A discrete variable is the one where the values taken by it are possible to count (usually the values are natural numbers)
On the other side, a continuous variable is the one that has an uncountable number of values. (usually the values are real numbers)
Considering these definitions we get:
a)The batting average of Joe’s favorite player is a continuous variable: True, this average can take any number among the real numbers.
b) The number of hot dogs that Joe bought is a discrete variable: True, Joe can only buy 1, 2, 3, 4... hot dogs, this set is countable and therefore is a discrete variable.
c) The number of strikeouts in the game is a continuous variable: False, the strikeouts are natural numbers (1, 2, 3, 4...) and therefore are countable and they are a discrete variable.
d) The Quakes standings in the league is a discrete variable: True. The standing of a team in a league is a discrete variable since it can be 1st place, 2nd place... and therefore it's countable.
Now, we can write the equation of that relates length and width:
(Equation #1)
The area of the yard can be expressed as (using equation #1 into #2):
(Equation #2)
Since the Area of the yard is , then equation #2 turns into:
Now, we rearrange this equation:
We can divide the equation by 5 :
We need to find the solution for this quadratic. Let's find the factors of 160 that multiplied yields -160 and added yields -12. Let's choose -20 and 8, since and . The equation factorised looks like this:
Therefore the possible solutions are W=20 and W=-8. We discard W=-8 since width must be a positive number. To find the length, we substitute the value of W in equation #1:
Therefore, the dimensions of the yard are W=20ft and L=40ft.