Hi guys, I'm struggling quite a bit on the 2017 NHT Exam 2.
I was wondering how to do MC Q8, Q11, Q18 and Q19. Thanks heaps!
8 ) We can find the area under the curve from x = -a to x = a
(0.5a)a - (0.5)(0.5a)a = a^2)
Essentially, the left hand side (the sloped line) of the function is cancelled out, because if you think about it, the average value in this region is 0!
Recall the average value is the value of y which forms a rectangle from x = -a to x = a, and the area of that rectangle is equivalent to the net signed area of f from x = -a to x = a.
So the average value can be given by y in:
Solving for y gives us the average value of a/2.
You can also set up a hybrid function and use the average value formula
 \space dx)
11) Let X = number of blue marbles. We want:
}=\Pr{(\hat{P}=\frac{3}{4})}+\Pr{(\hat{P}=\frac{4}{4})})
As per sampling from a
small population, we can write
}+\Pr{(\hat{P}=\frac{4}{4})}=\frac{\binom{5}{3}\binom{4}{1}}{\binom{9}{4}}+\frac{\binom{5}{4}\binom{4}{0}}{\binom{9}{4}})
Which should give you option C.
18) HINT: First, find the derivative f'(x). Then, recall the factor theorem. What does it mean that (x+2) is a factor of f'(x)? It means that when we substitute x=-2, we get 0 i.e. f'(-2)=0.
19) The probability we want is
}=\frac{\Pr{(D>8 \cap D>7)}}{\Pr{(D>7)}}=\frac{\Pr{(D=9)}}{\Pr{(D=8)}+\Pr{(D=9)}})
Now we use the formula given in the question
}}{\Pr{(D=8)}+\Pr{(D=9)}}=\frac{\log_{10}{(1+\frac{1}{9})}}{\log_{10}{(1+\frac{1}{8})}+\log_{10}{(1+\frac{1}{9})}} \\<br />=\frac{\log_{10}{\frac{10}{9}}}{\log_{10}{\frac{5}{4}}})
which after a bit of manipulation (hint: subtracting logs with the same logs means you divide what's in the brackets) should give option B.
Hope this helps! Please post if you're still stuck
Urgent question; my bound reference isn't really A4 when closed cause its thickness makes some pages jut out. Will it be allowed?
How badly do they stick out? Is the book now bigger than A4? If it's bigger than A4 - it's technically a breach of the rules for bound references. I would try to reduce the size if possible. Are you able to cut the end bits off?
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