A restaurant owner determines that the business is profitable only when it serves more than ${}40$ customers per night ($c > 40$). When graphing this profitability threshold on a number line, the boundary value of ${}40$ acts as a(n) ____ partition number.

A construction safety officer determines that a trench requires additional shoring if its depth, $d$, exceeds ${}5$ feet ($d > 5$). When representing this safety regulation on a number line, the boundary value of ${}5$ is an example of a zero partition number.

Performance Metrics Visualization

In various professional scenarios, a specific boundary value acts as a zero partition number to divide a number line into regions of valid and invalid solutions. Match each scenario with the specific value that serves as its zero partition number.

Identifying the Zero Partition Number in Logistics

Visualizing Safety Thresholds Using Partition Numbers