Question

b. select the possible range for the cost, c, of the materials needed to repave this section of the road.
a) $11,069.38 < c < $11,431.88
b) $11,069.38 ≥ c > $11,431.88
c) $11,069.38 ≤ c ≤ $11,431.88
d) $11,069.38 ≤ c < $11,431.88

Explanation:

Step1: Analyze Cost Range Logic

In cost estimation, the lower bound is included (since it's the minimum possible cost) and the upper bound is not included (or included depending on precision, but here we check the inequality signs). The correct range should have the cost \( c \) at least the minimum (\( \$11,069.38 \)) and less than the maximum (\( \$11,431.88 \)) or with appropriate inclusion. Wait, actually, for a range of possible costs, if the minimum is \( \$11,069.38 \) (inclusive) and maximum is \( \$11,431.88 \) (exclusive), the inequality is \( \$11,069.38 \leq c < \$11,431.88 \), which is option D. Wait, let's re - check the options:

Option A: \( \$11,069.38 < c < \$11,431.88 \) (excludes the minimum, which is not right as the minimum cost could be exactly \( \$11,069.38 \))

Option B: \( \$11,069.38 \geq c > \$11,431.88 \) (illogical, since \( c \) can't be both greater than \( \$11,431.88 \) and less than or equal to \( \$11,069.38 \))

Option C: \( \$11,069.38 \leq c \leq \$11,431.88 \) (includes the maximum, but maybe the maximum is not reachable, but wait, maybe I made a mistake. Wait, no, the key is the inequality signs. Wait, the correct range for a cost that is at least the minimum (inclusive) and at most the maximum (exclusive or inclusive). But in typical cost ranges, if the minimum is \( \$11,069.38 \) (you can spend at least that) and less than \( \$11,431.88 \) (you can't spend more than or equal to that), then the correct inequality is \( \$11,069.38 \leq c < \$11,431.88 \), which is option D. Wait, no, let's check the options again:

Wait the options are:

A) \( \$11,069.38 < c < \$11,431.88 \)

B) \( \$11,069.38 \geq c > \$11,431.88 \)

C) \( \$11,069.38 \leq c \leq \$11,431.88 \)

D) \( \$11,069.38 \leq c < \$11,431.88 \)

So, the cost \( c \) should be at least \( \$11,069.38 \) (so \( c\geq\$11,069.38 \)) and less than \( \$11,431.88 \) (so \( c < \$11,431.88 \)). So combining these, we get \( \$11,069.38 \leq c < \$11,431.88 \), which is option D.

Step2: Eliminate Incorrect Options

• Option A: Excludes the minimum cost value (\( \$11,069.38 \)), which is incorrect because the cost could be exactly \( \$11,069.38 \).
• Option B: The inequality is ill - formed as it requires \( c \) to be both greater than \( \$11,431.88 \) and less than or equal to \( \$11,069.38 \), which is impossible.
• Option C: Includes the upper bound (\( \$11,431.88 \)) as a possible cost, but if the range is "possible" and the upper limit is not reachable, this would be incorrect. The correct range should have \( c \) less than the upper bound (if the upper bound is not included) or equal. But based on the inequality logic, the correct one is D.

Answer:

D. \( \$11,069.38 \leq c < \$11,431.88 \)