Question

an electrician is hired to install a ceiling fan. she estimates that the installation will take no more than 45 minutes if the house is up to building code. if the house is not up to building code, she estimates that the installation will take longer than 120 minutes. which graph represents the number of minutes it could take her to install the fan?

Explanation:

Step1: Analyze the conditions

Let \(t\) be the time taken to install the fan. If the house is up - to - code, \(t\leqslant45\). If the house is not up - to - code, \(t > 120\).

Step2: Analyze the graph features

A closed circle is used for \(\leqslant\) or \(\geqslant\) (including the endpoint) and an open circle is used for \(>\) or \(<\) (not including the endpoint).
For \(t\leqslant45\), we have a ray going to the left (towards smaller values) starting from a closed circle (since \(t\) can be 45). For \(t > 120\), we have a ray going to the right (towards larger values) starting from an open circle (since \(t\) cannot be 120).

Answer:

The fourth graph (the one with a closed circle at 45 (and a ray to the left) and an open circle at 120 (and a ray to the right)).