Answer:
The original piece of wood is 108 cm
Step-by-step explanation:
From the given ratio, the shortest is of the ratio 5 and the longest is of the ratio 7
Let the original piece of wood be x
so the sum of the ratios will be;
5 + 6 + 6 + 7 = 24
the shortest length would be 5/24 * x
= 5x/24
the longest will be 7/24 * x = 7x/24
From the question;
7x/24 -5x/24 = 9
(7x-5x) = 24(9)
2x = 24(9)
x = (24 * 9)/2
x = 108 cm
Since f(g(x)) = g(f(x)) = x, hence the function f(x) and g(x) are inverses of each other.
<h3>Inverse of functions</h3>
In order to determine if the function f(x) and g(x) are inverses of each other, the composite function f(g(x)) = g(f(x))
Given the function
f(x)= 5-3x/2 and
g(x)= 5-2x/3
f(g(x)) = f(5-2x/3)
Substitute
f(g(x)) = 5-3(5-2x)/3)/2
f(g(x)) = (5-5+2x)/2
f(g(x)) = 2x/2
f(g(x)) = x
Similarly
g(f(x)) = 5-2(5-3x/2)/3
g(f(x)) = 5-5+3x/3
g(f(x)) = 3x/3
g(f(x)) =x
Since f(g(x)) = g(f(x)) = x, hence the function f(x) and g(x) are inverses of each other.
Learn more on inverse of a function here: brainly.com/question/19859934
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Answer:
Type I error.
Step-by-step explanation:
The decision to shut the process is triggered by the conclusion that the average height is significantly different from 66 mm.
This means that the null hypothesis, that states that the average height is not significantly different from 66 mm (μ=66), has been rejected.
If the null hypothesis is rejected, the error that can have been made is to reject a true null hypothesis, when the process is functioning to specification and the average length is not significantly different from 66.
This is a Type I error, that happens when a true null hypothesis is rejected.
Answer:
I'm bout to roast yo old potatoe head looking a*s