Make  \(a\)  the subject of  \(k = \dfrac{{a + b}}{{2ab}}\).

Todd is 33 years old and his daughter Amy is 3 years old.   In how many years’ time will Todd be 3 times the age of Amy?

Write \(1.\overline {776} \)  correct to one significant figure.

Calculate the compounded value of investment:
$8000 for 4 months at 6% per annum with interest compounded monthly.

Select the corresponding frequency table for the cumulative frequency graph shown.

Find the median of the scores.

\( \begin{array}{|c|c|} \hline
Score & Frequency \\ \hline
10 & 3 \\ \hline
20 & 8 \\ \hline
30 & 10 \\ \hline
40 & 15 \\ \hline
\end{array} \)

Find the interquartile range of the data represented in box-and-whisker plot.

\( \begin{array}{c|cccccc}
1 & 4 & 8 &&&& \\
2 & 2 & 6 & 9 &&& \\
3 & 0 & 3 & 4 & 7 & 8 & \\
4 & 1 & 2 & 4 &&& \\
\end{array} \)

A six-sided biased die is rolled 20 times and the number appearing uppermost is noted each time. The numbers uppermost on the six-sided die are:

\(4{\rm{ }}1{\rm{ }}6{\rm{ }}3{\rm{ }}5{\rm{ }}1{\rm{ }}4{\rm{ }}6{\rm{ }}3{\rm{ }}2{\rm{ }}5{\rm{ }}1{\rm{ }}6{\rm{ }}5{\rm{ }}2{\rm{ }}4{\rm{ }}2{\rm{ }}3{\rm{ }}5{\rm{ }}2\)

Estimate the experimental probability of rolling a “five” or “six” with this die.

7 cards numbered 2, 3, 4, 5, 6, 7, and 8 are placed in a hat. Two are taken simultaneously. Find the probability that both are odd. Answer to two decimal places.

A bag contains 2 black and 3 white discs. A disc is selected from the bag, its colour is noted, and it is then returned to the bag before a second disc is drawn. Find the probability that the discs have the same colours.