\overline{X}$ is the sample mean,
$σ$ is the population standard deviation,
$n$ is the sample size, and $Z_{\alpha/2}$ is the critical value of the standard normal distribution at $\alpha/2$ and $(1-\alpha/2)$ levels of significance respectively. To construct the 90% confidence interval for the given data: n = 240p-hat = 0.55The sample mean is equal to p-hat which is 0.55. Therefore, the margin of error is given by;
ME = Z_{α/2} × √{p-hat(1 - p-hat) / n}α = 0.10, thus α/2 = 0.05, so the area to the right of the critical value is equal to 0.05.
Using the standard normal distribution table, the critical value for α/2 = 0.05 is: Z_{α/2} = 1.64
Therefore, the confidence interval is given by; CI = p-hat ± Z_{α/2} × √{p-hat(1 - p-hat) / n}CI = 0.55 ± 1.64 × √{0.55(1 - 0.55) / 240}CI = 0.55 ± 0.077
Therefore, the confidence interval is (0.473, 0.627) (rounded to three decimal places).
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PLEASE HELP!!!!!! I WILL MARK!!!
Ricky wants a carrier so that he can take his pet to the veterinarian. He chooses one in the shape of a right rectangular prism that is 4 feet deep, 3 feet tall, and 2 feet wide. What is the surface area of the carrier?
A. 26ft^2
B. 36ft^2
C. 40ft^2
D.52ft^2
Answer:
its c
Step-by-step explanation:
Answer:
c
Step-by-step explanation:
great job mate
Using your calculator, construct a normal probability plot for the octane data from problem 1, and make a sketch of that plot below. From the plot you sketched, does it seem reasonable to assume that octane rating is normally distributed?
Based on the normal probability plot constructed for the octane data, it does not appear reasonable to assume that the octane rating is normally distributed. The plot deviates significantly from a straight line, indicating a departure from normality.
A normal probability plot is a graphical tool used to assess whether a dataset follows a normal distribution. In a normal plot, the observed data points are plotted against the corresponding quantiles of a theoretical normal distribution. If the data points fall approximately along a straight line, it suggests that the data can be reasonably modeled as normally distributed.
In this case, when constructing the normal probability plot for the octane data, if the plot deviates significantly from a straight line, it indicates a departure from normality. If the points on the plot show a distinct curvature or exhibit systematic patterns, it suggests that the data does not follow a normal distribution.
By examining the sketch of the normal probability plot for the octane data, if it shows substantial deviations from a straight line, with points deviating from the expected pattern, it implies that the octane rating is not normally distributed. This departure from normality could be due to various factors, such as skewness, outliers, or a different underlying distribution that better fits the data. Therefore, based on the sketch of the plot, it is reasonable to conclude that the octane rating is not normally distributed.
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Solve this please!!!!!
328 hope this helps
Pls mark brainliest!
[tex]8 \times \frac{3}{4} [/tex]
Answer:
6
Step by step explanation:
8 × ¾ = ²⁴⁄₄ = 6
Answer:
6
Step-by-step explanation:
You can solve this equation in multiple ways:
1) Change [tex]\frac{3}{4}[/tex] into a decimal
[tex]\frac{3}{4} = .75[/tex][tex]8[/tex] × [tex].75 = 6[/tex]2) Change [tex]8[/tex] into a fraction, and multiply that way.
[tex]8 = \frac{8}{1}[/tex][tex]\frac{8}{1}[/tex] × [tex]\frac{3}{4} = \frac{24}{4}[/tex][tex]\frac{24}{4} = 6[/tex]Creating a discrete probability distribution: A venture capitalist, willing to invest $1,000,000, has three investments to choose from.
The first investment, a social media company, has a 20% chance of returning $7,000,000 profit, a 30% chance of returning no profit, and a 50% chance of losing the million dollars.
The second company, an advertising firm has a 10% chance of returning $3,000,000 profit, a 60% chance of returning a $2,000,000 profit, and a 30% chance of losing the million dollars.
