Final answer:
Francis Cabot Lowell's establishment of the first integrated textile mill in New England is true. Indian alliances were significant for European powers in the southeastern U.S., which is also true. Wave-particle duality does not apply to macroscopic objects, making that statement false.
Step-by-step explanation:
The statement 'Francis Cabot Lowell built the first integrated textile mill in New England' is true. Lowell revolutionized the American textile industry by centralizing the textile manufacturing process under one roof, which was previously done in separate locations.
The assertion that 'Indian alliances were an important means of establishing power in the southeast for the European empires' is also true. Europeans often allied with various Native American tribes to bolster their influence and control over resources and territories in the Southeast of North America.
Regarding the claim that 'wave-particle duality exists for objects on the macroscopic scale', this is false. Wave-particle duality is a concept in quantum mechanics that applies to particles at the very small, quantum level, such as electrons and photons, not to objects that we interact with in everyday life on the macroscopic scale.