Answer:
∠1 = 116 ° , ∠2 = 32° , ∠3 = 116 ° and ∠4 = 32°
Step-by-step explanation:
∠2 = 32° (The diagonals of a rhombus bisect pairs of opposite angles)
Opposite sides of a rhombus are parallel ,so
∠2 = ∠4 (Alternate interior angles )
∠4 = 32°
32° + ∠4 + ∠3 = 180° (angle sum property of a triangle)
64° + ∠3 = 180°
∠3 = 180 - 64
∠3 = 116°
∠3 =∠1 (in a rhombus opposite angles are equal )
∠1 = 116°
{1,4,5,6,7,8} {7} find the intersection
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Answer:
{7}
Step-by-step explanation:
The only element common to both sets is 7. The intersection is {7}.
What type of object is pictured below?
O A. Point
O B. Ray
C. Segment
D. Line
Answer:
It is a ray because there are two points with a line passing through them which is extenging on one side but not on the other.
Evaluate the expression when a=-7 and y=3 3y-a
Answer:
3y-a
3.3-7
9-7
2
Step-by-step explanation:
first we have to do multiply by replacing the value of y and the subtract by using the value of a.
Hope this will be helpful for you
Solve the following 20!/17!
Answer:
6840
Step-by-step explanation:
20 ! = 20*19*18*17*.......1
17 =17*16*15*.....1
20!
-----
17!
20*19*18*17*.......1
---------------------------
17*16*15*.....1
Canceling like terms
20*19*18
------------
1
6840
Answer:
[tex]20!/17![/tex]
[tex]\frac{20!}{17!}=20\cdot \:19\cdot \:18[/tex]
[tex]20\cdot \:19\cdot \:18=6840[/tex]
[tex]OAmalOHopeO[/tex]
what is the quotient 3/8 ÷5/12
Answer:
9/10
Step-by-step explanation:
3/8 ÷5/12
Copy dot flip
3/8 * 12/5
Rewriting
3/5 * 12/8
3/5 * 3/2
9/10
find the total cost of 4 flats of plants at $12 each
An online retailer processed 60 merchandise return requests from Wyoming and Montana in a day. Return requests from Montana were 5 times as many as those from Wyoming. How many return requests were from Wyoming?
A) 10
B) 25
C) 15
D) 20
E) 5
The number of merchandise return requests for Wyoming is equal to 10.
Let merchandise return requests from Wyoming be W.
Let merchandise return requests from Montana be M.
Given the following data;
Total number of merchandise return requests for W and M = 60Translating the word problem into an algebraic equation, we have;
[tex]W + M = 60[/tex] .....equation 1
[tex]M = 5W[/tex] ......equation 2
To find the value of W, we would solve the system of equations by using the substitution method;
Substituting eqn 2 into eqn 1, we have;
[tex]W + 5W = 60\\\\6W = 60\\\\W = \frac{60}{6}[/tex]
Wyoming, W = 10 merchandise return requests.
Therefore, the number of merchandise return requests for Wyoming is equal to 10.
Find more information: https://brainly.com/question/8409825
a site is 90m long and 45m wide what is the area of the site
Answer:4050m^2
Step-by-step explanation:
Assuming that the site is rectangular
Area= l x W
90 X 45
=4050
Answer:
1050m
How I got the answer: I assume the site is a rectangle so I'll use the formula for finding the area of a rectangle. Using the formula length times width I solved this problem. The length is 90m. The width is 45. When a question says x meters long it means the length is x meters. In other words long = length wide = width in a math problem. 90 times 40 is 1050m
Suppose the daily customer volume at a call center has a normal distribution with mean 5,500 and standard deviation 1,000. What is the probability that the call center will get between 4,800 and 5,000 calls in a day
Answer:
0.0665 = 6.65% probability that the call center will get between 4,800 and 5,000 calls in a day.
Step-by-step explanation:
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Mean 5,500 and standard deviation 1,000.
