Answer:
<u>Marge's</u> present age = 14 ; <u>Dan's</u> present age = 29
Step-by-step explanation:
Let Marge's present age be = M
Dan's present age [D] : 14 years elder than Marge = M + 14
Marge Age = M - 8
Dan's Age = D - 8 = (M + 14) - 8 = M + 6
{Given} : Dan's age = 3 times Marge's age
M + 6 = 3 (M - 8)
M + 6 = 3M - 24
6 + 24 = 3M - M
30 = 2M
M = 30/2
M = 15 [Marge's present age]
Dan's present age [D] = M + 14 = 29
-7 and 8 are the solutions to the given equation system.
Therefore, the maximum distance between the y values of the two equations must lie exactly between their points of intersection. That is on x value:
x = (-7 + 8)/2 = 0.5
The maximum distance is:
y = 0.5 + 56 = 56.5
y = 0.5² = 0.25
56.5 - 0.25 = 56.25 units
The problem statement gives you the relationship between their speeds, and it gives you information you can use to find their total speed. You solve this by finding the total speed, then the proportion of that belonging to Bill.
The total speed is (120 mi)/(3 h) = 40 mi/h.
The speed ratio is ...
... Bill : Joe = 3 : 1
so the speed ratio Bill : Total is ...
... 3 : (3+1) = 3:4.
Bill's speed is (3/4)×(40 mi/h) = 30 mi/h.
Answer:
So then the best option is:
a. 7.32
Step-by-step explanation:
Previous concepts
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
Where SST represent the total sum of squares.
The degrees of freedom for the numerator on this case is given by 
where k =3 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 
From the info given we know that 
And 
From definition the F statisitc is defined as:
So then the best option is:
a. 7.32
