Answer
a) y | p(y)
25 | 0.8
100 | 0.15
300 | 0.05
E(y) = ∑ y . p(y)
E(y) = 25 × 0.8 + 100 × 0.15 + 300 × 0.05
E(y) = 50
average class size equal to E(y) = 50
b) y | p(y)
25 |
100 |
300 |
E(y) = ∑ y . p(y)
E(y) = 25 × 0.4 + 100 × 0.3 + 300 × 0.3
E(y) = 130
average class size equal to E(y) = 130
c) Average Student in the class in a school = 50
Average student at the school has student = 130
Since the given hexagon is a regular hexagon all it's sides will be of equal length. Now, we know that the Area of any regular hexagon is given by:
Where is the area of the regular hexagon
is the side length of the regular hexagon
Also, it's Perimeter is given by:
Thus, all that we need to do is to find the side length of any one of the sides and to do that let us have a look at at the data of vertices points given and find out which points are definitely adjacent to each other and are also easy to calculate.
A quick search will yield that D(8, 0) and E(4, 0) are definitely adjacent to each other.
Please check the attached file here for a better understanding of the diagram of the original regular hexagon. Points D and E indeed are adjacent to each other.
Let us now find the distance between the points D and E using the distance formula which is as:
Where is the distance.
and
are the coordinates of points D and E respectively. (please note that interchanging the values of the coordinates will not alter the distance
)
Applying the above formula we get:
We know that this distance is the side length of the given regular hexagon.
Now, if the sides of the given regular polygon are reduced by 40%, then the new length of the sides will be:
Thus, the area of the smaller hexagon will be:
unit squared
and the new smaller perimeter will be:
unit
Which are the required answers.
