A number cube has sides labeled 1 to 6. Hannah rolls the number cube 18 times. How many times can she expect to roll a number less than 3?
A.6
B.8
C.2
D.3

6

Step-by-step explanation:

The expected value is the number of rolls multiplied by the probability of each success on the roll (as success is the top face of the die is a 2 or a 1) and the probability of that success is 2/6 which reduces to 1/3

So the expected value in 18 rolls

= 18 x 1/3

1) 2/5

2) zero=0/1

3) zero=0/2

4) -4/5

5) undefined=3/0

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)