Let

denote the event that an HD is defective, and

the event that a particular HD was produced at facility

.
You are asked to compute



From the definition of conditional probabilities, the first two will require that you first find

. Once you have this, part (c) is trivial.
I'll demonstrate the computation for part (a). Part (b) is nearly identical.
(a)

Presumably, the facility responsible for producing a given HD is independent of whether the HD is defective or not, so

.
Use the law of total probability to determine the value of the denominator:

We know each of the component probabilities because they are given explicitly: 0.015, 0.02, 0.01, and 0.03, respectively. So

and thus

(b) Similarly,

(c)
12x - 4y = 20 Subtract 12x from both sides
-4y = -12x + 20 Divide both sides by -4
y = 3x - 5
Answer:
e°=100°
Step-by-step explanation:
Sum of angles in a triangle= 180°
70°+30°+x°=180°
100°+x=180
Collect like terms
x°=180-100
x°=80°
e° is an exterior angle
exterior angle =180- interior angle
180°- x°
180°- 80°
=100°
e°=100°
Let's follow the transformations that happen to A, to get to A' and A''.
Point A is at (-5, -2)
It moves to (-5, 2) which is where A' is located. Note the x coordinate stays the same while the y coordinate flips from negative to positive. This must mean we applied a reflection over the x axis.
That rule in general is 
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Now compare A'(-5,2) and A''(1,4). We can shift A' 6 units to the right and then 2 units up so we move from A' to A''.
Algebraically this is stated as 
Whatever the x coordinate is, add 6 to it. For the y coordinate, we add on 2.
Applying that rule to B'(-1,2) gets us to

which is the proper location of B''
The same applies to moving C' to C''

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In summary, we started off by reflecting over the x axis. Then we applied the translation rule of "shift to the right 6 units, shift up 2 units".
In terms of algebra, combining the rules
and
will have us end up with 