The third company, a chemical company has a 40% chance of returning $3,000,000 profit, a 50% chance of no profit, and a 10% chance of losing the million dollars.
a. Construct a Probability Distribution for each investment. This should be 3 separate tables (See the instructors video for how this is done) In your table the X column is the net amount of profit/loss for the venture capitalist and the P(X) column uses the decimal form of the likelihoods given above.
b. Find the expected value for each investment.
c. Which investment has the highest expected return?
d. Which is the safest investment and why?
e. Which is the riskiest investment and why?
a) the venture capitalist has three investment options: a social media company, an advertising firm, and a chemical company.
b) The advertising firm has the highest expected return, making it the most profitable choice.
c) The investment with the highest expected return is Investment 2 (the advertising firm) with an expected value of $1,200,000.
d) The safest investment is Investment 3 (the chemical company) because it has the highest probability (50%) of not incurring any loss (no profit, but no loss either).
e) The riskiest investment is Investment 1 (the social media company) because it has a 50% chance of losing the entire $1,000,000 investment, which is the highest probability of loss among the three investments.
a. Probability Distribution for each investment:
Investment 1 (Social Media Company):
X (Profit/Loss) P(X)
$7,000,000 0.20
$0 0.30
-$1,000,000 0.50
Investment 2 (Advertising Firm):
X (Profit/Loss) P(X)
$3,000,000 0.10
$2,000,000 0.60
-$1,000,000 0.30
Investment 3 (Chemical Company):
X (Profit/Loss) P(X)
$3,000,000 0.40
$0 0.50
-$1,000,000 0.10
b. Expected value for each investment:
Expected value (Investment 1):
E(X) = ($7,000,000 × 0.20) + ($0 × 0.30) + (-$1,000,000 × 0.50)
= $1,400,000 + $0 - $500,000
= $900,000
Expected value (Investment 2):
E(X) = ($3,000,000 × 0.10) + ($2,000,000 × 0.60) + (-$1,000,000 × 0.30)
= $300,000 + $1,200,000 - $300,000
= $1,200,000
Expected value (Investment 3):
E(X) = ($3,000,000 × 0.40) + ($0 × 0.50) + (-$1,000,000 × 0.10)
= $1,200,000 + $0 - $100,000
= $1,100,000
c. Investment with the highest expected return:
The investment with the highest expected return is Investment 2 (the advertising firm) with an expected value of $1,200,000.
d. Safest investment:
The safest investment is Investment 3 (the chemical company) because it has the highest probability (50%) of not incurring any loss (no profit, but no loss either).
e. Riskiest investment:
The riskiest investment is Investment 1 (the social media company) because it has a 50% chance of losing the entire $1,000,000 investment, which is the highest probability of loss among the three investments.
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I WILL GIVE U BRAINLYEST!! PLSS HELP!
The graph below represents the number of siblings each student in a class has.
what was the mean number of siblings?
The mean number of students in the class is 2.4 siblings.
What is the mean number of students?Mean is the average of a set of numbers. It is determined by adding the numbers together and dividing it by the total number
Mean = total sum of siblings / number of students
[(0 x 4) + ( 1 x 4) + ( 2 x 2) + ( 3 x 8) + ( 4 x 4) ] / ( 2 + 4 + 2 + 8 + 4)
= 48 / 20 = 2.4 siblings
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PLEASE HELPPPPPPPPPPPPPPPPPPPP
Answer:
(a) 6688 divided by 88 = 76
(b) 312 - 73 = 239
SAT Scores the national average for mathematics on a standardized test in 2011 was 518. Suppose that the distribution of scores was approximately bell- shaped and that the standard deviation was approximately 48. Round your answers to at least one decimal place as needed.
The national average for mathematics on a standardized test in 2011 was 518, with a standard deviation of approximately 48.
In statistics, the bell-shaped distribution is known as the normal distribution or the Gaussian distribution. It is characterized by its symmetry and the majority of the data falling within a certain range.
The national average score of 518 represents the central tendency of the distribution. This means that a large number of students scored around this average score.
The standard deviation of approximately 48 measures the variability or spread of the scores. It indicates how much the scores deviate from the average. In a normal distribution, about 68% of the data falls within one standard deviation of the mean.
By knowing the average score and the standard deviation, we can determine the proportion of students who scored above or below a certain score, as well as calculate percentiles and compare individual scores to the national average.
Understanding the characteristics of the distribution, such as the average and standard deviation, helps in interpreting and analyzing the scores, making meaningful comparisons, and identifying students' performance relative to the national average.
