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Oliga [24]
3 years ago
10

If A + B = 2X -2 and A -B equals 4X -8, find A and B

Mathematics
1 answer:
Keith_Richards [23]3 years ago
8 0
A=3X-3
B=-X+3
If A+B=2X-2, then using equalivant exchange A=2X-2-B and
B=2X-2-A
If A-B=4X-8, then A=4X-8+B and -B=4X-8-A(or B=-4X+8+A)
Since A equals both 2x-2-B and 4X-8+B we can add both equations to equal 2A=6X-6 now we devide that by 2 to get
A=3X-3
Do the exact same for B, so b equals both 2X-2-A and -4X+8+A
We can add them both to get 2B=-2X+6 and decide that by 2 to get B=-X+3
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Answer:

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And we can find the individual probabilities using the probability mass function

P(X=7)=(8C7)(0.9)^7 (1-0.9)^{8-7}=0.3826  

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Step-by-step explanation:

Previous concepts  

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".  

Solution to the problem

Let X the random variable of interest "number of automobiles with both headligths working", on this case we now that:  

X \sim Binom(n=8, p=0.9)  

The probability mass function for the Binomial distribution is given as:  

P(X)=(nCx)(p)^x (1-p)^{n-x}  

Where (nCx) means combinatory and it's given by this formula:  

nCx=\frac{n!}{(n-x)! x!}  

And for this case we want to find this probability:

P(X \geq 7) = P(X=7) +P(X=8)

And we can find the individual probabilities using the probability mass function

P(X=7)=(8C7)(0.9)^7 (1-0.9)^{8-7}=0.3826  

P(X=8)=(8C8)(0.9)^8 (1-0.9)^{8-8}=0.4305  

And replacing we got:

P(X \geq 7) = P(X=7) +P(X=8)=0.3826 +0.4305=0.8131

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Step-by-step explanation:

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