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The phrase "a satisfactorily high level" is correct and usable in written English.
It can be used to describe a degree of quality or performance that meets or exceeds expectations.
Example: "The project was completed at a satisfactorily high level, impressing both the clients and the stakeholders."
Alternatives: "an acceptably high standard" or "a sufficiently high degree".
Exact(1)
The pharmacokinetic analysis described here is obviously limited by this fact; but it does demonstrate that a satisfactorily high level of FVII coagulant activity is obtained with the chosen regimen, compared with the levels seen in the hemophilia population, when managed with 90 μg/kg.
Similar(59)
The results of the model showed a satisfactorily high projection level (Figure 4).
The results of the model showed a satisfactorily high projection level.
A satisfactorily high posterior probability of asthma is assumed, when the positive predictive value is ≥70%.
Protein identification results with statistically significant lower P and E values (<0.00005) and a satisfactorily higher fragment number (at least 10 fragments assigned) were manually validated.
The results indicated that cattle performed quite satisfactorily even when fed a very high level of dairy cattle manure.
It was a pretty high level race.
"The team showed a really high level.
He still plays at a high level".
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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