Two thousand brown trout are introduced into a small lake. the lake has a volume of 20,000 cubic meters. use a table to find the probability that three brown trout are found in any given cubic meter of the lake. a. find the average number of brown trout per cubic meter.
b. identify µ and x
c. use table 3 in appendix B to find the poison probability
d. interpret the results
e. determine whether the event is unusual. explain

tip $2.90

total $17.40

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)