Sean is biking with a constant speed towards town B from town A.   With the aid of wind, which has a speed of 2.5 km it takes him only one hour to reach the destination.   However, on the way back to town A he has to bike against the wind, and it takes him three hours to reach town A.   Find Sean’s speed.

Solve   \({9^x} = {3^x} + 6\).

Consider the sequence $7,14,28, \cdots $.   Find the number of terms that are less than $1{\rm{ }}000{\rm{ }}000$.

Find the vertical asymptote(s) of \(f\left( x \right) = \dfrac{1}{{{x^2} + 1}}\).

Find the amplitude and period of \(y = \tan 2x\).

Find the acute angle, correcting to the nearest degree, between the lines:   \(x + 2y = 4\) and \(5x – 2y = 3\).

Find \(\theta \), correcting to the nearest degree, if the area of the triangle is 12 cm².

Find the value of \(k \) that the straight lines \(y = 2kx + 6\) and \(y = \dfrac{x}{4} – 5\) are perpendicular.

Find the financial expectation of a ticket in a raffle.   The raffle has 500 tickets and there is one prize worth 200 dollars.

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

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