
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:
At 11:50
Step-by-step explanation:
1. Subtract the hours and the minutes separately
12: 20
<u>- 0</u>: <u> 30</u>
12: -10
2. If the minutes are negative, subtract 1 from the hours and add 60 to the minutes.
12: -10
<u> - 1</u>: <u>+ 60
</u>
11: 50
You should remind PJ about her deliveries at 11:50.
Answer: M < -3
.................................................
Step-by-step explanation:
4 - 3m > -5
4 - 3m > (-4 -5)
3m > -9
(3/3)m > (-9/3)
m<-3
Answer:
Step by Step:
multiply the cost by the percentage.
Then add the cost to the answer
Answer:200.70
The equation of the circle is (x - 1)^2 +(y + 9)^2 = 144
<h3>How to determine the circle equation?</h3>
The given parameters are:
Center, (a,b) = (1, -9)
Radius, r = 12
The circle equation is calculated as:
(x - a)^2 + (y- b)^2 = r^2
This gives
(x - 1)^2 +(y + 9)^2 = 12^2
Evaluate the exponent
(x - 1)^2 +(y + 9)^2 = 144
Hence, the equation of the circle is (x - 1)^2 +(y + 9)^2 = 144
Read more about circle equations at:
brainly.com/question/10618691
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