ANSWER
EXPLANATION
Method 1
Vertically opposite angles are equal, therefore
This implies that,
We simplify to get,
Dividing through by 3 gives,
Also,
This implies that,
We simplify the right hand side to get,
We divide both sides both sides by 2 to get,
Method 2
Angles on straight line sums to 180°.
This implies that,
Also,
The sum of any arithmetic sequence is the average of the first and last terms times the number of terms.
Any term in an arithmetic sequence is:
a(n)=a+d(n-1), where a=initial term, d=common difference, n=term number
So the first term is a, and the last term is a+d(n-1) so the sum can be expressed as:
s(n)(a+a+d(n-1))(n/2)
s(n)=(2a+dn-d)(n/2)
s(n)=(2an+dn^2-dn)/2
However we need to know how many terms are in the sequence.
a(n)=a+d(n-1), and we know a=3 and d=2 and a(n)=21 so
21=3+2(n-1)
18=2(n-1)
9=n-1
10=n so there are 10 terms in the sequence.
s(n)=(2an+dn^2-dn)/2, becomes, a=3, d=2, n=10
s(10)=(2*3*10+2*10^2-2*10)/2
s(10)=(60+200-20)/2
s(10)=240/2
s(10)=120
The common ratio of sequential values is
18.2/26 = 0.7
The missing value is
12.74*0.7 = 8.918
The appropriate choice is ...
d. 8.918
Answer:
a.) 60
Step-by-step explanation:
Margin of Error formula = z × s/√n
z = z score of confidence interval
We are given z score of 99% = 2.58
s = Standard deviation = $36
Margin of Error= ± 12
n= unknown
= 12 = 2.58 × 36/√n
12 × √n = 92.88
√n = 92.88/12
√n = 7.74
Square both sides
(√n)² = 7.74²
n = 59.9076
Approximately n ≈ 60
Therefore, the required sample size = 60