This means that [tex]\mu = 5500, \sigma = 1000[/tex]
What is the probability that the call center will get between 4,800 and 5,000 calls in a day?
This is the p-value of Z when X = 5000 subtracted by the p-value of Z when X = 4800. So
X = 5000
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{5000 - 5500}{1000}[/tex]
[tex]Z = -0.5[/tex]
[tex]Z = -0.5[/tex] has a p-value of 0.3085.
X = 4800
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{4800 - 5500}{1000}[/tex]
[tex]Z = -0.7[/tex]
[tex]Z = -0.7[/tex] has a p-value of 0.2420.
0.3085 - 0.2420 = 0.0665
0.0665 = 6.65% probability that the call center will get between 4,800 and 5,000 calls in a day.
Determine whether the following problem involves a permutation or combination. (It is not necessary to solve the problem.)
How many different -letter passwords can be formed from the letters S, T, U, W, X, Y, and Z if no repetition of letters is allowed?
The problem involves (combination or permiation) because the (order or number) of letters selected (does or does not) matter.
Answer:
Step-by-step explanation:
The order matters
stuwxyz is different than zyxwuts
You have 7 letters
The number of permutations is 7! which is 7*6*5*4*3*2*1 = 5040
A company manufactures televisions. The average weight of the televisions is 5 pounds with a standard deviation of 0.1 pound. Assuming that the weights are normally distributed, what is the weight that separates the bottom 10% of weights from the top 90%?
Answer:
[tex]0.2564\text{ pounds}[/tex]
Step-by-step explanation:
The 90th percentile of a normally distributed curve occurs at 1.282 standard deviations. Similarly, the 10th percentile of a normally distributed curve occurs at -1.282 standard deviations.
To find the [tex]X[/tex] percentile for the television weights, use the formula:
[tex]X=\mu +k\sigma[/tex], where [tex]\mu[/tex] is the average of the set, [tex]k[/tex] is some constant relevant to the percentile you're finding, and [tex]\sigma[/tex] is one standard deviation.
As I mentioned previously, 90th percentile occurs at 1.282 standard deviations. The average of the set and one standard deviation is already given. Substitute [tex]\mu=5[/tex], [tex]k=1.282[/tex], and [tex]\sigma=0.1[/tex]:
[tex]X=5+(1.282)(0.1)=5.1282[/tex]
Therefore, the 90th percentile weight is 5.1282 pounds.
Repeat the process for calculating the 10th percentile weight:
[tex]X=5+(-1.282)(0.1)=4.8718[/tex]
The difference between these two weights is [tex]5.1282-4.8718=\boxed{0.2564\text{ pounds}}[/tex].
Answer:
0.2564
Step-by-step explanation:
90th percentile, we use the formula X=μ + Zσ,
Where u = mean and sigma = standard deviation and Z = 1.282
The mean is 5 and sigma = .1
X = 5+1.282(.1)
X = 5.1282
10th percentile, we use the formula X=μ + Zσ,
Where u = mean and sigma = standard deviation and Z = -1.282
The mean is 5 and sigma = .1
X = 5-1.282(.1)
X = 4.8718
The difference is
5.1282 - 4.8718
0.2564
plzz help with this question
Answer: 51 liters of fuel are required
Step by step: start by seeing how many times 476 can go into 1428
(1428/476=3)
Then take your sum of that and multiply it by 17 since that’s the number that correlates with 476
(17x3=51) therefore your answer is 51 liters
Samples of rejuvenated mitochondria are mutated (defective) in 3% of cases. Suppose 13 samples are studied, and they can be considered to be independent for mutation. Determine the following probabilities.
(a) No samples are mutated.
(b) At most one sample is mutated.
(c) More than half the samples are mutated.
Round your answers to two decimal places (e.g. 98.76).
Answer:
a) 0.6730 = 67.30% probability that no samples are mutated.
b) 0.9436 = 94.36% probability that at most one sample is mutated.
c) 0% probability that more than half the samples are mutated.
