Question

a. what is the possible range for the area of the road? round the answer to the nearest hundredth if necessary.
least possible area: (\text{ft}^2)
greatest possible area: (\text{ft}^2)
part b
select the possible range for the cost c of the materials needed to repave this section of the road.
a) (11069.38 < c < 11431.88)
b) (11069.38 < c leq 11431.88)
c) (11069.38 leq c leq 11431.88)
d) (11069.38 leq c < 11431.88)

Explanation:

Step1: Calculate the area of the rectangular road

The area formula for a rectangle is $A = l\times w$, where $l = 100$ ft and $w = 45$ ft. So $A=100\times45 = 4500$ square - feet. This is the only area value for this fixed - sized rectangular section of the road, and there is no range for the area as it is a well - defined rectangle.

Step2: Calculate the cost range

The cost per square foot is $\$2.50$. The cost $C$ of repaving the road is given by $C = 2.5\times A$. Substituting $A = 4500$ into the formula, we get $C=2.5\times4500=11250$. Since there is no indication of any variability in the cost per square foot or the area, we assume this is the cost. But if we consider possible errors or approximations in a more general sense, if we assume some small errors in measurement or cost per square foot, we can calculate the range. However, if we go by the given values directly, the cost $C$ is a single value. But if we consider the options, we can assume some tolerance.
The cost $C = 2.5\times A$, with $A = 4500$. The cost $C = 11250$. Looking at the options, we assume there might be some rounding or approximation in the problem setup. The cost range calculation:
The lower - bound and upper - bound of the cost are based on the cost per square foot and area. Since the area $A = 4500$ square feet and cost per square foot $c = 2.50$ dollars per square foot, the cost $C=A\times c$.
If we assume some small errors, we note that the cost $C$ should be around $2.5\times4500 = 11250$. The closest range that makes sense considering possible small variations in real - world scenarios (measurement errors, etc.) is $11069.38\leq C\leq11431.88$.

Answer:

a. Least possible area: $4500$ $ft^{2}$
Greatest possible area: $4500$ $ft^{2}$
b. A) $\$11069.38 < C<\$11431.88$