Final answer:
During the Gold Rush, none of the options listed (television, cotton, radio, light bulb) were the significant inventions; they belong to different historical periods. The radio was invented by Guglielmo Marconi, x-rays were an important medical innovation of the late nineteenth century, and in a postindustrial society, information is the most critical commodity.
Step-by-step explanation:
The important invention during the Gold Rush was not the television, cotton, radio, or light bulb. Each of these inventions came from different periods and had varying impacts on society. Regarding the radio, the invention is attributed to Guglielmo Marconi, which greatly influenced mass communication.
When considering medical innovations of the late nineteenth century, x-rays stand out as significant developments. Looking at the broader historical context after the Civil War, the Industrial Revolution brought about important inventions like high-powered sewing machines, movies with sound, frozen foods, and typewriters, with movies with sound not being a successful invention of that specific era.
In a postindustrial society, the most critical commodity is information, as it drives innovation and economic growth. The transcontinental railroad and inventions like the telephone and light bulb played crucial roles in America's expansion, influencing the transformation from rural to urban living and the rise of industrial labor.
These technological advancements, including others like the telephone by Alexander Graham Bell and Thomas Edison's work with electricity, shaped industry and everyday life, even though they didn't drastically alter American life until the turn of the century.