Question: The battery life of some mobile phones was recorded. Some of the results are displayed in the incomplete histogram and frequency table below. Work out the missing value that completes the frequency table. Frequency density graph in the bottom-left: x-axis labeled $\text{Battery life (hours)}$ from $15$ to $35$, y-axis labeled $\text{Frequency density}$; there are two green bars, one over $15 \leq x < 20$ and another over $28 \leq x < 30$. Battery life, $x$ (hours) Frequency $15 \leq x < 20$ $130$ $20 \leq x < 22$ $28$ $22 \leq x < 28$ $300$ $28 \leq x < 30$ [blank]

1. **State the problem:** We need to find the missing frequency for the interval $28 \leq x < 30$ in the frequency table. 2. **Recall the formula for frequency density:** $$\text{Frequency density} = \frac{\text{Frequency}}{\text{Class width}}$$ 3. **Use the histogram information:** The histogram shows frequency densities for intervals. We can use the known frequencies and class widths to find frequency densities for intervals with known data. 4. **Calculate frequency densities for known intervals:** - For $15 \leq x < 20$: - Class width = $20 - 15 = 5$ - Frequency = $130$ - Frequency density = $\frac{130}{5} = 26$ - For $20 \leq x < 22$: - Class width = $22 - 20 = 2$ - Frequency = $28$ - Frequency density = $\frac{28}{2} = 14$ - For $22 \leq x < 28$: - Class width = $28 - 22 = 6$ - Frequency = $300$ - Frequency density = $\frac{300}{6} = 50$ 5. **Use the histogram to find frequency density for $28 \leq x < 30$:** The histogram shows a green bar over $28 \leq x < 30$ with a frequency density of $20$ (estimated from the graph). 6. **Calculate the missing frequency:** - Class width for $28 \leq x < 30$ is $30 - 28 = 2$ - Frequency density = $20$ - Frequency = Frequency density $\times$ Class width = $20 \times 2 = 40$ **Final answer:** The missing frequency for $28 \leq x < 30$ is $40$.