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4 years ago

What is the missing angel in the triangle 37,90,

Mathematics

1 answer:

Hatshy [7]4 years ago

6 0

Answer:

The answer is 53

Step-by-step explanation:

We know that all the angles in a triangle add up to 180. So we do 37+90= 127

180-127= 53

Hope I helped!

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A building has n floors numbered 1,2,...,n, plus a ground floor g. at the ground floor, m people get on the elevator together, a

fomenos

Let $X_i$ be the random variable indicating whether the elevator does not stop at floor $i$ , with

$X_i=\begin{cases}1&\text{if the elevator does not stop at floor }i\\0&\text{otherwise}\end{cases}$

Let $Y$ be the random variable representing the number of floors at which the elevator does not stop. Then

$Y=X_1+X_2+\cdots+X_{n-1}+X_n$

We want to find $\mathrm{Var}(Y)$ . By definition,

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

As stated in the question, there is a $\dfrac1n$ probability that any one person will get off at floor $n$ (here, $n$ refers to any of the $n$ total floors, not just the top floor). Then the probability that a person will not get off at floor $n$ is $1-\dfrac1n$ . There are $m$ people in the elevator, so the probability that not a single one gets off at floor $n$ is $\left(1-\dfrac1n\right)^m$ .

So,

$\mathbb P(X_i=x)\begin{cases}\left(1-\dfrac1n\right)^m&\text{for }x=1\\\\1-\left(1-\dfrac1n\right)^m&\text{for }x=0\end{cases}$

which means

$\mathbb E[Y]=\mathbb E\left[\displaystyle\sum_{i=1}^nX_i\right]=\displaystyle\sum_{i=1}^n\mathbb E[X_i]=\sum_{i=1}^n\left(1\cdot\left(1-\dfrac1n\right)^m+0\cdot\left(1-\left(1-\dfrac1n\right)^m\right)$
$\implies\mathbb E[Y]=n\left(1-\dfrac1n\right)^m$

and

$\mathbb E[Y^2]=\mathbb E\left[\left(\displaystyle\sum_{i=1}^n{X_i}\right)^2\right]=\mathbb E\left[\displaystyle\sum_{i=1}^n{X_i}^2+2\sum_{1\le i$

Computing $\mathbb E[{X_i}^2]$ is trivial since it's the same as $\mathbb E[X_i]$ . (Do you see why?)

Next, we want to find the expected value of the following random variable, when $i\neq j$ :

$X_iX_j=\begin{cases}1&\text{if }X_i=1\text{ and }X_j=1\\0&\text{otherwise}\end{cases}$

If $X_iX_j=0$ , we don't care; when we compute $\mathbb E[X_iX_j]$ , the contributing terms will vanish. We only want to see what happens when both floors are not visited.

$\mathbb P(X_iX_j=1)=\left(1-\dfrac2n\right)^m$
$\implies\mathbb E[X_iX_j]=\left(1-\dfrac2n\right)^m$
$\implies2\displaystyle\sum_{1\le i$

where we multiply by $n(n-1)$ because that's how many ways there are of choosing indices $i,j$ for $X_iX_j$ such that $1\le i$ .

So,

$\mathrm{Var}[Y]=n\left(1-\dfrac1n\right)^m+2n(n-1)\left(1-\dfrac2n\right)^m-n^2\left(1-\dfrac1n\right)^{2m}$

4 0

3 years ago

What is the sum of 23| 17/27+8/9 ?

Ymorist [56]

Answer:

the answer is c

Step-by-step explanation:

add the sum

4 0

4 years ago

Find the distance between the points (-3,6)and(-3,-7)

elena-14-01-66 [18.8K]

Answer:

13 this needed to be 20 characters long just ignore

Step-by-step explanation:

Just took the test

3 0

3 years ago

Given side a is 41 units, side b is 23 units and the included angle is 70°. Find the area

Lelu [443]

Answer:

886.13sq. units

Step-by-step explanation:

If the figure is a triangle

Area of the triangle = 1/2 ab sintheta

Given

a = 41 units

b = 23 units

theta = 70°

Area of the triangle = 1/2 * 41 * 23 sin 70

Area of the triangle = 943 sin70

Area of the triangle = 943(0.9397)

Area of the triangle = 886.13

Hence the area of the triangle is 886.13sq. units

5 0

3 years ago

A color printer prints 21 pages in 9 minutes. How many pages does it print per minute? Round your answer to the nearest hundredt

hichkok12 [17]

Answer:

2.33 = x

Step-by-step explanation:

pages minutes

21 9

x 1

Cross multiply.

21×1 = 9×x

21 9x

9 9

9 cancels 9 leaving x. and 21 divided by 9 equals 2.33 pages. NB. both sides are divided by 9 because we want x by itself and what you do to one side, you have to do to the other.

8 0

3 years ago