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Answer:
Width 150 meters.
Length = 350 meters.
Step-by-step explanation:
Let us assume the width of the fence = k meters
So, both sides = k + k = 2k meters
Also, the TOTAL fencing length = 600 m
So, the one side length of the fence = (600 - 2 k) meters
AREA = LENGTH x WIDTH
⇒ A(k) = (600 - 2k) (k)
or, A = -2k² + 600 k
The above equation is of the form: ax² +bx + C
Here: a = - 2 , b = 600 and C = 0
As a< 0, the parabola opens DOWNWARDS.
Here, x value is given as:
Solving for the value of k similarly, we get:
Thus the desired width = k = 150 meters
So, the desired dimensions of the plot is width 150 meters.
And length = 650 - 2k = 650 - 300 = 350 meters.
Since the dice are fair and the rolling are independent, each single outcome has probability 1/15. Every time we choose
We have and
, because the dice are fair.
Now we use the assumption of independence to claim that
Now, we simply have to count in how many ways we can obtain every possible outcome for the sum. Consider the attached table: we can see that we can obtain:
- 2 in a unique way (1+1)
- 3 in two possible ways (1+2, 2+1)
- 4 in three possible ways
- 5 in three possible ways
- 6 in three possible ways
- 7 in two possible ways
- 8 in a unique way
This implies that the probabilities of the outcomes of are the number of possible ways divided by 15: we can obtain 2 and 8 with probability 1/15, 3 and 7 with probability 2/15, and 4, 5 and 6 with probabilities 3/15=1/5
