Consider the following pair of equations:
1 answer:
Answer:
The lines representing these equations intercept at the point (-4,2) on the plane.
Step-by-step explanation:
When we want to find were both lines intercept, we are trying to find a pair of values (x,y) that belongs to both equations, which means that it satisfies both equations at the same time.
Therefore, we can use the second equation that gives us the value of y in terms of x, to substitute for y in the first equation. Then we end up with an equation with a unique unknown, for which we can solve:
Next we use this value we obtained for x (-4) in the same equation we use for substitution in order to find which y value corresponds to this:
Then we have the pair (x,y) that satisfies both equations (-4,2), which is therefore the point on the plane where both lines intercept.
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Answer:
a) 4.9 % of all parts is defective or 0.049 of the total parts.
b) 0.5102 is the probability that the defective part was supplied by S1
Step-by-step explanation:
N is the total number of parts from supplier S1, S2 and S3.
N1 = 0.5*N is the total number of part supplied by S1
N2 = 0.2*N is the total number of part supplied by S2
N3 = 0.3*N is the total number of part supplied by S3
a) if Nd1 is the number of defective parts from supplier S1, Nd2 is the number of defective parts from supplier S2 and Nd3 is the number of defective parts from supplier S3, the the total defective parts Nd is:
Nd = Nd1 + Nd2 + Nd3, where
Nd1 = 0.05*N1 = 0.05*0.5*N = 0.025*N,
Nd2 = 0.03*N2 = 0.03*0.2*N = 0.006*N,
Nd3 = 0.06*N3 = 0.06*0.3*N = 0.018*N,
Then Nd = Nd1 + Nd2 + Nd3 = 0.049*N, so Nd/N = 0.049
b)
for the last expression I used the Bayes tehorem.
is the probability that occur S1 given that d (defective) is true. This a conditional probability.
see at https://en.wikipedia.org/wiki/Bayes%27_theorem