Answer: 0.6767
Step-by-step explanation:
Given : Mean =
errors per page
Let X be the number of errors in a particular page.
The formula to calculate the Poisson distribution is given by :_

Now, the probability that a randomly selected page does not need to be retyped is given by :-

Hence, the required probability :- 0.6767
Answer:

Step-by-step explanation:
Given
See attachment for diagram
Required
The equation to find x
First, calculate the area of the big rectangle using:

So:

The smaller rectangle

The difference between this areas give the area of the shaded region.
So:


Open brackets

Collect like terms


<em>The above equation can be used to solve for x</em>
Let's factorise it :

![\: {\qquad \dashrightarrow \sf {x}^{3} (x + 3) + [-5(x + 3)] }](https://tex.z-dn.net/?f=%5C%3A%20%7B%5Cqquad%20%20%5Cdashrightarrow%20%5Csf%20%20%20%20%7Bx%7D%5E%7B3%7D%20%28x%20%2B%203%29%20%2B%20%5B-5%28x%20%2B%203%29%5D%20%20%7D)
Using Distributive property we get :



⠀
Therefore,

Answer:
Option (3).
Step-by-step explanation:
Option (1).
3(x - 1) = x + 2(x + 1) + 1
3x - 3 = x + 2x + 2 + 1
3x - 3 = 3x + 3 [Not True]
Therefore, this equation is not an identity.
Option (2).
x - 4(x + 1) = -3(x + 1) + 1
x - 4x - 4 = -3x - 3 + 1
-3x - 4 = -3x - 2 [Not true]
Therefore, this equation is not an identity.
Option (3).
2x + 3 = 
2x + 3 = 2x + 1 + 2
2x + 3 = 2x + 3 [True]
Therefore, this equation is an identity.
Option (4).

3x - 1.5 = 3x + 3 - x - 2
3x - 1.5 = 2x + 1 [Not true]
Therefore, this equation is not an identity.