Final answer:
The correct answer is 'b. No, because an equivalent ratio is not specified.' This is because an equivalent ratio means that the two ratios can be expressed as the same when either simplified or scaled, and in this case, no other ratio is specified that can be directly compared to 4:7.
Step-by-step explanation:
In order to determine if Matthew's training session consisted of an equivalent ratio of the distance he ran to the distance he cycled, we need to understand what constitutes an equivalent ratio. An equivalent ratio essentially means the two ratios can be simplified or can be scaled up or down to become the same exact ratio. For example, if he had run 2 miles and cycled 3.5 miles, that would have been an equivalent ratio to 4:7 because both 2:3.5 and 4:7 simplify to the same ratio when you double the numbers in the first ratio (2x2:3.5x2=4:7).
Given that Matthew ran 4 miles and cycled 7 miles, his ratio of running to cycling is 4:7. This is not an equivalent ratio to any other unless we are discussing a ratio that can be simplified to or expanded from 4:7. Therefore, the correct choice is: b. No, because an equivalent ratio is not specified. The training session's ratio is unique to itself and does not imply there is an equivalent ratio simply because the two distances have a specific ratio.