Answer:
The given series converges and 
Step-by-step explanation:
Given is 108, -18, 3,...
It is an alternate series. An alternate series is convergent if:
1. The series is decreasing.
2. If the last term (n-th term) of series converges to 0.
<u>Since each next term is less than its preceding term, so it is decreasing.</u>
First term, a = 108
Second term = -18
Common ratio, r = -18/108 = -1/6
General term, aₙ = a*rⁿ = 108*(-1/6)ⁿ
<u>When n increases to infinity, the exponent term will decreases to zero, and last term (n-th term) will converge to 0 as well.</u>
Hence, the given series converges.
Now limit will be: 
Hence,
Answer:
1. Yes
2. They could change the 60° angle into a different one.
Step-by-step explanation:
1. Two triangles are the same if they share two side lengths with the same angle between them.
2. Since the triangles are equal if they share two side lengths with the same angle between them, if they changed the angle between 3 and 5, it'd no longer be the same triangle.
Prime numbers 2,3,5,7,11,13,17,19,23
so 2+3+5=10 no
3+5+7=15 no
3+5+11=19 Yes this is your answer
Answer:
its type hard to see ngl
Step-by-step explanation:
Answer:
A. -1.6; not significant
Step-by-step explanation:
The z-score of a data set that is normally distributed with a mean of 
and a standard deviation of 
, is given by:
.
From the question, the test score is: 
, the mean is 
, and the standard deviation is 
.
We just have to plug these values into the above formula to obtain:
.
This simplifies to: 
.
.
We can see that the z-score falls within two standard deviations of the mean.
Since 
the value is not significant.
The correct answer is A. -1.6; not significant
