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Svetradugi [14.3K]
3 years ago
15

∆ABC ~ ∆WXY. What is the value of x? (show work)

Mathematics
1 answer:
Sphinxa [80]3 years ago
5 0
Set a proportion. They are similar triangles.

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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
2 years ago
If x+y=6 and xy =2find x³+y³(please help me fast with explanation also please) T^T​
Maurinko [17]

Answer: x³+y³=180

Step-by-step explain:                                                                                            let's remember the formula                                                                                 x³+y³=(x+y)(x²-xy+y²) and also  x³+y³=(x+y)³-3xy(x+y)                                              then                                                                                      \displaystyle\boldsymbol{ x^3+y^3=\underbrace{(x+y)^3}_{6}-3\underbrace{xy}_{2}\underbrace{(x+y)}_6}=\\\\6^3-3\cdot 2\cdot 6=216-36=180                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                

6 0
3 years ago
Calculate the values of the expression below 2 ( 3 (5 + 2) -1)<br>​
Otrada [13]

Answer:

= 40

Step-by-step explanation:

2 ( 3 (5 + 2) -1)

= 2 * 20

= 40

7 0
3 years ago
Read 2 more answers
The following diagram shows part of the graph of the function f(x)= -12x + 26 and g(x) = -(1/5) ^ -x + 2 + 3 what are the soluti
Nina [5.8K]
The answer would be D. For you to find the solution you would need to look at the x from the coordinates.
6 0
2 years ago
I need it in a linear equation please i need help
klio [65]

Answer:

Caterer One: C = 55n

Caterer Two: C = 40n + 550

Caterer Three: C = 35n + 800

Step-by-step explanation:

4 0
2 years ago
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