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The phrase "a rather high degree" is correct and usable in written English.
It can be used to describe a significant or considerable level of something, often in a formal or academic context.
Example: "The study revealed that participants exhibited a rather high degree of satisfaction with the new product."
Alternatives: "a significant level" or "a considerable extent".
Exact(12)
Perhaps for that reason, it has a rather high degree of difficulty as a business proposition.
Most of these approaches originated in engineering disciplines where linearity is commonly (approximately) given, but naturally evolved networks exhibit a rather high degree of nonlinearity.
It was shown that the kinetic order of this reaction with respect to the reactive ends of the dilithium initiator is close to zero, indicating a rather high degree of aggregation of the dilithium initiator.
As expected, in the rubber left hand condition people did not experience ownership of the hand, but somewhat surprisingly they reported a rather high degree of touch duplication.
However, it has been repeatedly shown that self-reports can usually claim a rather high degree of validity [ 39, 40].
The activity diary was rated to have been a support to perform physical activity according to the recommendations, for 12 of the women, to a rather high degree to very high degree.
Similar(47)
In English poetry, with its reliance on masculine rhymes, rhymes themselves are harder to find, and they have a rather higher degree of significance.
As a consequence of the rather high degree of difference to the parent peptide, foldamers frequently exhibit reduced inhibitory activity, but additional optimization efforts can compensate this initial drawback.
Despite the rather high degree of specific integration achieved in several different CNS regions, these processes are usually defective and long-distance connections are not rewired.
The higher frequency and larger degree of deviation between predicted and observed mixture toxicity found in the present study in comparison to previous results [14, 15] suggests that the rather high degree of reliability of mixture toxicity predictions established so far in the scientific literature cannot be directly transferred to the regulatory context.
The rather high degree of specialisation and the low required case number of the introduced annual minimum volume standards, on which the joint self-governing body agreed upon however, had the effect that these five minimum volumes cover only 23.128 cases representing 0.14% of all hospital cases.
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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