Is the simplified form of 2square root of 3 ⋅ square root of 12 rational?
1 answer:
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First check for the critical points of <em>f</em> by checking where the first-order derivatives vanish.
Notice how the point (1, 2) lies on the line <em>y</em> = 2<em>x</em> ; at this point, we get a value of <em>f</em>(1, 2) = -5 (MIN).
Next, check the points where the boundary lines intersect, which occurs at the points (0, 0), (0, 2), and (1, 2). We already checked the last one. We find <em>f</em>(0, 0) = 1 (MAX) and <em>f</em>(0, 2) = -3.
Now check on the boundary lines themselves. If <em>x</em> = 0, then
which has a maximum value of -3 when <em>y</em> = 2 (so we get the same critical point as before).
If <em>y</em> = 2, then
with a maximum of -5 when <em>x</em> = 1.
If <em>y</em> = 2<em>x</em>, then
with the same maximum of -5 when <em>x</em> = 1.
Answer:
The number of people, of the twelve, who will win a prize is 5.
Step-by-step explanation:
In a standard deck of cards there are 52 cards.
The 52 cards are divided into 4 suits: Hearts, Diamonds, Spades and Clubs, each of 13 cards.
Each of the 12 people draws 2 cards from their standard deck of cards.
Compute the probability of selecting at least 1 diamond as follows:
P (At least 1 diamond) = 1 - P (No diamond)
The probability of selecting at least 1 diamond is 0.4412.
If a person draws at least 1 diamond he wins a prize.
The expected number of people who will win the prize is:
E (Wins a prize) = n × P (At least 1 diamond)
Thus, the number of people of the twelve who will win a prize is 5.