The phrase "be determined by" can be replaced with a variety of synonyms. These include, but are not limited to, depend on, be influenced by, be controlled by, hinge upon, rest on, be based on, be decided by, be guided by, be regulated by, be subject to, and be swayed by. Each of these words or phrases expresses the idea that something is influenced or determined by external factors, rather than being entirely autonomous. The right synonym to use will depend on the context in which the phrase appears, and which word best captures the intended meaning. By expanding your vocabulary in this way, you can express your thoughts and ideas with greater precision and clarity.