Final answer:
The first statement is false because the ratio does not correctly represent the rate of decrease. The second statement is true because multiplying the decrease in height in 1/2 hour by 2 gives the unit rate in centimeters per hour.
Step-by-step explanation:
The student is looking at how to calculate the rate of change and unit rate in the context of a burning candle.
The statement that the ratio 6 3/4|1/2 describes the rate the candle burns in centimeters per hour is false. The correct ratio should reflect the amount the candle has decreased over a period of time. Since the candle decreases by 10 cm - 6 3/4 cm, which is 3 1/4 cm or 13/4 cm during 1/2 hour, the correct ratio for the rate would be 13/4 per 1/2 hour, not the initial height.
The second statement, that the product 13/4 x 2 can be used to find the unit rate in centimeters per hour, is true. To find a unit rate, we calculate how much the candle decreases in one hour which would involve multiplying the amount it decreased in 1/2 hour (13/4 cm) by 2.
This calculation shows how understanding ratios, proportions, and the concept of a unit rate can be applied to real-world scenarios like burning candles.