Final answer:
A rate of 5/7 gallons per minute is a unit rate but does not correspond to the ratio 5:7, as the ratio implies a relationship between two different quantities while the rate is a measure of a single quantity per unit of time. The correct answer is false.
Step-by-step explanation:
The question is whether a rate of 5/7 gallons per minute corresponds to the unit rate of 5/7 and if it also corresponds to the ratio 5:7. To clarify these terms, a unit rate is a rate with a denominator of one in a specific context, while a ratio is a relationship between two numbers indicating how many times the first number contains the second.
When we say we have 5/7 gallons per minute, it means that for every minute, 5/7 of a gallon of fluid flows. It is a unit rate because it expresses the amount per one minute. However, it does not correspond to the ratio 5:7. The ratio 5:7 would mean that for every 5 units of one quantity, there are 7 units of another quantity. There is no direct relationship between the two concepts in this context.
Therefore, the answer is false.