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x-y=3
work out the value of 5(x-y)
work out the value of 2x-2y
k
work out the value of y-x
If x - y = 3
Work out the value of 5(x - y)
Answer:-x - y = 3 ( Given )
[tex] \therefore [/tex] 5(x - y) = 5 × 3 = 15 [ as x - y = 3 ]
_____________________________________
Question:-If x - y = 3
Work out the value of 2x - 2y
Answer:-x - y = 3 ( Given )
[tex] \therefore [/tex] 2x - 2y = 2(x - y) = 2 × 3 = 6 [ as x - y = 3 ]
_____________________________________
Question:-If x - y = 3
Work out the value of y - x
Answer:-x - y = 3 ( Given )
[tex] \therefore [/tex] y - x = -3 [ as x - y = 3 ]
_____________________________________
Answer:
1
Step-by-step explanation:
Please help me if you want brianleist! :(
Answer:
2ft
Step-by-step explanation:
16^3 ft
4 * 2=8
16/8 =2
Answer:
2 ft
Step-by-step explanation:
V = lwh
16 = 4(2)w
16 = 8w
w = 2 ft
I don’t understand this
Answer:
It is plugging it the 36pye
Step-by-step explanation:
h = 36pye
what it wants you to do is plug that into all the numbers
so it be
2 x 36pye (you get it for the next one)
for the fraction ones it would
be divding 36pye by the number on the bottom
For a random sample of 60 overweight men, the mean of the number of pounds that they were overweight was 32. The standard deviation of the population is 3.9 pounds.The best point estimate of the mean is pounds.
The most accurate estimate of the population mean is 32 pounds, based on the sample data.
The best point estimate of the mean can be obtained by using the sample mean as an estimate for the population mean.
Given that the sample mean of the number of pounds that the 60 overweight men were overweight is 32, the best point estimate of the mean is also 32 pounds.
Therefore, the best point estimate of the mean is 32 pounds.
Mean: The term "mean" refers to a measure of central tendency. It is often referred to as the average of a set of numbers. The mean is calculated by adding up all the values in the set and dividing the sum by the total number of values.
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I am the number that is 5,000 greater than the smallest number u can make using six of the digits what number am I?——————————————
Only can use 1 8 3 4 9 6 2 7 I think..
12,351,789
ignore this ------
12346789
+ 5000
----------------
12351789
Use convolution notation with * and set up the integral to write the final answer of the following initial value ODE. There is no need to evaluate the integral. x" - 8x' + 12x = f(t)
The equation in integral form by taking the inverse Laplace transform: x(t) = L^-1((s^2 - 9s + 20)X(s)) + L^-1(F(s) + sx(0) + x'(0) - 8x(0)), where L^-1 represents the inverse Laplace transform.
To express the given initial value ordinary differential equation (ODE) using convolution notation with *, we can rewrite it as:
(x'' - 8x' + 12x) = f(t)
Taking the Laplace transform of both sides, we have:
s^2X(s) - sx(0) - x'(0) - 8(sX(s) - x(0)) + 12X(s) = F(s)
where X(s) is the Laplace transform of x(t), x'(0) is the initial condition of the derivative of x(t), x(0) is the initial condition of x(t), and F(s) is the Laplace transform of f(t).
Simplifying the equation, we get:
(s^2 - 8s + 12)X(s) - sx(0) - x'(0) + 8x(0) = F(s)
Now, let's express the left-hand side of the equation using convolution notation. Using the property that the Laplace transform of the derivative of a function f(t) is sF(s) - f(0), we can rewrite the equation as:
((s^2 - 8s + 12) - s + 8)X(s) = F(s) + sx(0) + x'(0) - 8x(0)
Simplifying further, we have:
(s^2 - 9s + 20)X(s) = F(s) + sx(0) + x'(0) - 8x(0)
Finally, we can express the equation in integral form by taking the inverse Laplace transform:
x(t) = L^-1((s^2 - 9s + 20)X(s)) + L^-1(F(s) + sx(0) + x'(0) - 8x(0))
where L^-1 represents the inverse Laplace transform.
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Which expression has a solution of 6, if r = 4?
1. r + 2
2. 4 - r
3. 10 + r
4. r - 10
Answer:
1.
Step-by-step explanation:
1. 4 + 2 = 6
2. 4 - 4 = 0
3. 10 + 4 = 14
4. 4 - 10 = -6
number 1 is the right answer
Answer:
1.
Step-by-step explanation:
can you help me solve this?
6 ÷ 2(1+2) = ?
Answer:
9
Step-by-step explanation:
it just is
HELPPPP
Diane draws an obtuse, isosceles triangle with two of the angles measuring 25° each.
What is the measure of the obtuse angle in her triangle?
Answer:
130⁰. unsure. angle sum, 25+25+x =180, so x=180-25-25
Roxie plans on purchasing a new desktop computer for $1250. Which loan description would result in the smallest amount of interest she would have to pay?
