Answer:
D) All three have the same correlation coefficient.
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To express the height as a function of the volume and the radius, we are going to use the volume formula for a cylinder: 
where
is the volume
is the radius
is the height
We know for our problem that the cylindrical can is to contain 500cm^3 when full, so the volume of our cylinder is 500cm^3. In other words:
. We also know that the radius is r cm and height is h cm, so 
and 
. Lets replace the values in our formula:
Next, we are going to use the formula for the area of a cylinder:
where
is the area
is the radius
is the height
We know from our previous calculation that, so lets replace that value in our area formula:
By the commutative property of addition, we can conclude that:
where
We know for our problem that the cylindrical can is to contain 500cm^3 when full, so the volume of our cylinder is 500cm^3. In other words:
Next, we are going to use the formula for the area of a cylinder:
where
We know from our previous calculation that
By the commutative property of addition, we can conclude that:
There are ways of drawing a 4-card hand, where
is the so-called binomial coefficient.
There are 13 different card values, of which we want the hand to represent 4 values, so there are ways of meeting this requirement.
For each card value, there are 4 choices of suit, of which we only pick 1, so there are ways of picking a card of any given value. We draw 4 cards from the deck, so there are
possible hands in which each card has a different value.
Then there are total hands in which all 4 cards have distinct values, and the probability of drawing such a hand is