Answer:
Step-by-step explanation:
Given that:
X(t) = be the number of customers that have arrived up to time t.
... = the successive arrival times of the customers.
(a)
Then; we can Determine the conditional mean E[W1|X(t)=2] as follows;




Now 
(b) We can Determine the conditional mean E[W3|X(t)=5] as follows;

Now; 
(c) Determine the conditional probability density function for W2, given that X(t)=5.
So ; the conditional probability density function of
given that X(t)=5 is:

We are given coordinates of the triangle: A(2,2), B(7,1) and C(8,-4).
We need to rotated 90° counterclockwise about the origin.
In order to find the new coordinates of rotatation 90°counterclockwise about the origin, we can apply rule (h, k) ---> (-k,h).
Where (h,k) are the coordinates of original image on axes and (-k,h) are the coordinates of rotated image.
In resulting coordinates of the image first swap the x and y coordinates of the original image and then make the sign opposite of each x-coordinate.
On applying rule (h, k) ---> (-k,h), we get
A(2,2) --> A'(-2,2)
B(7,1) --> B'(-1,7)
C(8,-4) --> C'(4,8)
Answer:
Question 1: Option C, 2x^2(x - 3)(x^2 + 3x + 9)
Question 2: Options 1, 2, 5
Step-by-step explanation:
Question #3
Step 1: Factor
2x^5 − 54x^2
2x^2(x^3 - 27)
<em>2x^2(x - 3)(x^2 + 3x + 9)</em>
<em />
Answer: Option C, 2x^2(x - 3)(x^2 + 3x + 9)
Question #2
p(x) = 4x^6 + 32x^3
<u>Step 1: Factor</u>
4x^6 + 32x^3
4x^3(x^3 + 8)
<em>4x^3(x + 2)(x^2 - 2x + 4)</em>
<em />
Answer: Options 1, 2, 5