Two apples and three peaches cost \($1.35\),  while four apples and nine peaches cost \($3.75\).   Find the cost of each.

Find \(c \), if the vertex of \(y = {x^2} – 6x + c\) is \(\left( {3, – 11} \right)\).

Find the largest angle in the triangle, correcting to the nearest degree.

Ben drove from Town A to Town B, a distance of \( 60 \) km, at an average speed of \( 80 \) km/h. He cycled back at an average speed of \( 20 \) km/h. Find his average speed for the whole journey.
Note that it is not \( \textit{50} \) km/h.

For a “55 days interest-free” credit card, calculate the interest charged on a purchase of \$4900 made on 12 December and repaid on 25 February next year with a purchase interest rate of 17% per annum.

Given the principal is \$4800, the interest rate is 9% per annum and the monthly repayment is \$400, find the principal reduced during the first 2 months.

Cooper takes out a \$76000 home loan. The terms of the loan are 5.1% per annum compounded monthly over 22 years, with monthly repayments.
Find the following, correct to the nearest cent.

The table shows the mean and standard deviation of times in the 100-m by the same group of athletes on four different days. It also shows Kate’s time on each of these days. On what day did Kate give her best performance?

\( \begin {array} {|c|c|c|} \hline
day & mean & standard \ deviation & Kate’s \ time \\ \hline
1^{\text {st}} \ day & 10.22 & 0.16 & 10.15 \\ \hline
2^{\text {nd}} \ day & 10.45 & 0.18 & 10.31 \\ \hline
3^{\text {rd}} \ day & 10.17 & 0.11 & 10.08 \\ \hline
4^{\text {th}} \ day & 10.21 & 0.13 & 10.12 \\ \hline
\end{array} \)

For normally distributed data \(X \sim N\left( {25,{3^2}} \right)\), find the value of \(k\) for \(\Pr \left( {X < k} \right) = 0.348\), correcting to two decimal places.

Calculate the compounded value of investment:
$6000 for 15 months at 4.5% per annum with interest compounded monthly.