Final answer:
The quote suggesting that Americans were divinely ordained to spread democratic institutions and their culture, thus sharing their values with foreign peoples, is associated with the concept of Manifest Destiny. This belief was particularly endorsed by figures like Horace Greely in the 19th century.
Step-by-step explanation:
The individual who expressed the belief that the United States has a duty to share its values with foreign nations can be identified from one of the provided quotes regarding the idea of Manifest Destiny. This notion is discussed in the second quote, which explains how Americans were thought to be divinely ordained to expand democratic institutions and their culture across the continent, which inherently includes spreading these values to the native inhabitants. This concept, which was prevalent in the 19th century, is attributed to political and public figures who believed that it was America’s destiny to not only expand its territory but also its cultural and democratic values to others. One such figure who encapsulated this sentiment was newspaper editor Horace Greely, mentioned in the third quote, who encouraged Americans to 'Go west, young man' as part of this national endeavor.
The quote that directly addresses the United States’ perceived duty to spread its values is: “The idea was simple: Americans were destined—and indeed divinely ordained—to expand democratic institutions throughout the continent. As they spread their culture, thoughts, and customs, they would, in the process, expose the native inhabitants to Protestant institutions and, more importantly, new ways to develop the land.” This statement captures the essence of the belief that the United States has a duty to share its values with foreign peoples.