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The phrase 'depend on whether' is correct and usable in written English
It is often used in a causal sense, meaning that one thing will happen if another thing happens (or does not happen). Example sentence: The success of the project will depend on whether all participants are willing to cooperate.
Exact(57)
Millions of lives depend on whether or not the world steps up now".
Penalties like fines depend on whether a fine is stipulated in the lease.
Much could also depend on whether and how the United States responds militarily to the attacks.
Much would depend on whether the first stage, ordinary degrees, could be taught in two years.
Maybe it will depend on whether either team asks him to throw out the first pitch.
So, their performances depend on whether the rules can describe maneuver characteristics exactly and completely.
Convergence properties depend on whether constant or time varying step sizes are used.
(Table 1) may depend on whether the entity is nonprofit or for-profit.
Decisions regarding migration partly depend on whether the move is viewed to be permanent or temporary.
Valuation should depend on whether the time for physical exercise replaces leisure time or labour time.
These both depend on whether or not you can sell a product that customers like.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com