Can you explain the answer for me and you

There's a formula for that.

... P(A∪B) = P(A) + P(B) - P(A∩B)

Filling in the given values, we have

... P(A∪B) = 2/3 + 4/5 - 3/5 = 10/15 + 12/15 - 9/15

... P(A∪B) = 13/15 . . . . . . . . matches selection B

the quotient is 4x^2 - 27x + 167 with a remainder of -996

step-by-step explanation:

in synthetic division, use -6 as the divisor and use the coefficients {4, -3, 5, 6}:

-6     )   4     -3     5     6

                -24   162 -1002

          4   -27   167   -996

thus, the quotient is 4x^2 - 27x + 167 with a remainder of -996.

note:   your "4x°-3x+5x+6" is ambiguous / incomplete.   i had to assume that you meant '4x^3 - 3x^2 + 5x + 6."

452,489 to the nearest thousand is 452,000