The rows add up to
, respectively. (Notice they're all powers of 2)
The sum of the numbers in row
is
.
The last problem can be solved with the binomial theorem, but I'll assume you don't take that for granted. You can prove this claim by induction. When
,
so the base case holds. Assume the claim holds for
, so that
Use this to show that it holds for
.
Notice that
So you can write the expansion for
as
and since
, you have
and so the claim holds for
, thus proving the claim overall that
Setting
gives
which agrees with the result obtained for part (c).
Answer:
126
Step-by-step explanation:
There are 9 city council members.
We have to choose 4 of them.
We have to use the combination as :
where, 9 is the population size
4 is the sample size.
Therefore, the total number of possible samples without replacement is given as :
= 126
Answer:
69.08 yd
Step-by-step explanation:
Answer:
326
Step-by-step explanation:
l x w
7x8
25x6
4x30
326