Answer:


Step-by-step explanation:
Given



Required
Find P(A) and P(B)
We have that:
--- (1)
and
--- (2)
The equations become:
--- (1)

Collect like terms


Make P(A) the subject

--- (2)


Substitute: 
![[0.770 - P(B)] * P(B) = 0.144](https://tex.z-dn.net/?f=%5B0.770%20-%20P%28B%29%5D%20%2A%20P%28B%29%20%3D%200.144)
Open bracket

Represent P(B) with x

Rewrite as:

Expand

Factorize:
![x[x - 0.45] - 0.32[x - 0.45]= 0](https://tex.z-dn.net/?f=x%5Bx%20-%200.45%5D%20-%200.32%5Bx%20-%200.45%5D%3D%200)
Factor out x - 0.45
![[x - 0.32][x - 0.45]= 0](https://tex.z-dn.net/?f=%5Bx%20-%200.32%5D%5Bx%20-%200.45%5D%3D%200)
Split

Solve for x

Recall that:

So, we have:

Recall that:

So, we have:


Since:

Then:


Answer:
The lodging cost of the room is $ 41.28
Step-by-step explanation:
Given as :
The rate of room including taxes = $ 45
The state tax = 6 %
The city tax = 2 %
The municipal tax = 1 %
So, The total tax = 6 % + 2 % + 1 % = 9 %
Let The lodging cost = $ x
So, According to question
x + 9 % of x = $ 45
Or, x + 0.09 × x = 45
Or, 1.09 × x = 45
∴ x =
= $ 41.28
Hence The lodging cost of the room is $ 41.28 Answer
Answer:
Perimeter = 16 units
Area = 15 squared units
Step-by-step explanation:
ABCD is a rectangle.
It's length l = 5 units
and width w = 3 units
Perimeter of ABCD = 2(l + w) = 2(5 + 3) = 2*8 = 16 units
Area of ABCD = 5*3 = 15 squared units.
If the two triangles are congruent, then WX=PQ, because they are corresponding(by the order of the letters WXY and PQR). So if they are congruent, then we can say 5n-2=63, by the transitive property. The rest of the problem only requires Pemdas. Add 2 to both sides (5n=65), divide both sides by 5 (n=13), and you find that n=13.