Normal or natural variations in the quality of production output that are due purely to chance are _____.

Mathematics

1 answer:

nydimaria [60]2 years ago

6 0

Normal or natural variations in the quality of production output that are due purely to chance are common causes.

According to the statement

we have to tell about the that cause which effect the quality and production output in the normal and natural variation.

So, For this purpose, we know that the

Common cause variation is present when the control chart of a process measure shows a random pattern of variation with all points within the control limits. When a control chart shows common cause variation, a process measure is said to be in statistical control or stable.

And due to this cause there is a lot of effect on the natural variations in the quality of production output.

So, Normal or natural variations in the quality of production output that are due purely to chance are common causes.

Learn more about common cause variation here

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The quotient of (x^3+3x^2-4x-12)/(x^2+5x+6)

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Answer: The quotient is (x-2).

Step-by-step explanation:

Since we have given that

$f(x)=(x^3+3x^2-4x-12)\\\\and\\\\g(x)=x^2+5x+6\\\\So,\ \frac{\left(x^3+3x^2-4x-12\right)}{\left(x^2+5x+6\right)}$

Now, we have to find the quotient of the above expression.

So, here we go:

$Factorise\ (x^3+3x^2-4x-12)\\\\=\left(x^3+3x^2\right)+\left(-4x-12\right)\\\\=-4\left(x+3\right)+x^2\left(x+3\right)\\\\=\left(x+3\right)\left(x^2-4\right)$

Now, we will divide the above simplest form with g(x):

$\frac{\left(x+3\right)\left(x^2-4\right)}{\left(x+2\right)\left(x+3\right)}\\\\=\frac{x^2-4}{x+2}\\\\=\frac{\left(x+2\right)\left(x-2\right)}{x+2}\ using\ (a^2-b^2)=(a+b)(a-b)\\\\=x-2$