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The phrase "depends significantly" is correct and usable in written English.
It can be used to describe a situation where something has a significant impact on something else and is a determining factor in the outcome. Example: The success of this project depends significantly on the cooperation of all team members.
Exact(60)
The position-dependent energy resolution of the FI CCDs depends significantly on the ACIS focal plane (FP) temperature.
Weyant: It depends significantly on who is collecting the tax.
In short, the health of American small businesses depends significantly on credit.
A man's working capacity depends significantly on his muscular strength.
The suggested method depends significantly on the computer computation.
It depends significantly on us, and the policies we, and our leaders, choose to adopt – nationally, regionally, and globally.
Yet the complex nature of theological debate depends significantly on rhetorical strategies, often with simple wordplay and allegorizing.
"Recovery in the United States depends significantly on recovery in those large and previously rapidly growing economies".
Yes, the effectiveness of competition, particularly in a field such as healthcare, depends significantly on getting the "rules of the game" right.
More than five years after the conflict began with the overthrow of Saddam Hussein, the American military presence now depends significantly, if not completely, on Iraqi acquiescence.
The performance of PEM fuel cells depends significantly on an appropriate flow field design.
More suggestions(15)
tends significantly
indicates significantly
depends appreciably
depends noticeably
depends considerably
depends greatly
spends significantly
depends dramatically
determining significantly
expands significantly
responds significantly
prior significantly
principle significantly
define significantly
needs significantly
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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