Step-by-step explanation:
For each sample, there are only two possible outcomes. Either it is mutated, or it is not. The probability of a sample being mutated is independent of any other sample, which means that the binomial probability distribution is used to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
Samples of rejuvenated mitochondria are mutated (defective) in 3% of cases.
This means that [tex]p = 0.03[/tex]
13 samples are studied
This means that [tex]n = 13[/tex]
(a) No samples are mutated.
This is P(X = 0). So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{13,0}.(0.03)^{0}.(0.97)^{13} = 0.6730[/tex]
0.6730 = 67.30% probability that no samples are mutated.
(b) At most one sample is mutated.
This is:
[tex]P(X \leq 1) = P(X = 0) + P(X = 1)[/tex]
So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{13,0}.(0.03)^{0}.(0.97)^{13} = 0.6730[/tex]
[tex]P(X = 1) = C_{13,1}.(0.03)^{1}.(0.97)^{12} = 0.2706[/tex]
Then
[tex]P(X \leq 1) = P(X = 0) + P(X = 1) = 0.6730 + 0.2706 = 0.9436[/tex]
0.9436 = 94.36% probability that at most one sample is mutated.
(c) More than half the samples are mutated.
This is:
[tex]P(X > 6.5) = P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10) + P(X = 11) + P(X = 12) + P(X = 13)[/tex]
Then
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 7) = C_{13,7}.(0.03)^{7}.(0.97)^{6} \approx 0[/tex]
Using two decimal digits precision, all will be 0. So
0% probability that more than half the samples are mutated.
-
An ice – cream cone is first filled to
rd of its capacity with strawberry and
3
then the remaining part of the cone
is equally filled with vanilla,
strawberry and chocolate. What
fraction of ice-cream filling is
strawberry?
Answer:
1/3
Step-by-step explanation:
1/3 is the correct answer as there are three flavours and are equally filled which will result to 1/3 of each flavour.
Hope it helps you. Have a good day
The delivery man checks his route for deliveries.
The map has a scale of 1:250,000.
The distance between the bakery and his last delivery is 35 cm
What is the actual distance?
km.
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Answer:
87.5 km
Step-by-step explanation:
Actual distance is 250000×35 cm = 87.5×10^5 cm = 87.5 km
_____
There are 100 cm in 1 m, and 1000 m in 1 km, so 100,000 cm = 10^5 cm in 1 km
A study on the latest fad diet claimed that the amounts of weight lost by all people on this diet had a mean of 21.9 pounds and a standard deviation of 5.3 pounds.
Step 2 of 2 :
If a sampling distribution is created using samples of the amounts of weight lost by 78 people on this diet, what would be the standard deviation of the sampling distribution of sample means? Round to two decimal places, if necessary.
Answer:
The standard deviation of the sampling distribution of sample means would be of 0.7 pounds.
Step-by-step explanation:
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Mean of 21.9 pounds and a standard deviation of 5.3 pounds.
This means that [tex]\mu = 21.9, \sigma = 5.3[/tex]
If a sampling distribution is created using samples of the amounts of weight lost by 78 people on this diet, what would be the standard deviation of the sampling distribution of sample means?
This is s when n = 78, so:
[tex]s = \frac{5.3}{\sqrt{78}} = 0.6[/tex]
The standard deviation of the sampling distribution of sample means would be of 0.7 pounds.
Can somebody help me to solve this?
