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:
Jake does have enough to buy a dog bone that cost $1.49
Step-by-step explanation:
6 quarters = $1.50
2 dimes = $0.20
1 nickel = $0.05
So add it all together: $1.50 + $0.20 + $0.05 = $1.75
Answer: x = 38.4
Step-by-step explanation:
7-x/3 = -1-x/8
1. Add 1 to both sides
8-x/3 = -x/8
2. Add x/3 to both sides
8 = x/3 - x/8
3. Multiply x/3 by 8/8 and x/8 by 3/3 to get the same number under the quotient
8 = 8x/24 - 3x/24
4. calculate the difference between 8x/24 - 3x/24
8 = 5x/24
5. Multiply both sides by 24/5, and there is the answer
38.4 = x