2(x + 2) + 2 = 2(x + 3) + 1
2x + 4 + 2 = 2x + 6 + 1
2x + 6 = 2x + 7 - NO SOLUTION
(subtract 2x from both sides, then 6 = 7 FALSE)
2x + 3(x + 5) = 5(x – 3)
2x + 3x + 15 = 5x - 15
5x + 15 = 5x - 15 - NO SOLUTION
4(x + 3) = x + 12
4x + 12 = x + 12 - ONE SOLUTION
4 – (2x + 5) = (–4x – 2)
4 - 2x - 5 = -4x - 2
-2x - 1 = -4x - 2 - ONE SOLUTION
5(x + 4) – x = 4(x + 5) – 1
5x + 20 - x = 4x + 20 - 1
4x + 20 = 4x + 19 - NO SOLUTION
Answer:
Expected value = 190
Variance = 4000
Step-by-step explanation:
Let X be the number of the trials until the third success of the bad pump.
This implies that X is a negative binomial distribution
having θ = 20% = 0.2.
Now, if for example it will take X trials to use up the three pumps, then the total time is 10 min/trials + extra 10 minutes for the 3 bad pumps
This means the total time is written as;
T = 10X + (10 + 10 + 20)
T = 10X + 40
Mean which is also expected value of X is;
μ_x = 3/0.2 = 15
Variance of X is; σ²_x = 40
Thus;
Mean of T will be;
μ_T = 10μ_x + 40
μ_T = 10(15) + 40
μ_T = 190
Also, variance of T will be;
σ²_T = 10²•σ²_x
σ²_T = 100 × 40
σ²_T = 4000
The formula for the area of the circle is:

All you have to do is plug in 8 for r :)
1/2x + 1 = 2/3x
1/2x - 2/3x = -1
-x/6 = -1
x = 6
Hope this helps!