If the length, width, and height of a cube all change by a factor of 9, what happens to the volume of the cube?

The volume will increase 729 fold.

Step-by-step explanation:

If the length, width, and height of a cube all change by a factor of 9.

The answer is 729 fold, or 9 cubed.

As if original length is l

The original width is w

And original height is h

Volume = l x w x h

But when all change by a factor of 9, we get

9l x 9w x 9h

= 729 fold

Therefore, the volume will increase 729 fold.

85.560%

step-by-step explanation:

conditional probability is defined as:

p(a|b) = p(a∩b) / p(b)

in other words, the probability that a occurs, given that b has occurred = the probability that both a and b occur / the probability that b occurs.

in this example:

p(turns 64 | turns 44) = p(turns 64 & turns 44) / p(turns 44).

if someone turns 64, they must have already turned 44, so:

p(turns 64 | turns 44) = p(turns 64) / p(turns 44)

on page 42, we see that of the original 100,000, 94944 turn 44, and 81234 turn 64.   therefore:

p(turns 64 | turns 44) = 81234 / 94944

p(turns 64 | turns 44) = 0.85560