What key role those a cost-benefit analysis play? How is it used?

Computing, Analysing & Comparing : 'Benefit' of projects per unit 'Cost' incurred.

Explanation:

Cost Benefit Analysis is used to ascertain Benefit of a decision with regards to its cost. The decisions might be various : investing in a project, hiring a labour etc. The cost & benefits of the decision are measured in 'net present value', as costs / benefits (specially) might be scattered over a long period of time, & they need to be adjusted for price change then.

Benefit - Cost Ratio (as per Cost Benefit Analysis) : =

Total Benefit in Net present value

Total Cost in Net present value  

If a project / decision has higher Benefit - Cost ratio, it provides more benefit per unit of cost & vice versa in case of low Benefit - Cost ratio. A project with high Benefit - Cost ratio would be preferred over the one having lower benefit - cost ratio.

explanation: doctrine of respondeat superior is a legal doctrine that is commonly used in tort. this principle makes an employer or principal legally responsible for the wrongful acts done by an employee or agent, if such acts occur within the scope of the employment or agency.

i would say their habit of breaking down.