All categories

3 years ago

That was my grandson question I haven’t a clue what that mean

Mathematics

1 answer:

Eduardwww [97]3 years ago

6 0

That would be the zero identity property. Hope it helps!

You might be interested in

The graph of the function f is shown. f(4) =<br> A) 0 <br> B) 1 <br> C) 4 <br> D) 5

sdas [7]

Let me first give you an overview of the coordinate plane. The coordinate plane has an x-axis that runs horizontally left to right and a y-axis that runs vertically up and down. The axes intersect at a right angle at the origin, which is (0, 0). If you have a point, say (2, 5), then the point is located two steps to the right of the origin and five steps up. Remember to always go left and right first before going up and down. This is because the y-coordinate depends on the x-coordinate.

Sometimes the y-coordinate is called f(x), which is the function value at a given x-value. Again, this is because f(x) depends on the x-value.

The numerical value of f(4) is how ever many steps up or down the graph is (the graph is a visual representation of f(x) points). At x = 4, the graph is at 1, so f(4) = 1.

Please comment with any further questions!

7 0

3 years ago

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

. Rebecca David earns $427.50 per week as manager at Marlin

lilavasa [31]

Answer: 124

Step-by-step explanation:

4 0

3 years ago

Which statement is not true

Ede4ka [16]

Answer is D

TanB should be 4/3

here in the options it is 5/3 which is not true

7 0

3 years ago

Alisha has a $15,000 car loan with a 6 percent interest rate that is compounded annually. How much will she have paid at the end

Harlamova29_29 [7]

6 percent intrest per year for 5 years I think is the same as 30 percent for 5 years
so $15,000 x .3 is $4500
$15,000 + $4500 = $19,500
not 100 percent sure if this is correct but I think its right.
Sorry if I am wrong not 100% sure.

8 0

3 years ago