
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:
Part A: He spends an average of $8.50 per day
Part B: He would save $17 per week
Step-by-step explanation:
There are 180 boys in the school.
40% of the students are girls.
120/40 = x/60
multiply 120 by 60
divide 7200 by 40
3000000÷1.125=2666666.6667
Round off to 2666667 people.
Feel free to correct this if wrong.