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------------------------------------------------ Each inch on an engineer's scale is divided into 10 increments that represent 1¢. A line measured with an engineer's scale that is 3 inches plus 3 increments would be:

a) 30¢
b) 33¢
c) 36¢
d) 39¢

(b) 33¢. Using an engineer's scale where each inch represents 10¢, a line measured as 3 inches plus 3 increments would total 33¢, since three inches equates to 30¢ and the three additional increments add another 3¢.

Explanation:

The student has asked how to represent a line that is measured as 3 inches plus 3 increments using an engineer's scale where each inch is divided into 10 equal segments and each segment represents 1 cent (¢). To calculate the total representation in cents, we need to simply add up the cents represented by the inches and increments. Each inch is 10¢, so 3 inches would be 30¢. Each increment represents 1¢, and since we have 3 increments, this gives us an additional 3¢. Hence, the total representation is 33¢ (30¢ from the inches plus 3¢ from the increments).

To put it into a simple equation:

3 inches * 10¢/inch + 3 increments * 1¢/increment = 30¢ + 3¢ = 33¢

Therefore, the correct answer is (b) 33¢.