Apolling company conducts an annual poll of adults about political opinions. the survey asked a random sample of 308 adults whether they think things in the country are going in the right direction or in the wrong direction. 46% said that things were going in the wrong direction. complete parts a and b below. a) calculate the margin of error for the proportion of all adults who think things are going in the wrong direction for 95% confidence. b) would the margin of error be larger or smaller for 85% confidence?

hello from mrbilldoesmath!

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

discussion:

in general, the factorization of a^3 + b^3 is

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

in our case note that 343 = 7^3 and 216 = 6^3 so the equation becomes:

343x^3 + 216y^3 = (7x)^3 + (6y)^3

if you think of a (above) as 7x and b as 6y the factorization becomes

343x^3 + 216y^3 =

((7x + 6y) (   (7x)^2 - 7x*6y + (6y)^2)   =

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

you,

mrb

(a + b) (a^2 - a b + b^2)

if the angular bisector of an triangle bisects the opposite side, prove that the other two sides are equal.