MathDB

5

Part of 2018 MIG

Problems(2)

2018 Individual #5

Source:

5/5/2022
Some of the values produced by two functions, f(x)f(x) and g(x)g(x), are shown below. Find f(g(3))f(g(3)) \begin{tabular}{c||c|c|c|c|c} xx & 1 & 3 & 5 & 7 & 9 \\ \hline\hline f(x)f(x) & 3 & 7 & 9 & 13 & 17 \\ \hline g(x)g(x) & 54 & 9 & 25 & 19 & 44 \end{tabular}
<spanclass=′latex−bold′>(A)</span>3<spanclass=′latex−bold′>(B)</span>7<spanclass=′latex−bold′>(C)</span>8<spanclass=′latex−bold′>(D)</span>13<spanclass=′latex−bold′>(E)</span>17<span class='latex-bold'>(A) </span>3\qquad<span class='latex-bold'>(B) </span>7\qquad<span class='latex-bold'>(C) </span>8\qquad<span class='latex-bold'>(D) </span>13\qquad<span class='latex-bold'>(E) </span>17
2018 Individual
2018 Team #5

Source:

1/18/2023
A fair six sided die is rolled to give a number nn. A fair two sided coin is then flipped n2n^2 times. Find the expected number of heads flipped. Express your answer as a common fraction.
2018 Team