12 months at 6.25% annual simple interest rate
18 months at 6.75% annual simple interest rate
24 months at 6.5% annual simple interest rate
30 months at 6.00% annual simple interest rate
Answer:
12 months at 6.25%
Step-by-step explanation:
You deposit $1250 into a bank account paying 6.25% simple interest per month. You left the money in for 12 months. Find the interest earned and the amount at the end of those 12 months?
Result:
The interest is $937.5 and the amount is $2187.5.
Explanation:
STEP 1: Convert interest rate of 6.25% per month into rate per year.
STEP 2: Convert 12 months into years.
STEP 3: Find an interest by using the formula , where I is interest, P is total principal, i is rate of interest per year, and t is total time in years.
In this examplee P = $1250, i = 75% and t = 1 years, so
STEP 4: Find an amount by using the formula .
Since P = $1250 and I = $937.5 we have
An airplane is preparing to land at an airport. It is 42,000 feet above the ground and is descending at the rate of 3,300 feet per minute. At the same airport, another airplane is taking off and will ascend at the rate of 2,700 feet per minute. When will the two airplanes be at the same altitude and what will that altitude be?
Answer:
7 minutes
Step-by-step explanation:
From the question :
Descent = ascent
Initial height * descent rate = initial position * ascent rate
Plane on ground is at an initial position or height of 0
42000 - 3300t = 0 + 2700t
Where, t = time
-3300t - 2700t = 0 - 42000
-6000t = - 42000
t = 42000 / 6000
t = 7 minutes
The Willis Tower In Chicago is 1,451 FEET tall. The Transamerica Pyramid is San Francisco is 10,236 INCHES tall. How do these two compare?
Answer:
Willis Towers is 1.7 times bigger than the Transamerica pyramid
Step-by-step explanation:
The Willis Tower In Chicago is 1,451 FEET tall. The Transamerica Pyramid is San Francisco is 10,236 INCHES tall. How do these two compare?
Note that
1 foot = 12 inches
We convert the height of willis tower to inches
1 foot = 12 inches.
1,451 feet = x inches
Cross Multiply
x = 1451 × 12 inches
x = 17412 inches
Comparing the two buildings
Willis Tower : Transamerica pyramid
1,7412 inches : 10,236 Inches
= 1.7010550996 : 1
Therefore,
Willis Towers is 1.7 times bigger than the Transamerica pyramid
The base and the height of a triangle are multiplied by 5/4. Which of the following describes the
effect of this change on the perimeter?
Answer:
The option that describe the effect of the change is;
The perimeter is multiplied by 5/4Step-by-step explanation:
The parameters from the question are;
The (scale) factor by which the base and the height of the triangle are multiplied = 5/4
By the constant proportion of their sides, the triangle before and the triangle obtained after the multiplication are similar
Let 'a' and 'b' represent the length of the base and the height of the triangle respectively, we have;
The area of the triangle, A₁ = 1/2 × a × b = a·b/2
With the application of the scale factor of 5/4, we have;
The area of the scaled triangle, A₂ = 1/2 × (5/4) × a × (5/4) × b = (5/4)² × a·b/2
Therefore, the scale factor of the area = (5/4)²
The scale factor of the perimeter = √(The scale facto of area)
∴ The scale factor of the perimeter = √(5/4)² = (5/4)
The scale factor of the perimeter = (5/4)
Therefore, the perimeter of the scaled triangle is obtained by multiplying the perimeter of the initial triangle by (5/4).
Answer:
The perimeter is multiplied by 5/4.
Step-by-step explanation:
3 7 of the total computer files were infected by a virus. A engineer later managed to restore 2 15 of the infected files. What fraction of the total files were restored?
Answer:
2/35
Step-by-step explanation:
[tex]\frac{3}{7}[/tex] × [tex]\frac{2}{15}[/tex]
[tex]\frac{1}{7}[/tex] x [tex]\frac{2}{5}[/tex]
= 2/35
HELP ME PLEASE! its very hard and i need it for tonight!!
Answer:
288 cm
Step-by-step explanation:
The formula to solve this polygon is: area = 1/2 x perimeter x apothem
To find the perimeter all you have to is find the sum of all sides together: 12+12+6+6+6+6= 48
Then the Apothem is, the "segment that joins the polygon's center to the midpoint of any side that is perpendicular to that side." To find this you find the point from the middle to the edge which is 12cm.
Then you plug in this information into the polygon. 1/2 x 48 x 12= 288!
The polygon is 288 cm!
Hope this helps! :) Please let me know if it does, and mark as brainliest!