The waste gate on a turbo-charger regulates the quantity of:

The waste gate on a turbo-charger is an essential component that helps manage the engine's performance by regulating the flow of exhaust gases to the turbine. When the engine is generating sufficient boost and the desired pressure is achieved, the waste gate opens to allow a portion of the exhaust gases to bypass the turbine. This action prevents excessive boost pressure, which can lead to engine knocking or damage.

By controlling the amount of exhaust gas that flows through the turbine, the waste gate helps to maintain optimal performance and efficiency of the turbocharger. This contributes to more stable engine operation, enhances the responsiveness of the turbo, and ensures that the engine does not operate beyond its design limits.

The other options refer to different functions that do not accurately describe the primary role of the waste gate. For example, the air mixture entering the induction manifold and the atmosphere entering the compressor are related to the air intake system but are not regulated by the waste gate. Furthermore, the exhaust gas that leaves the compressor is a different stage of the turbocharger's operation and does not pertain to the bypass function of the waste gate.