<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>
Before I put out my answer, I just want make note that sec() = 1 / cos() and csc () = 1 / sin ()
1) Once you distribute cos()sin() to sec(), the cos() will cancel out with the sec() to make it just sin(), and once cos()sin() is distributed to csc(), the sin() will cancel out with the cos()
2) After doing that you should just be left with sin() + cos()
3) And since no more simplification can be done, that is your answer :D
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Answer:
A) x² + 2x + 6
B) x² + 2x - 7
C) ¼(x²+2x+1))
D) 6x²+12x+6
E) -x²-2x-1
Step-by-step explanation:
A) f(x) + 5 =x²+2x+1 + 5
= x² + 2x + 6
B) f(x)-8,=x^2+2x+1-8
= x² + 2x - 7
C) ¼f(x) = ¼(x²+2x+1)
D) 6f(x) = 6(x²+2x+1) = 6x²+12x+6
E) -f(x) = -(x²+2x+1) = -x²-2x-1
