Answer:
a. .0125
Step-by-step explanation:
For each part, there are only two possible outcomes. Either it is defective, or it is not. The probability of a part being defective is independent of any other part. This means that the binomial probability distribution is used to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
In which 
is the number of different combinations of x objects from a set of n elements, given by the following formula.
And p is the probability of X happening.
2% defective parts.
This means that 
A sample of nine parts from the production process is selected.
This means that 
What is the probability that the sample contains exactly two defective parts?
This is P(X = 2).
0.0125 = 1.25% probability that the sample contains exactly two defective parts. The correct answer is given by option a.
V=x(8-2x)(10-2x) or expanded
V=x(4x^2-36x+80)
V=4x^3-36x^2+80x
...
If you were to graph the above equation for V(x) you will see a maximum point where the "y" value is maximized, but be careful as V will increase without bound at values of x that are not part of the domain, ie, in this case x<8/2, x<4 to have any meaning...The proper domain of this function is:
x=(0,4), Mathematically finding this point quickly is by differentiating it with respect to x...
dV/dx=12x^2-72x+80, The maximum volume will occur when dV/dx=0 and the x value is within the correct domain...
12x^2-72x+80=0 (using the quadratic formula for ease)
x=(72±√1344)/24, and since x<4
x≈1.472in (to the nearest one thousandth of an inch)
The 1st expression is the only one that reproduces the terms being added.
Answer:
Find the horizontal asymptotes by comparing the degrees of the numerator and denominator.
Vertical Asymptotes:
x
=
−
2
,
7
Horizontal Asymptotes:
y
=
0
No Oblique Asymptotes
Step-by-step explanation:
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