Final answer:
E. coli (Escherichia coli) is the prokaryote among the options given; it is a bacterium without a nucleus and membrane-bound organelles, unlike eukaryotic cells which include amoebae, paramecia, and euglenas.
Step-by-step explanation:
The organism that is a prokaryote among the options given is E. coli (Escherichia coli). Prokaryotic cells are characterized by the lack of a nucleus and membrane-bound organelles, which is the case with E. coli, a well-known bacterium. In contrast, amoebae, paramecia, and euglenas are all eukaryotes because they have a nucleus and organelles within their cells. Among the options provided, only E. coli fits the description of a prokaryotic organism.
It is important to understand that eukaryotic cells, such as those of amoebae, paramecia, and euglenas, are more complex and have distinct nuclei, while bacterial prokaryotic cells, like E. coli, and archaean prokaryotic cells do not have true nuclei or other membrane-bound organelles. E. coli reproduces via binary fission, a process that is common to prokaryotic cells of both bacteria and archaea.