Answer:
a) 48.408
b) 1.235
Step-by-step explanation:
a)
The average hardness value xbar can be computed as
xbar=sum of values/number of values
xbar=(46.5+46.9+49.4+50.3+49.8+48.8+47+47.7+48.3+49.4+47.8+49)/12
xbar=580.9/12
xbar=48.408 (rounded to 3 decimal places).
The average hardness value is 48.408.
b)
The standard deviation hardness value s can be computed as

x x-xbar (x-xbar)
²
46.5 -1.90833 3.64174
46.9 -1.50833 2.27507
49.4 0.99167 0.98340
50.3 1.89167 3.57840
49.8 1.39167 1.93674
48.8 0.39167 0.15340
47.0 -1.40833 1.98340
47.7 -0.70833 0.50174
48.3 -0.10833 0.01174
49.4 0.99167 0.98340
47.8 -0.60833 0.37007
49.0 0.59167 0.35007
Total 16.7692




s=1.235 (rounded to 3 decimal places)
The standard deviation hardness value is 1.235.
T(n)=6-1=5
that means all terms are 5 because n does not appear on the right hand side.
However, if T(n)=6n-1, then
first term = T(1)=6(1)-1=5,
but second term T(2)=6(2)-1=11...
Answer: 2
Step-by-step explanation:
Recall from the laws of Logarithms:
Log a - Log b = Log ( a/b )
That means
Log 200 - Log 2 = Log ( 200/2)
= Log 100 , which could be written as
Log 
Recall from laws of Logarithms:
Log
= b Log a
Therefore:
Log
= 2 Log 10
Also from law of Logarithm
Log 10 = 1
Therefore 2 Log 10 = 2 x 1
= 2
#9 the sum of two angles is 90 degrees, creating a right angle.
#10 the sum of the two angles is 180 because the form a supplementary angle