Answer:
B
Step-by-step explanation:
Given
[tex]\sqrt{ab}[/tex] = [tex]\sqrt{bc}[/tex] ( square both sides )
ab = bc ( divide both sides by b ) , then
a = c
Given
[tex]\sqrt{ac}[/tex] = [tex]\sqrt{4c^4}[/tex] ( square both sides )
ac = 4[tex]c^{4}[/tex] ( but a = c) , so
4[tex]c^{4}[/tex] = c² ( subtract c² from both sides )
4[tex]c^{4}[/tex] - c² = 0 ← factor out c² from each term on the left side
c²(4c² - 1) = 0 ← 4c² - 1 is a difference of squares
c²(2c - 1)(2c + 1) = 0
Equate each factor to zero and solve for x
c² = 0 ⇒ c = 0
2c - 1 = 0 ⇒ 2c = 1 ⇒ c = [tex]\frac{1}{2}[/tex]
2c + 1 = 0 ⇒ 2c = - 1 ⇒ c = - [tex]\frac{1}{2}[/tex]
But c > 0 , then c = [tex]\frac{1}{2}[/tex] → B
Use the figure to find x.
Answer:
[tex] x = 8.57[/tex]
Step-by-step explanation:
Here two triangles are given to us , which are attached to each other . Here we can use the concept of Trigonometry to find out the value of x. The angles of the triangle are 60° and 45° . Let the common side be p .
Step 1: Use the ratio of tan in upper triangle
[tex]\rm\implies tan60^o = \dfrac{perpendicular}{base} [/tex]
Substitute the respective values ,
[tex]\rm\implies \sqrt3=\dfrac{p}{7} [/tex]
Cross multiply ,
[tex]\rm\implies p = 7\sqrt3 [/tex]
Step 2: Use the ratio of cos in lower triangle
[tex]\rm\implies cos45^o = \dfrac{base}{hypontenuse} [/tex]
Substitute the respective values ,
[tex]\rm\implies \dfrac{1}{\sqrt2}=\dfrac{x}{7\sqrt3} [/tex]
Cross multiply ,
[tex]\rm\implies x= \dfrac{7\sqrt3}{\sqrt2} [/tex]
Put the approximate values of √2 and √3
[tex]\rm\implies x= \dfrac{7\times 1.732}{1.414} [/tex]
This equals to ,
[tex]\rm\implies \boxed{\blue{\rm \quad x = 8.57\quad}} [/tex]
Hence the value of x is 8.57 .
Answer:
The value of x is [tex]\frac{7\sqrt{6}}{2}[/tex]
Solution given:
AB=7
BD=x
<BAC=60°
<DBC=45°
In right angled triangle ABC
Tan 60°=opposite/adjacent
Tan 60°=BC/AB
Substitute value
[tex]\sqrt{3}[/tex]=[tex]\frac{BC}{7}[/tex]
BC=[tex]7\sqrt{3}[/tex]
again
againIn right angled triangle BCD
againIn right angled triangle BCDUsing Cos angle
Cos 45=adjacent/hypotenuse
Cos45°=BD/BC
Substituting value
[tex]\frac{\sqrt{2}}{2}=\frac{x}{7\sqrt{3}}[/tex]
Doing criss cross multiplication
[tex]\frac{\sqrt{2}}{2}*7\sqrt{3}=x[/tex]
x=[tex]\frac{7\sqrt{6}}{2}[/tex]
Which of the following is the most accurate statement about statistics?
a) We can absolutely be 100% certain in accurately generalizing the characteristics of entire population based on the sample data
b) By analyzing data, we may be able to identify connections and relationships in our data
c) We can explore in the midst of variation to better understand our data
d) limited data or experience likely generates less confidence
e) Non of the above
Answer:
b) By analyzing data, we may be able to identify connections and relationships in our data.
Step-by-step explanation:
In statistics decisions are based on probability sampling distributions. As statics is collection and analysis of data along with its interpretation and presentation.i need the answer no explanation
Answer:
the answer is option D because it cant be division or multiplication and minus does not work
Answer:
log 1/9 * log k
Step-by-step explanation:
[tex]\frac{1}{9} /k[/tex] = 1/9 * k/1 = 1/9 * k
Point P is plotted on the coordinate grid. If point S is 12 units to the left of point P, what are the coordinates of point S? On a coordinate grid from negative 12 to positive 12 in increments of 2, a point P is plotted at the ordered pair 6, negative 4. (6, −16) (−6, −16) (−6, −4) (6, 4)
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Answer:
(−6, −4)
Step-by-step explanation:
Translating a point 12 units left subtracts 12 from its x-coordinate.
