
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:
720 in^3.
Step-by-step explanation:
12 * 60 = 720.
Answer:
Step-by-step explanation:
I gather that you need to find the area of the sector and then subtract from it the area of the segment to get the area of the triangle (although there are other ways in which to find the area of the triangle).
The area of a sector is:
where our angle is given as 34, pi is 3.1415, and the radius is 5:
and if you multiply and divide that all out you get that the area of the sector is:
A = 7.417
Now subtract from it the area of the segment, 2.209. to get the area of the triangle:
7.417 - 2.209 = 5.208
Answer:
C
15 + x
Step by step explanation
For Company X, the initial cost is 30 cents plus 5 cents per minute, so the expression would be 30 + 5x (x would represent minutes.
For Company Y, the initial cost is 15 cents plus 4 cents per minute, so the expression would be 15 + 4x (x would represent minutes.)
Then subtract the expression of Y from the expression of X to show the difference in value between Y and X.
So, 30 + 5x - (15 +4x)
Distribute the subtraction sign.
30 + 5x - 15 - 4x
Solve across.
15 + x
Answer: The answer is (B)
Explanation: The answer is (B) because, there are 2 zeros so that means that there would have to be a 2 behind the 10 and then there is 2,3,4,and 9. We take out the 9 and use the other numbers, bring over the decimal and now you have
.