Final answer:
To determine the number of signs needed for an 8.4-mile-long trail, with signs 1.4 miles apart, you divide the trail length by the sign spacing and add one extra for the starting point, totaling 7 signs.
Step-by-step explanation:
The student's question pertains to determining the number of signs needed for a hiking trail in a state park. With the trail being 8.4 miles long and signs to be placed every 1.4 miles, we must calculate the total number of 1.4-mile segments along the trail. Since we also need signs at both the beginning and the end of the trail, we will add those in our calculation.
We start by dividing the total length of the trail by the distance between signs: 8.4 miles ÷ 1.4 miles per sign = 6 signs. However, because we need a sign at the very beginning as well, we add one more sign to this count, resulting in 6 + 1 = 7 signs in total required for the trail.