Atransformer with a turns ratio (secondary/primary) of 1: 10 is used to step down the voltage from a 120-v wall socket to be used in a battery recharging unit. what is the voltage supplied to the recharger?

The voltage ratio of a transformer is nominally equal to the turns ratio.

If you connect 120 volts AC to one side of the 1:10 transformer, you'll
get 12 volts out of the other side if you connected it up the correct way,
or 1200 volts if you connected things up backwards.

Note that it has to be AC.  If the input to a transformer is DC, then the
output is always smoke.

One splits the atoms and molecules  the other combines them