1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
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

You might be interested in
Question 3
matrenka [14]

Answer:

about 5 boxes

Step-by-step explanation:

2 *40/15 Please give brainliest

6 0
2 years ago
Read 2 more answers
Which of the following is a perfect square trinomial?
shutvik [7]

Answer:

A.

Step-by-step explanation:

Take a look at what happens when squaring either of these...

(ax-by)^2=(ax-by)(ax-by)=a^2x^2-2abxy+b^2y^2\\\\(ax+by)^2=(ax+by)(ax+by)=a^2x^2+2abxy+b^2y^2\\

Notice a couple of patterns.

1.  The last term has a positive coefficient.  That rules out answer choices C and D.

2.  The coefficient of the middle term is either +2ab \text{ or } -2ab .  So what are <em>a</em>  and <em>b</em>?  <em>a</em> is the square root of the x^2 term and <em>b</em> is the square root of the y^2 term.

25x^2 \Rightarrow a=5\\\\9y^2 \Rightarrow b=3\\\\ab=15\\\\2ab=30

The middle coefficient needs to be either +30 or -30.  The answer is choice A.

5 0
3 years ago
Please Help!
rosijanka [135]

Answer:

x^2 - 12x..............................

6 0
2 years ago
Write an equation in slope-intercept form of the line.
alexira [117]

Answer:

y=x-3

Step-by-step explanation:

To find slope, use m=y2-y1/x2-x1, using values of x and y from two different points. Once you have found slope, take another point and use the point-slope equation y-y1=m(x-x1) and substitute in slope for m and the point for x1 and y1. Isolate y by subtracting y1 from both sides.

3 0
3 years ago
Need help plzzzzz The first one and the second one plZ
solong [7]

From both sides of the equation, 4 should have been subtracted.

The solution should look like this:

X + 4  =  28

From each side, subtract  4 :

<em>X  =  24</em>

I'd like to demonstrate more steps, but the answer has already popped up, so there aren't any more steps.

4 0
3 years ago
Other questions:
  • Can someone please help me imma die :((((
    14·2 answers
  • HELP WITH MY WHOLE TEST ;-; jensnshsjsjjsjsjsjsjsksksmsknnknksnisi
    7·2 answers
  • ASAP h(t)=-5t^2+5t+10<br><br> Please help me find roots and roots equation
    9·1 answer
  • NEED HELP ASAP!!
    8·1 answer
  • What is the slope of the line in the graph?
    9·1 answer
  • 6. Graph the following line.<br> X=5<br> x-intercept =<br> y-intercept =
    12·1 answer
  • What is the slope of a line parallel to line Y= 3x +2
    5·2 answers
  • Jill sold half of her comic books then bought 16 more, she now has 36. With how many did she begin with? Break it down please
    9·1 answer
  • James bought of a pound of dried cherries and of a pound of dried cranberries. How much dried fruit did he buy? [Write your answ
    5·1 answer
  • Which of these triangles appears notto be congruent to any others shown
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!