Final answer:
The rock containing fossil shark teeth and fossils of Archimedes likely formed during the Carboniferous period, specifically the Mississippian subperiod, due to the presence of the Archimedes bryozoans which existed around 359 to 323 million years ago.
Step-by-step explanation:
If an outcrop of sedimentary rock contains fossil shark teeth and fossils of Archimedes, the rock could have formed during the time period when these organisms existed. Archimedes is a genus of extinct bryozoans that were commonly found during the Mississippian subperiod of the Carboniferous period (approximately 359 to 323 million years ago). Shark teeth found in sedimentary rocks can span a wide range of ages, as sharks have a fossil record that dates back to the early Devonian period (over 400 million years ago) and continue to exist today.
To determine more precisely when the rock may have formed, we would look for index fossils, which are fossils known to be from a specific geological time frame. Since the question specifies shark teeth and fossils of Archimedes, it suggests the rock likely formed during the Carboniferous period when Archimedes was known to exist. However, without additional context or specific identification of the shark teeth, the age of the rock could be broader. Further paleontological analysis would be needed to narrow down the time period more accurately.