Problem
Lesson 1: Starter 1. $\$ 6000$ is invested in an account that earns simple interest at the rate of $3.5 \%$ per annum. What is the total interest earned in the first four years is? 2. A car is travelling at $95 \mathrm{~km} / \mathrm{h}$. How far will it travel in 2 hours and 30 minutes? 3. Each student in a class is given a packet of lollies. The teacher records the number of red lollies in each packet using a frequency table. \begin{tabular}{|c|c|} \hline $\begin{array}{c}\text { Number of red lollies } \\ \text { in each packet }\end{array}$ & Frequency \\ \hline 0 & 2 \\ \hline 1 & 4 \\ \hline 2 & 2 \\ \hline 3 & 7 \\ \hline 4 & 3 \\ \hline 5 & 1 \\ \hline \end{tabular} What is the relative frequency of a packet of lollies containing more than 3 red lollies? 4. Minjy invests $\$ 2000$ for 2 years. The simple interest is calculated at a rate of $6 \%$ per annum. V is the total value of the investment at the end of this period? 5. The blood alcohol content (BAC) of a male's blood is given by the formula; \[ B A C_{\text {male }}=\frac{10 N-7.5 \mathrm{H}}{6.8 M}, \text { where } \] $N$ is the number of standard drinks consumed, $\boldsymbol{H}$ is the number of hours drinking and $M$ is the person's mass in $\mathrm{kgs}$. Calculate the BAC of a male who consumed 4 standard drinks in $3.5 \mathrm{hrs}$ and weighs $68 \mathrm{kgs}$ to 2 decimal places. 3
Solution
Step 1 ：1. Calculate the total interest earned in the first four years using the formula I = P * R * T: \(I = 6000 * 0.035 * 4\)
Step 2 ：2. Calculate the distance the car will travel in 2 hours and 30 minutes using the formula Distance = Speed * Time: \(Distance = 95 * 2.5\)
Step 3 ：3. Calculate the relative frequency of a packet of lollies containing more than 3 red lollies: \(\frac{4}{19}\)
Step 4 ：4. Calculate the total value of Minjy's investment at the end of 2 years using the formula for simple interest and adding it to the principal amount: \(V = 2000 + (2000 * 0.06 * 2)\)
Step 5 ：5. Calculate the BAC of a male using the given formula and values for N, H, and M: \(BAC_{male} = \frac{10 * 4 - 7.5 * 3.5}{6.8 * 68}\)
