() = 0.50, () = 0.70, ( ∪ ) = 0.85 Are the events, and , independent in this situation? You must provide reasoning for your answer.

Independent events

Step-by-step explanation:

Given

Required

Determine the relationship between the events

To do this, we simply calculate P(A n B) using:

and

So, we have:

and

Since:

Then: the events are independent

hello from mrbilldoesmath!

answer:

(7 x + 6 y) (49 x^2 - 42 x y + 36 y^2)

discussion:

the trick is to recognize that 343 = 7^3 and 216 = 6^3 and, in general,

a^3 + b^3 =   (a + b) (a^2 - a b + b^2).

in our case

343x^3+216y^3   =   (7x)^3 + (6y)^3

so take a = 7x and b = 6y in the above equation to get the answer.

you,

mrb