What is the area of triangle PQR? Round to the nearest tenth of a square unit.

Mathematics

2 answers:

larisa86 [58]3 years ago

7 0

ANSWER

111.3 square units.

EXPLANATION

The formula for calculating the area of a triangle is.

$Area = \frac{1}{2} \times base \times height$
Let us the side of the triangle with side 12 units to be the base of the triangle.

Then the height of the triangle can be determined from the diagram using trigonometry.

$\sin(68 \degree) = \frac{height}{20 }$

$height = 20 \sin(68 \degree)$

$height = 18.54$

We now plug in the values in to the formula to obtain,

$Area = \frac{1}{2} \times 12 \times 18.54$

$Area = 111.3 \: square \: units$

See graph

joja [24]3 years ago

6 0

111.3 square units according to e2020

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I'm assuming a 5-card hand being dealt from a standard 52-card deck, and that there are no wild cards.

A full house is made up of a 3-of-a-kind and a 2-pair, both of different values since a 5-of-a-kind is impossible without wild cards.

Suppose we fix both card values, say aces and 2s. We get a full house if we are dealt 2 aces and 3 2s, or 3 aces and 2 2s.

The number of ways of drawing 2 aces and 3 2s is

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and the number of ways of drawing 3 aces and 2 2s is the same,

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so that for any two card values involved, there are 2*24 = 48 ways of getting a full house.

Now, count how many ways there are of doing this for any two choices of card value. Of 13 possible values, we are picking 2, so the total number of ways of getting a full house for any 2 values is

$2\dbinom{13}2\dbinom42\dbinom43=3744$