A rectangular prism has a base area of 24 cm² and a height of 5 cm. Calculate its volume. A swimming pool in the shape of a rectangular prism has a volume of 600 m³. The length is 20 m and the width i

The volume of the prism is $\boxed{\text{}120 \text{ cm}^3\text{}}$

12. A swimming pool in the shape of a rectangular prism has a volume of $600 \text{ cubic metres}$. The length is $20 \text{ metres}$ and the width is $15 \text{ metres}$.

a) Determine the depth of the pool.

$\text{Volume} = \text{Length} \times \text{Width} \times \text{Depth}$.
We are given the volume, length, and width, and need to find the depth.

The depth of the pool is $\boxed{\text{}2 \text{ m}\text{}}$

b) Explain how you used the volume formula to find the depth.

I used the formula for the volume of a rectangular prism, $\text{Volume} = \text{Length} \times \text{Width} \times \text{Depth}$. I substituted the known values for the volume, length, and width, and then rearranged the formula to solve for the unknown depth by dividing the volume by the product of the length and width.

c) If the pool needs to be drained and refilled, and it takes 2 hours to fill 100 cubic metres, how long will it take to fill the entire pool? Show your working.

We are given that it takes 2 hours to fill $100 \text{ m}^3$.

It will take $\boxed{\text{}12 \text{ hours}\text{}}$ to fill the entire pool.

13. A school collected data on student attendance over a term. The data shows (in percentages): 95, 92, 88, 95, 90, 87, 95, 91.

a) Calculate the mean, median, and mode for this data.

87, 88, 90, 91, 92, 95, 95, 95.
There are $n=8$ data points.

Since there are 8 data points (an even number), the median is the average of the two middle values (the 4th and 5th values).
The ordered data is: 87, 88, 90, 91, 92, 95, 95, 95.

The mode is the value that appears most frequently.
In the data set (87, 88, 90, 91, 92, 95, 95, 95), the value 95 appears three times, which is more than any other value.

The mean is $\boxed{\text{}91.625\text{}}$, the median is $\boxed{\text{}91.5\text{}}$, and the mode is $\boxed{\text{}95\text{}}$

b) Analyse which measure of central tendency best represents the typical attendance rate.

The median or the mean would best represent the typical attendance rate. The mode (95%) is the most frequent attendance, but it might not be typical if other values are spread out. The mean (91.625%) gives an average, while the median (91.5%) represents the middle value, less affected by extreme values if they were present. Given the data, all three are quite close.

c) Justify your choice with reference to the data.

I would choose the median (91.5%) as the best representation. The data set is fairly symmetrical without extreme outliers, and the median is robust to any potential skewness or outliers. While the mean (91.625%) is very close, the median provides a clear central point of the ordered data. The mode (95%) is the most frequent, but it's at the higher end of the data, and not necessarily the "typical" central value.