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Determine whether each statement is some×, always, or never true. Give an example or a counterexample.

A ratio is a rate.
a) Some×
b) Always
c) Never
d) No answer

1 Answer

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Final answer:

A ratio is some× a rate, meaning that while some ratios can be rates, not all ratios are rates. A rate is a type of ratio with different units or one that represents a quantity changing over time, such as 'miles per hour'. Ratios that don't meet this criterion, such as the comparison of the width and length of a rectangle, are not rates.

Step-by-step explanation:

The student asks whether a ratio is always a rate. To answer this question, it's important to understand the definitions of both terms. A ratio is a comparison of two quantities, which can be expressed in different forms like fractions, with a colon, or with the word "to" (for example, 2/3, 2:3, or "2 to 3"). On the other hand, a rate is a specific type of ratio where the two quantities being compared have different units, and often it represents how one quantity changes in relation to another per unit of measure.

A rate is a ratio when it compares two different units, such as miles per hour or price per item. However, not all ratios are rates because they might not involve different units or a change per unit measure. An example of a ratio that is not a rate is comparing the number of apples to oranges in a fruit bowl (e.g., 3 apples to 2 oranges).

The correct answer to the question is some. This means that while some ratios are rates, not all of them are. An example of a ratio that is a rate would be going 60 miles in 1 hour (60 mph), and a counterexample would be the ratio of the width to the length of a rectangle, which isn't necessarily a rate because it doesn't involve a change over time or different units.

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