Answer:
And 
The difference is that MSA takes incount the variation between the groups and the grand mean, and the MSW takes in count the variation within groups respect to the mean of each group
.
Step-by-step explanation:
Analysis of variance (ANOVA) "is used to analyze the differences among group means in a sample".
The sum of squares "is the sum of the square of variation, where variation is defined as the spread between each individual value and the grand mean"
If we assume that we have 
groups and on each group from 
we have 
individuals on each group we can define the following formulas of variation:
And we have this property
The degrees of freedom for the numerator on this case is given by 
where k represent the number of groups.
The degrees of freedom for the denominator on this case is given by 
.
And the total degrees of freedom would be 
We can find the
And
The difference is that MSA takes incount the variation between the groups and the grand mean, and the MSW takes in count the variation within groups respect to the mean of each group
.
And the we can find the F statistic 
Answer:
2427.26 $
Step-by-step explanation:
Just use this formula when you have such type of problems:
N = N° (1 + %)^t
Where N = final amount
N°= initial amount
t = peroid of time
Now let's solve:
N = 1000(1 + 0.03)^30
N = 2427.26
Answer:
15.
Step-by-step explanation:
450 / 2 = 225.
225= 3 * 3 * 5 * 5
So √225 = 3 * 5 = 15.
Answer:
21 kWh
Step-by-step explanation:
1. Subtract 25% from the original amount.
25% of 28 kWh is ...
0.25 × 28 kWh = 7.00 kWh
Subtracting this from 28 kWh, we find the usage after reduction to be ...
28 kWh - 7 kWh = 21 kWh
__
2. We know that if we reduce 100% of a quantity by 25%, then the resulting amount is (100 -25)% = 75% of the original. As a fraction, this is 75/100 = 3/4 of the original amount. Then the reduced usage is ...
(3/4) × (28 kWh) = 3·(7·4)/4 kWh = 3·7 kWh = 21 kWh
__
Mario must reduce his usage to 21 kWh or less.
