New mexico was most valuable to both the union and the confederacy because

It provided trade access to the west coast and Mexico.

Explanation:

The New Mexico Territory included the modern states of New Mexico and Arizona as well as the south of Nevada. Both Confederate and Union authorities alleged ownership over the territory, and many major battles took place there, because it was key in the Trans-Mississippi Theater of the American Civil War, as well as a trade access point to the west coast and Mexico.

united states reinforcements contributed greatly to three allied victories in france at: cantigny (first major american battle), argonne (the largest in the united states military history, involving 1.2 million american soldiers), and château-thierry (one of the first actions under general pershing).

a. theta waves. this is because the person is in a light sleep which means the brain waves would show these kind of waves.