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2 years ago

Find the perimeter of the figure to the nearest hundredth.

Mathematics

1 answer:

bekas [8.4K]2 years ago

8 0

Answer:

38.56

Step-by-step explanation:

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Suppose that W1, W2, and W3 are independent uniform random variables with the following distributions: Wi ~ Uni(0,10*i). What is

nadya68 [22]

I'll leave the computation via R to you. The $W_i$ are distributed uniformly on the intervals $[0,10i]$ , so that

$f_{W_i}(w)=\begin{cases}\dfrac1{10i}&\text{for }0\le w\le10i\\\\0&\text{otherwise}\end{cases}$

each with mean/expectation

$E[W_i]=\displaystyle\int_{-\infty}^\infty wf_{W_i}(w)\,\mathrm dw=\int_0^{10i}\frac w{10i}\,\mathrm dw=5i$

and variance

$\mathrm{Var}[W_i]=E[(W_i-E[W_i])^2]=E[{W_i}^2]-E[W_i]^2$

We have

$E[{W_i}^2]=\displaystyle\int_{-\infty}^\infty w^2f_{W_i}(w)\,\mathrm dw=\int_0^{10i}\frac{w^2}{10i}\,\mathrm dw=\frac{100i^2}3$

so that

$\mathrm{Var}[W_i]=\dfrac{25i^2}3$

Now,

$E[W_1+W_2+W_3]=E[W_1]+E[W_2]+E[W_3]=5+10+15=30$

and

$\mathrm{Var}[W_1+W_2+W_3]=E\left[\big((W_1+W_2+W_3)-E[W_1+W_2+W_3]\big)^2\right]$

$\mathrm{Var}[W_1+W_2+W_3]=E[(W_1+W_2+W_3)^2]-E[W_1+W_2+W_3]^2$

We have

$(W_1+W_2+W_3)^2={W_1}^2+{W_2}^2+{W_3}^2+2(W_1W_2+W_1W_3+W_2W_3)$

$E[(W_1+W_2+W_3)^2]$

$=E[{W_1}^2]+E[{W_2}^2]+E[{W_3}^2]+2(E[W_1]E[W_2]+E[W_1]E[W_3]+E[W_2]E[W_3])$

because $W_i$ and $W_j$ are independent when $i\neq j$ , and so

$E[(W_1+W_2+W_3)^2]=\dfrac{100}3+\dfrac{400}3+300+2(50+75+150)=\dfrac{3050}3$

giving a variance of

$\mathrm{Var}[W_1+W_2+W_3]=\dfrac{3050}3-30^2=\dfrac{350}3$

and so the standard deviation is $\sqrt{\dfrac{350}3}\approx\boxed{116.67}$

# # #

A faster way, assuming you know the variance of a linear combination of independent random variables, is to compute

$\mathrm{Var}[W_1+W_2+W_3]$

$=\mathrm{Var}[W_1]+\mathrm{Var}[W_2]+\mathrm{Var}[W_3]+2(\mathrm{Cov}[W_1,W_2]+\mathrm{Cov}[W_1,W_3]+\mathrm{Cov}[W_2,W_3])$

and since the $W_i$ are independent, each covariance is 0. Then

$\mathrm{Var}[W_1+W_2+W_3]=\mathrm{Var}[W_1]+\mathrm{Var}[W_2]+\mathrm{Var}[W_3]$

$\mathrm{Var}[W_1+W_2+W_3]=\dfrac{25}3+\dfrac{100}3+75=\dfrac{350}3$

and take the square root to get the standard deviation.

8 0

3 years ago

What is the solution set for x2+25=0

Masja [62]

Step-by-step explanation:

${x}^{2} + 25 = 0 \\ \therefore {x}^{2} = - 25 \\ \therefore {x} = \sqrt{ - 25} \\ \therefore {x} = \pm\sqrt{ - 1 \times 25} \\ \therefore {x} = \pm \sqrt{ 25} \times \sqrt{ - 1} \\ \therefore {x} = \pm5 \: i \\ \therefore {x} = \{ - 5i, \: \: 5i \} \: \\ is \: the \: solution \: set.$

7 0

3 years ago

*HELP PLEASE* <br> Will get BRAINLIEST answer!!!!

photoshop1234 [79]

When solving these proportions we just remember when moving a number from one side to the other if it started in the numerator it ends up in the denominator and vice versa.

I'll do it in two steps here for teaching purposes; it's not too hard to go directly to the answer.

$\dfrac{13}{7} = \dfrac{10}{v}$

$13 v = 7(10)$

$v= \dfrac{7 \cdot 10 }{13} = \dfrac{70}{13} \approx 5.4$

5 0

3 years ago

Read 2 more answers

What is the 5-digit code?

kvv77 [185]

9514 1404 393

Answer:

4 2 6 1 7 or 1 2 4 3 7

Step-by-step explanation:

4 are correct of 1,3,4,6,7

3 are correct of 0,2,3,6,7

1 is correct of 0,3,6,8,7 -- so not both 3 and 6, meaning 1, 4, 7 are correct

Correct digits so far are 1, 4, 7 and one of {3, 6}. Line 2 tells another is 0 or 2; line 3 tells it is not 0. This adds 2 to the list of correct digits.

This makes the correct digits 1, 2, {3, 6}, 4, 7. We don't know whether the last digit is 3 or 6.

Looking at digits correctly placed, line 2 tells us the code is either ...

_ 2 6 _ 7 or _ 2 _ 3 7

Then line 1 fills in those blanks as ...

4 2 6 1 7 or 1 2 4 3 7

Either of these codes agrees with all of the clues.

3 0

2 years ago

Use the circular mirror shown

aliina [53]

Multiply 15 x 3.14. You'll get 47.1. Thats the area

3 0

2 years ago