1. **Stating the problem:** We have a histogram with three temperature intervals and their corresponding frequency densities: - $4 \leq t < 6$ with height $x = 3$ - $6 \leq t < 8$ with height $y = 5$ - $8 \leq t < 12$ with height $z = 1$ 2. **Understanding frequency density and histogram bars:** The area of each bar in a histogram represents the frequency for that interval. The area is calculated as: $$\text{Area} = \text{width} \times \text{height}$$ where height is the frequency density. 3. **Calculate the frequency for each interval:** - For $4 \leq t < 6$: $$\text{width} = 6 - 4 = 2$$ $$\text{frequency} = 2 \times 3 = 6$$ - For $6 \leq t < 8$: $$\text{width} = 8 - 6 = 2$$ $$\text{frequency} = 2 \times 5 = 10$$ - For $8 \leq t < 12$: $$\text{width} = 12 - 8 = 4$$ $$\text{frequency} = 4 \times 1 = 4$$ 4. **Summary:** The frequencies for the temperature intervals are: - $4 \leq t < 6$: 6 - $6 \leq t < 8$: 10 - $8 \leq t < 12$: 4 These frequencies represent the counts or occurrences in each temperature range based on the histogram data.