In a year-long music course, you are required to attend 12 concerts. Last season, the lengths of the concerts were 92, 101, 98,
112, 80, 119, 92, 90, 116, 106, 78, and 65 minutes. Find the five-number summary for the data. Which boxplot would best represent the data?
1 answer:
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If 
is true, then 
is false, which in turn means 
is true.
If is false, then is true, and so is false.
So, because
in both cases, the statement is a tautology (always true).
If you were to put this in a table, you would have one column each for
. In the first column () you can think of as an independent variable that can only take two values, true and false. In the next column (), you would negate the value in the previous column. And so on.
It should roughly look like this:
p ... ~p ... ~(~p)
T ... F ... T
F ... T ... F
If
So, because
If you were to put this in a table, you would have one column each for
It should roughly look like this:
p ... ~p ... ~(~p)
T ... F ... T
F ... T ... F
ANSWER
672cm²
EXPLANATION
The area of a regular hexagon is given by the formula,
where a=14cm is the apothem and p=96cm is the perimeter of the regular hexagon.
We substitute the values into the formula,
Therefore the approximate area of the hexagon is 672cm²