The sum of a geometric sequence is:
s(n)=a(1-r^n)/(1-r), s(n)=nth sum, a=initial value, r=common ratio, n=term #
In this case we are told that a=6 and r=1/3 so:
s(n)=6(1-(1/3)^n)/(1-1/3)
s(n)=6(1-(1/3)^n)/(2/3)
s(n)=9(1-(1/3)^n), so the sum of the first 5 term is:
s(5)=9(1-(1/3)^5))
s(5)=9(1-(1/243))
s(5)=9(242/243)
s(5)=2178/243
s(5)=242/27
s(5)=8 26/27 ...if you wanted an approximation s(5)≈8.96 to the nearest hundredth...
(-6x-2)-(-3x+5)= -24x+14
-6x-2+3x-5=-24x+14
-3x-7=24x+14
— —
-3x -3x
Answer:
it is sixty six inches
Step-by-step explanation:
double the radius
It takes 11 seconds to scan one person. So we have this ratio to start with
11 seconds: 1 person
Divide both sides by 11 to get this new ratio
1 second: 1/11 person
1 second: 0.0909 person
So in 1 second, 0.0909 of a person can be scanned. This statement seems silly because we can't have a fraction of a person, but it helps with the next part as shown below. The next step is to multiply both sides by 1800 to get....
1 second: 0.0909 person
1800*1 second: 1800*0.0909 person
1800 seconds: 163.62 persons
In a span of 1800 seconds (equivalent to 30 minutes), about 163 people's lunches can be scanned. Unfortunately, none of the answer choices are 163. The closest thing is 180, but that is an overestimate. So I would ask your teacher if there is a typo somewhere.
Note: if it took exactly 10 seconds for each student (instead of 11), then the answer would be 1800*(1/10) = 1800*0.10 = 180.
Answer:
Step-by-step explanation:
A = (7 + 4)(24) ÷ 2 = 132 units²
