Which sequences are arithmetic? Check all that apply.
2 answers:
Answer:
Option C and E are correct.
The sequences which are arithmetic:
18, 5.5, -7, -19.5, -32,....
16, 32, 48, 64, 80
Step-by-step explanation:
Arithmetic sequence states that a sequence in which a common difference between each consecutive term is constant.
Common difference(d) = for every natural number n.
Option A:
-5, 5, -5, 5, -5, .....
5-(-5) = 5+5 = 10 ,
-5 -5 = -10 .....
Since, the common difference for the given sequence is not constant.
Option B:
96, 48, 24, 12, 6
48 -96 = -48
24-48 = -24 ....
Common difference for the given sequence is not constant.
Option C:
18, 5.5, -7, -19.5, -32,....
5.5-18 = -12.5
-7 -5.5 = -12.5 ....
∴Common difference for the sequence is constant.
Option D:
-1, -3, -9, -27, -81 ,....
-3 -(-1) = -3+1 = -2
-9-(-3) = -9+3 = -6 ....
∴Common difference for the sequence is not constant.
Option E:
16, 32, 48, 64, 80
32-16 = 16
48 - 32 = 16 and so on...
∴Common difference for the sequence is constant.
Therefore, the sequences which are arithmetic are:
18, 5.5, -7, -19.5, -32,....
16, 32, 48, 64, 80
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Answer:
x=
Step-by-step explanation:
Step 1: Multiply both sides by x,
gx=−c+x
Step 2: Add -x to both sides.
gx+−x=−c+x+−x
gx−x=−c
Step 3: Factor out variable x.
x(g−1)=−c
Step 4: Divide both sides by g-1.
x=
Hope this helps!
Answer:
r = 0.9825; good correlation.
Step-by-step explanation:
One formula for the correlation coefficient is
The calculation is not difficult, but it is tedious.
1. Calculate the intermediate numbers
We can display them in a table.
<u> </u><u>x</u> <u> y </u> <u> xy </u> <u> x² </u> <u> y² </u>
-3 -40 120 9 1600
1 12 12 1 144
5 72 360 25 5184
<u> 7</u> <u>137</u> <u> 959</u> <u>49</u> <u>18769 </u>
Σ = 10 181 1451 84 25697
2. Calculate the correlation coefficient
The closer the value of r is to +1 or -1, the better the correlation is. The values of x and y are highly correlated.