Hey there :) I'm pretty sure that your answer is D) ∠S ≅ <span>∠Y because corresponding angles of similar triangles are congruent.

I think that it is the answer because if you shift your paper around, and look at the angles from different views, you can tell that angles S and Y are congruent, or the same, because of the way that both angles are at the end of the longer sides of both triangles.

So, your answer is D!

~Hope this helped!~</span>

8 0

3 years ago

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There are 10 balls in an urn, numbered from 1 to 10. If 5 balls are selected at random and their numbers are added, what is the

Kisachek [45]

Let $B_i$ denote the value on the $i$ -th drawn ball. We want to find the expectation of $S=B_1+B_2+B_3+B_4+B_5$ , which by linearity of expectation is

$E[S]=E\left[\displaystyle\sum_{i=1}^5B_i\right]=\sum_{i=1}^5E[B_i]$

(which is true regardless of whether the $X_i$ are independent!)

At any point, the value on any drawn ball is uniformly distributed between the integers from 1 to 10, so that each value has a 1/10 probability of getting drawn, i.e.

$P(X_i=x)=\begin{cases}\frac1{10}&\text{for }x\in\{1,2,\ldots,10\}\\0&\text{otherwise}\end{cases}$

and so

$E[X_i]=\displaystyle\sum_{i=1}^{10}x\,P(X_i=x)=\frac1{10}\frac{10(10+1)}2=5.5$

Then the expected value of the total is

$E[S]=5(5.5)=\boxed{27.5}$

8 0

2 years ago