Plug in the volume and radius into the formula, then multiply.
Answer:
(a) 0.09
(b) 0.06
(c) 0.0018
(d) 0.9118
(e) 0.03
Step-by-step explanation:
Let <em>A</em> = boards have solder defects and <em>B</em> = boards have surface defects.
The proportion of boards having solder defects is, P (A) = 0.06.
The proportion of boards having surface-finish defects is, P (B) = 0.03.
It is provided that the events A and B are independent, i.e.

(a)
Compute the probability that either a solder defect or a surface-finish defect or both are found as follows:
= P (A or B) + P (A and B)

Thus, the probability that either a solder defect or a surface-finish defect or both are found is 0.09.
(b)
The probability that a solder defect is found is 0.06.
(c)
The probability that both defect are found is:

Thus, the probability that both defect are found is 0.0018.
(d)
The probability that none of the defect is found is:
![P(A^{c}\cup B^{c})=1-P(A\cup B)\\=1-P(A)-P(B)+P(A\cap B)\\=1-P(A)-P(B)+[P(A)\times P(B)]\\=1-0.06-0.03+(0.06\times0.03)\\=0.9118](https://tex.z-dn.net/?f=P%28A%5E%7Bc%7D%5Ccup%20B%5E%7Bc%7D%29%3D1-P%28A%5Ccup%20B%29%5C%5C%3D1-P%28A%29-P%28B%29%2BP%28A%5Ccap%20B%29%5C%5C%3D1-P%28A%29-P%28B%29%2B%5BP%28A%29%5Ctimes%20P%28B%29%5D%5C%5C%3D1-0.06-0.03%2B%280.06%5Ctimes0.03%29%5C%5C%3D0.9118)
Thus, the probability that none of the defect is found is 0.9118.
(e)
The probability that the defect found is a surface finish is 0.03.
Answer:
Option D, (x + 2)(x - 6)
Step-by-step explanation:
<u>Step 1: Factor
</u>
x^2 - 4x - 12
x^2 - 6x + 2x - 12
(x - 6)(x + 2)
(x + 2)(x - 6)
Answer: Option D, (x + 2)(x - 6)
There seems to be a flaw with this question because it says that there are five x-intercepts but the given information only gives you 4 x-intercepts to work with.
Even means the graph is symmetric about the y-axis
The best answer is <span>A.(–6, 0), (–2, 0), and (0, 0)
because you do not have to worry about another point (0,0). Plus we need (-6,0) for it to be symmetric with (6,0).
Consider function f(x) = x²(x-6)(x+6)(x+2)</span>²(x-2)<span>². It is even and fits these conditions as it has x-intercepts at (6,0), (-6,0), (-2,0), (2,0), and (0,0). again, the question does not tell us the fifth x-intercept, so we need to assume that there is another one that needs to be there...and so (-2,0) must have (2,0) for it to be even as well.</span>