Explanation:

Sure! Here's an explanation of the idioms and statements:

- To hang fire

- Means to delay or hesitate. It's used when someone is postponing a decision.

- Not relevant to the context of suspecting unusual behavior.

- To bite the dust

- Means to fail or be defeated, often used when someone or something is eliminated.

- Has no connection to suspecting or investigating odd behavior.

- A dog in the manger

- Refers to someone who hoards resources or possessions they do not need, preventing others from using them.

- Does not fit with the context of suspicion or investigation.

- To smell a rat

- Means to suspect that something is wrong or someone is being deceitful.

- This correctly applies to a detective suspecting odd behavior.