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The breathing rate and pulse rate are related proportionally. If the breathing rate increases, so does the pulse rate. The pulse rate is an indication of the breathing rate.
Check for a pulse and breathing. No pulse, no breathing, give CPR.
For the condition of no breathing and no pulse, immediately commence CPR.
Check to see if they have a pulse, or are breathing. If they have both, no CPR is needed. If they have a pulse but aren't breathing, you can perform rescue breathing only without chest compressions. If they do not have a pulse and aren't breathing, you perform rescue breathing and chest compressions.
No. Monitor the pulse, and give rescue breathing if needed.
CPR.
When someone is not breathing and does not have a pulse
First perform an Initial Assessment. Open the airway, Check for breathing, if there is no breathing give two rescue breaths. If the rescue breaths go in and make the chest clearly rise check for a pulse. IF there is no pulse begin CPR.
It is possible to have a pulse but no breathing as in asphyxiation, but the reverse is impossible, without a pulse you basically aren't alive, that pulse is a symbol of blood pumping through your body. Good answer above. I should add that, in some subjects, that pulse may be there but not be palpable.
Agonal breathing will not support life; rescue breathing (or CPR if no pulse) is required.
An infant in need of CPR will not be breathing and will not have a pulse. Also, the infant will be turning a blueish color.
An infant in need of CPR will show no movement, breathing, or a pulse.