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mylen [45]
3 years ago
11

A surveyor wishes to lay out a square region with each side having length L. However, because of measurement error, he instead l

ays out a rectangle in which the north-south sides both have length X and the east-west sides both have length Y. Suppose that X and Y are independent and that each is uniformly distributed on the interval [L − A, L + A] (where 0 < A < L). What is the expected area of the resulting rectangle?
Mathematics
1 answer:
RoseWind [281]3 years ago
4 0

Step-by-step explanation:

Area, A = Length,x × Breadth,y

A=xy

When x and y are independent, E(xy) = E(x)E(y)

As x and y have the same distribution, U[L-A,L+A], they have the same mean.

We could argue by symmetry that E(x) = L and E(y) + L, also.

We can also reason this from the fact that, if X ~ U[L-A, L+A], f(x) = 1/(2A) from L-A to L+A

Therefore

E(x)= \int\limits {f(x)} \, dx \\\\=\int\limits^{(L+A)}_{(L-A)} {\frac{1}{2A}x } \, dx

=\int\limits^{(L+A)}_{(L-A)} {\frac{1}{2A}x } \, dx \\\\=[\frac{1}{4A}x^2 ]\limits^{(L+A)}_{(L-A)}

=1/(4A)(L+A)2 - 1/(4A)(L-A)2

= 1/(4A)(L2 + 2AL + A2) - 1/(4A)(L2 - 2AL + A2)

=1/(4A)(2AL+2AL)

= 1/(4A)(4AL)

= L

Thus, E(xy) = E(x)E(y) = L×L = L²

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just olya [345]

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Answer: Lets say that each tower can be build with 1 block, then you can build 257 towers

Explanation:

I hope this helped!

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8 0
2 years ago
Can someone please tell me the aswer​
Artist 52 [7]

Answer:

2x-2+3x

Step-by-step explanation:

2x-2+3x

combine like terms (2x + 3x = 5x)

So 2x-2+3x = 5x-2

3 0
3 years ago
Instructions
Naya [18.7K]

Answer:

yes

Step-by-step explanation:

youre trying to find when -1/4x + 3/2 = -x+ 3

so if you set it up like that and then solve for x you get 2

then, you know that 2 is your x value so just plug in x into one of the equations to get the y value

(i used -x+3 bc its easier)

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also heres the graph

5 0
3 years ago
What is the common difference between the elements of the arithmetic sequence below?
Tanya [424]
<h3> - - - - - - - - - - - - - ~<u>Hello There</u>!~ - - - - - - - - - - - - - </h3>

➷ -22.5 - (-18) = -4.5

-27 - (-22.5) = -4.5

The common difference is 4.5

➶Hope This Helps You!

➶Good Luck :)

➶Have A Great Day ^-^

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7 0
3 years ago
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Firlakuza [10]

Answer: x=−2

Step-by-step explanation:

Let's solve your equation step-by-step.

4(8−x)−32=98−5(3x+24)

Step 1: Simplify both sides of the equation.

4(8−x)−32=98−5(3x+24)

(4)(8)+(4)(−x)+−32=98+(−5)(3x)+(−5)(24)(Distribute)

32+−4x+−32=98+−15x+−120

(−4x)+(32+−32)=(−15x)+(98+−120)(Combine Like Terms)

−4x=−15x+−22

−4x=−15x−22

Step 2: Add 15x to both sides.

−4x+15x=−15x−22+15x

11x=−22

Step 3: Divide both sides by 11.

11x /11 = −22 /11

x=−2

8 0
3 years ago
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