P(6, -4) +(-12, 0) = S(-6, -4)
Is this true or false ??
=============================================================
Explanation:
We'll use these two properties of integrals [tex]\displaystyle \text{If f(x) is an even function, then } \int_{-a}^{a}f(x)dx = 2\int_{0}^{a}f(x)dx[/tex]
[tex]\displaystyle \text{If f(x) is an odd function, then } \int_{-a}^{a}f(x)dx = 0[/tex]
These properties are valid simply because of the function's symmetry. For even functions, we have vertical axis symmetry about x = 0; while odd functions have symmetry about the origin.
------------------------
Here's how the steps could look
[tex]\displaystyle \int_{-7}^{7}(ax^8+bx+c)dx=\int_{-7}^{7}((ax^8+c)+bx)dx\\\\\\\displaystyle \int_{-7}^{7}(ax^8+bx+c)dx=\int_{-7}^{7}(ax^8+c)dx+\int_{-7}^{7}(bx)dx\\\\\\\displaystyle \int_{-7}^{7}(ax^8+bx+c)dx=\left(2\int_{0}^{7}(ax^8+c)dx\right)+(0)\\\\\\\displaystyle \int_{-7}^{7}(ax^8+bx+c)dx=2\int_{0}^{7}(ax^8+c)dx\\\\\\[/tex]
Therefore, the given statement is true. The values of a,b,c don't matter. You could replace those '7's with any real number you want and still end up with a true statement.
We can see that ax^8+c is always even, while bx is always odd.
------------------------
Side note:
For the second step, I used the idea that [tex]\int(f(x)+g(x))dx=\int f(x)dx+\int g(x)dx\\\\[/tex]
which allows us to break up a sum into smaller integrals.
which relation is a function?
Answer:
Choice A.
Step-by-step explanation:
Every other choice has multiple of the same x-values that have different corresponding y-values.
Find x and explain how you found x
Answer:
x=60
Step-by-step explanation:
There are different ways to find x but this is what I found easiest.
To solve first note that AOD and CFB are vertical angles; this means that they are congruent. AOD consists of two angles with the measurements of 90 and x. CFB consists of two angles with the measurements of 30 and 2x. So, to find x set add the adjacent angles and set them equal to the other pair of angles. The equation would be [tex]90+x=30+2x[/tex]. First, subtract x from both sides; this makes the equation [tex]90=30+x[/tex]. Then, subtract 30 from both sides. This gives the final answer, x=60.
1289 +(-1236) + (2434) =
0 -1431
O 2345
O 2487
0 -1956
Answer:
This answer is 2487
which will be the third one
Hope this help
How
many solutions are there to the equation below?
4(x - 5) = 3x + 7
A. One solution
B. No solution
O C. Infinitely many solutions
SUB
Answer:
A one solution
Step-by-step explanation:
4(x - 5) = 3x + 7
Distribute
4x - 20 = 3x+7
Subtract 3x from each side
4x-3x-20 = 3x+7-3x
x -20 = 7
Add 20 to each side
x -20+20 = 7+20
x = 27
There is one solution
Answer:
Step-by-step explanation:
Let's simplify that before we make the decision, shall we? We'll get rid of the parenthesis by distribution and then combine like terms.
4x - 20 = 3x + 7 and combining like terms and getting everything on one side of the equals sign:
1x - 27 = 0. Since that x has a power of 1 on it (linear), that means we have only 1 solution. If that was an x², we would have 2 solutions; if that was an x³, we would have 3 solutions, etc.
WILL GIVE BRAINLIEST!!!
Find the number of all the 2-digit numbers satisfying the following congruences x ≡ 3(mod7), x ≡ 2(mod5).
