A fair six-sided die is rolled 66 times. Theoretically, about how many times should a roll of "6 occur?​

11

Step-by-step explanation:

On a fair six-sided die, there is a chance of rolling each number. Therefore, for each of the rolls, the number 6 has a chance of being rolled. This can be read as for every 6 rolls, one 6 should appear.

Since the die is being rolled 66 times, we have the following proportion:

, where is the theoretical number of times a roll of "6" occurs.

Multiply both sides by 66:

34

step-by-step explanation:

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