The statement that the operating system of a computer is responsible for is:
Managing memory allocation for all applications.
The operating system is responsible for managing system resources, including memory, to ensure that applications run efficiently and do not interfere with one another.
The other tasks mentioned, such as providing a way for users to create text documents, allowing users to access the internet, and allowing users to write programs, are typically facilitated by application software that runs on top of the operating system, rather than being direct responsibilities of the operating system itself.