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3 years ago

6

Evelyn has a first name, 2 middle names, and a last name. In how many different ways could Evelyn arrange the initials of her na

me?

1 answer:

tatyana61 [14]3 years ago

4 0

Answer:

4! = 4×3×2×1= 24

in 24 different ways

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50%

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Which is the inverse of the function a(d)=5d-3? And use the definition of inverse functions to prove a(d) and a-1(d) are inverse

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Given

$a(d) = 5d - 3$

Solving (a): Write as inverse function

$a(d) = 5d - 3$

Represent a(d) as y

$y = 5d - 3$

Swap positions of d and y

$d = 5y - 3$

Make y the subject

$5y = d + 3$

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Replace y with a'(d)

$a'(d) = \frac{d}{5} + \frac{3}{5}$

Prove that a(d) and a'(d) are inverse functions

$a'(d) = \frac{d}{5} + \frac{3}{5}$ and $a(d) = 5d - 3$

To do this, we prove that:

$a(a'(d)) = a'(a(d)) = d$

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$a(a'(d)) = a(\frac{d}{5} + \frac{3}{5})$

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$a(a'(d)) = \frac{5d}{5} + \frac{15}{5} - 3$

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$a(a'(d)) = d$

Solving for: $a'(a(d))$

$a'(a(d)) = a'(5d - 3)$

Substitute 5d - 3 for d in $a'(d) = \frac{d}{5} + \frac{3}{5}$

$a'(a(d)) = \frac{5d - 3}{5} + \frac{3}{5}$

Add fractions

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$a(a'(d)) = a'(a(d)) = d$

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