1. False. Plymouth was founded due to religious persecution, but Jamestown was founded for economic purposes. They were in search of various resources to profit from (eg: gold).
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2. True. The London Company was effectively the king's way of issuing charters to various colonies to set up. People bought stock in the company, and that money in turn was used to fund the ships, crew, supplies, etc to sail over to America. The money was also given to the king as well to allow for the charters to be legally valid.
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3. False. Different groups of people founded each region. One single person didn't found either area.