(mc) what effect did the entry of the united states into world war 1 have on the course of the war a.) it pushed russia out of the war b.) it opened a new front in the fighting c.) it bring a quick victory to the allies d.) it led to a large number of causalities

Correct  c) It helped bring a quick victory to the Allies.

The United States had been providing some support to the Allies prior to its own entry into the war.  But when the US joined the effort fully with a declaration of war, that not only meant the arrival of fresh US troops but a commitment of even more American dollars to the Allies' war effort.  The American commitment greatly boosted the morale of British and French troops on the Western front and demoralized the German troops.

As to the other answers ...

Russia did pull out of the war, but that was because it went through a revolution and change of government in its own country, not because of American involvement.  Russia's fight was with Germany on the Eastern front, whereas the US entered the war on the Western front.The United States entered the war on the Western front where the British and French had already been fighting the Germans.There were still additional casualties after the Americans entered the war, but bringing the war to an end sooner cut down on the huge losses of life that had been happening.

The answer would be option a , b, and c.