U= { x | x is the name of one of the states of in the us}
a = {x | x ∈ u and x begins with the letter a}
i = {x | x ∈ u and x begins with the letter i}
p = {x | x ∈ u and x begins with the letter p}
n = {x | x ∈ u and x begins with the letter n}
o = { x | x ∈ u and x begins with the letter o}

find:
n(p')
n(a' ∪ n)
n(i' ∩ o')
n(p∩n)

!

Step-by-step explanation:

We can start with some helpful facts:

and all subsets are mutually exclusive.

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n(P') = n(U) -n(P) = 50 -1 = 49

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n(A' ∪ N) = n(A') = n(U) -n(A) = 50 -4 = 46

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n(I' ∩ O') = n(U) -n(I) -n(O) = 50 -4 -3 = 43

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n(P∩N) = 0 . . . . no states begin with the letter P and also with the letter N.

For reference, here is a list of the relevant states:

{Alabama, Alaska, Arizona, Arkansas, Idaho, Illinois, Indiana, Iowa, Nebraska, Nevada, NewHampshire, NewJersey, NewMexico, NewYork, NorthCarolina, NorthDakota, Ohio, Oklahoma, Oregon, Pennsylvania}

step-by-step explanation:

i think something is missing in your question because y-1=(x-12) would not pass through the point (-4,-3). because if you replace x by -4 your are supposed to find y=-3 which is not the case her. if you replace x by -4 you find =-15.

i assume the right equation is y-1=1/4*(x-12) because this one is passing through both your points (if you are interested to know how i found that out i can tell you).

in this equation if i replace x by -4 i find y=-3 and if i replace x by 12, i find y=1 so the line representing this equation is passing through those 2 points.

then the standard form of the equation is finding an expression of y in function of x

y-1=1/4*(x-12)

y=x/4-3+1

y=x/4-2

hope that .

do you confirm there was a mistake in the question?

step-by-step :