Final answer:
Based on standard English capitalization rules, the correct sentences are 'C. The Black Sea is surrounded by European and Asian countries.' and 'D. Mike spent the summer rafting down various American rivers.' because they use proper capitalization for place names and proper adjectives.
Step-by-step explanation:
The student's question pertains to identifying which sentences are written correctly based on an unspecified style manual. Without the specific rules from the manual, we have to rely on standard English grammar and capitalization rules. Typically, proper nouns like 'Gobi Desert', 'Black Sea', and names of specific places like 'California Coast' and 'Rocky Mountains' should be capitalized. Generic terms like 'desert', 'sea', 'coast', and 'mountains' are not usually capitalized unless they are part of the official place name. Based on this, the sentence 'C. The Black Sea is surrounded by European and Asian countries.' appears correct because 'Black Sea' is the proper name of a sea. Likewise, the sentence 'D. Mike spent the summer rafting down various American rivers.' is written correctly since 'American' is a proper adjective referring to a specific nationality and 'rivers' is a generic term not requiring capitalization in this context.