A recreational club organized three different groups to visit the zoo.
Group A had 12 adults and 5 children.
Group B had 20 adults and 6 children.
Group C had 16 adults and 3 children.
The information can be represented by the matrix \(\mathbf L=\begin{pmatrix}12&5\\20&6\\16&3\end{pmatrix}\).
The entrance fee for an adult and a child is $49 and $34 respectively. Represent the entrance fees in a \(2\times1\) column matrix \(\mathbf M\).[1]
Evaluate the matrix \(\mathbf C=\mathbf{LM}\).[1]
Evaluate \(\mathbf P=\begin{pmatrix}1&1&1\end{pmatrix}\mathbf C\). State what the elements of \(\mathbf P\) represents.[1]
A map is drawn to a scale of 1 : 250 000.
The Mandai Boardwalk is 3.3 km. Calculate the distance, in centimetres, of the Mandai Broadwalk on the map.[2]
A lake is represented by an area of \(8\text{ cm}^2\) on the map. Calculate the actual area, in square kilometres, of the lake.[2]
Given that \(E\) is 130% of \(D\) and \(\dfrac23E=\dfrac12F\). Express the ratio of \(D:E:F\) in its simplest form.[3]
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Answer:(a)(i) \(\begin{pmatrix}49\\34\end{pmatrix}\) (ii) \(\begin{pmatrix}758\\1184\\886\end{pmatrix}\) (iii) \((2828)\): total fees in dollars. (b)(i) \(1.32\text{ cm}\) (ii) \(50\text{ km}^2\). (c) \(30:39:52\).