Permutation :The number of ways to choose a sample of r elements from a set of n distinct objects where order does matter and replacements are not allowed.

$nPr = \frac{n!}{(n-r)!}$

Factorial : There are n! ways of arranging n distinct objects into an ordered sequence.

Considering a situation when n = r in a permutation, nPr reduces to n!, a simple factorial of n.

Proof: 3P3 = 3!

n = 3 and r = 3

$3P3 = \frac{3!}{(3-3)!}$

$3P3 = \frac{3!}{(0)!}$

But 0! = 1

3P3 = 3!

3 0

3 years ago

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What is the area of the trapezoid to the nearest tenth? <br> PICTURE BELOW ⬇⬇⬇⬇

Nastasia [14]

Answer:

62.4 ft²

Step-by-step explanation:

The unmarked horizontal dimension at the bottom of the triangle is ...

(8 ft)sin(30°) = 4 ft

The unmarked vertical dimension of the triangle (the height of the trapezoid) is ...

(8 ft)cos(30°) ≈ 6.93 ft

Then the area of the trapezoid is given by the formula ...

A = (1/2)(b1 +b2)h

A = (1/2)((4 ft+7 ft) +(7 ft))(6.93 ft) ≈ 62.4 ft²

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The mnemonic SOH CAH TOA can remind you of the relationships between right triangle dimensions and angles.

Sin = Opposite/Hypotenuse ⇒ Hypotenuse×Sin = Opposite

Cos = Adjacent/Hypotenuse ⇒ Hypotenuse×Cos = Adjacent

6 0

3 years ago