Final answer:
The heating and cooling specialist requires 454.2 feet of duct material in total, but there are only two 5-foot pieces in stock, resulting in a shortfall of 444.2 feet.
Step-by-step explanation:
The student asks a Mathematics question regarding a heating and cooling specialist needing two pieces of duct to buy with lengths of 450 feet and 4 1/5 feet. There are two pieces in stock that are 5 feet long each. We need to calculate the excess material after cutting these lengths from the stock pieces.
First, convert 4 1/5 feet to an improper fraction: 4 1/5 = (4 × 5 + 1)/5 = 21/5 feet. Now, sum the lengths: 450 feet + (21/5) feet = 450 feet + 4.2 feet = 454.2 feet needed in total.
Two pieces of 5 feet stock gives us 10 feet. After cutting off the needed 454.2 feet, this leaves us with:
10 feet - 454.2 feet = -444.2 feet. This is a negative number, indicating that the stock is insufficient by 444.2 feet.