Can I attach two transformers in parallel to the same AC wire

Can I attach two transformers in parallel to the same 120 VAC wire. I want to put in a 120VAC to 30VAC and a 120 VAC to 9VDC transformers on the same power cord. Is this safe and will it lower the output voltages or current of either transformer? Would it be best to ground to the neutral or gnd for both or should I do one for each transformer?

Everything you plug into the sockets of your power mains is connected in parallel. The mains uses heavy gauge wire to be able to supply the proper power to all the loads without brownouts. The only thing you have to be careful of is you don't draw so much current from any socket that you blow the circuit breakers.

In the case of a power cord, you just have to be sure all the things plugged in [ie, in parallel] don't draw more current than the cord is rated for.