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The phrase "depends much on" is grammatically correct and can be used in written English.
It is often used to indicate that the outcome or result of a situation is influenced by certain factors or conditions. Example: The success of this project depends much on the cooperation and dedication of all team members.
Exact(39)
The system performance depends much on the turbine, which is one of the core components of the S-CO2 Brayton cycle.
Where one stands in this debate depends much on the scope of evidence considered relevant to the question (Devereaux 1998).
The answer to this question depends much on what is put into place if the UK were to leave the EU.
His later notoriety depends much on an account of his life in a book, From Israel To Damascus: The Painful Road To Blood, Betrayal And Deception, by one of his bodyguards called Robert Hatem, otherwise known as "Cobra".
Its quality depends much on whether the tape used lies flat and curves continuously (which can be achieved only by using bobbins) or is ready-woven, in which case it has to be gathered at the bends and corners, and inevitably puckers.
The mechanical performance of precipitation hardening alloy depends much on the nature of precipitates.
Similar(21)
An indecisive man, he depended much on the influence of his counselors and his Jesuit confessors.
How the younger players will develop will depend much on the opportunities they are given.
The optimum covariate designs depend much on the methods of construction of the basic PBIB designs.
However, occupation time does not depend much on the type of vehicles.
Their chances depend much on removing Chanderpaul quickly in the morning".
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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