Answer:
6 total
3 positive 2 digit numbers: 17, 52, 87
3 negative 2 digit numbers: -18, -53,-88
Step-by-step explanation:
We are given
x ≡ 3(mod7), x ≡ 2(mod5) and we want x to be two digits long.
x ≡ 3(mod7) means x-3=7k and
x ≡ 2(mod5) means x-2=5m where k and m are integers.
We need to find an x that satisfies both.
So some multiples of 7 are 7,14,21,28,35,42,49,56,63,70,77,84,91,98
Some multiples or 5 are
5,10 15,20,25,30 35,40,45,45,50,55,60,65,70
Now add 3 to first list for x=7k+3
10,17,24,31,38,45,52,59,66,73,80,87,94,101
Now add 2 to second list for x=5m+2
7,12 17,22,27,32 37,42,47,52,57,62,67,72
We only want to look at 2 digit numbers... just need to expand second list more:
Now add 2 to second list for x=5m+2
7,12,17,22,27,32,37,42,47,52,57,62,67,72,77,82,87,92,97,
That's all we need.
So let's write our lists and see the common numbers in them:
List 1: 10,17,24,31,38,45,52,59,66,73,80,87,94,101
List 2:
7,12,17,22,27,32,37,42,47,52,57,62,67,72,77,82,87,92,97
Common numbers: 17, 52, 87
Considering negative numbers as well:
x=7k+3:
3, -4, -11, -18, -25, -32,-39, -46, -53, -60, -67, -74, -81, -88, -95
x=5m+2:
2,-3,-8,-13,-18,-23,-28,-33,-38,-43,-48,-53,-58,-63,-68,-73,-78,-83,-88,-93,-98
Common 2digit numbers:
-18, -53,-88
D. -2 - (+5)
please help me
this questions lesson name is adding and substracting integers
so if u know this answer please help.
Answer:
-7
Step-by-step explanation:
-2-(+5)
=-2+5
=-7
neg 2 minus pos 5 equal to neg 7
A neg plus a pos is a neg
Construct the confidence interval for the population standard deviation for the given values. Round your answers to one decimal place. n=21 , s=3.3, and c=0.9
Answer:
The correct answer is "[tex]2.633< \sigma < 4.480[/tex]".
Step-by-step explanation:
Given:
n = 21
s = 3.3
c = 0.9
now,
[tex]df = n-1[/tex]
[tex]=20[/tex]
⇒ [tex]x^2_{\frac{\alpha}{2}, n-1 }[/tex] = [tex]x^2_{\frac{0.9}{2}, 21-1 }[/tex]
= [tex]31.410[/tex]
⇒ [tex]x^2_{1-\frac{\alpha}{2}, n-1 }[/tex] = [tex]10.851[/tex]
hence,
The 90% Confidence interval will be:
= [tex]\sqrt{\frac{(n-1)s^2}{x^2_{\frac{\alpha}{2}, n-1 }} } < \sigma < \sqrt{\frac{(n-1)s^2}{x^2_{1-\frac{\alpha}{2}, n-1 }}[/tex]
= [tex]\sqrt{\frac{(21-1)3.3^2}{31.410} } < \sigma < \sqrt{\frac{(21.1)3.3^2}{10.851} }[/tex]
= [tex]\sqrt{\frac{20\times 3.3^2}{31.410} } < \sigma < \sqrt{\frac{20\times 3.3^2}{10.851} }[/tex]
= [tex]2.633< \sigma < 4.480[/tex]
Work out the area of a rectangle with base, b = 36mm and perimeter, P = 94mm.
Answer:
396
Step-by-step explanation:
A = bw
A = 36w
P = 2w + 2b
94 = 2w + 2(36)
94 = 2w + 72
-72 -72
--------------------
22 = 2w
---- ----
2 2
11 = w
A = 36(11)
A = 396
The area of the rectangle will be 396.