<span>0.002
For 6 systems with exactly 3 failures, you need to calculate 6 pick 3 or 6!/(3!3!) = 720/(6*6)=720/36=20 different combinations of 3 systems to fail. Now the probability of each of those failures will be the probability of the subsystems not failing times the probability of the subsystems fail. So 0.95^3 * 0.05^3 for 3 subsystem not failing time 3 subsystems failing. So 0.95^3 * 0.05^3 = 0.857375*0.000125 = 0.000107172. And multiply by the 6 pick 3 calculated earlier, gives.
0.000107172 * 20 = 0.002143438
And rounding to the nearest thousandth, gives 0.002</span>
Answer:
Statement 1
The graph has a minimum.
This statement is true. The graph has a minimum at x = -1 that is f(-1) = -9.
Statement 2
The graph has a maximum.
The statement is false. As there is no downward curve nor a rigid endpoint but the graph is continuous in upward direction.
Statement 3
The graph has zeros of -4 and 2.
The statement is true because f(-4) = 0 and f(2) = 0.
Statement 4
The vertex is located at (-1, -9).
The statement is true as apparent in the graph.
Statement 5
The solution of the quadratic function represented by the graph is (-1, -9).
The statement is false. Solution of the graph is at the point where f(x) becomes zero. At (-1,-9), f(x) = -9. Hence solution is not at point (-1,-9).
Statement 6
The y-intercept of the graph is (0, -8).
The statement is true. y-intercept of a graph is where the graph intercept the y-axis which means x = 0. As x = 0 at (0, -8), it is the y-intercept of the graph.
A). |x| = |-x|
This is always true.
The definition of 'absolute' value is 'size of the number without its sign'.
That's what this expression says.
b). |x| = -|x|
This is never true, because an absolute value is never negative.
This one would true if x=0 . So maybe some people might say
it's sometimes true, but that doesn't feel right to me. I say never.
c). |-x| = -|x|
This looks to me like exactly the same situation as (b),
and I would say all the same things about it.
<span>three million twenty eight thousand two=3,028,002
</span>
