Recall the binomial theorem.

1. The binomial expansion of
is

Observe that


When we multiply these by
,
•
and
combine to make 
•
and
combine to make 
and the sum of these terms is

2. The binomial expansion is

We get the
term when
:

Answer:
5.1
Step-by-step explanation:

0.4663 * 11 = x
x = 5.1293
x = 5.1
Step-by-step explanation:
Tax charge
80 × 6.75/100 = 5.4
Cost + tax charge
80 + 5.4 = 85.4
Tip (15% of cost and tax)
85.4 × 15/100 = 12.81
(Cost + tax charge + tip)
85.40 + 12.81 = 98.21
therefore, $95 is not enough.
Answer:
D 40,000nm
Step-by-step explanation: 1nm/10^-9m * 10^-6/1um = 10^3 nm/um
Therefore in 40 microns there are:
40um * 10^3 nm/um = 40 * 10^3 nm = 40,000 nm