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The phrase "are mostly engaged by" is correct and usable in written English.
It can be used to describe the primary involvement or participation of a group or individuals in a particular activity or context.
Example: "The volunteers are mostly engaged by community outreach programs that aim to support local families in need."
Alternatives: "are primarily involved with" or "are mainly occupied by".
Exact(2)
Using confirmatory factor analysis, lifestyle patterns have been extracted from leisure activities which are mostly engaged by both tourists and residents.
The huge variance in individual disengagement for literacy and numeracy may suggest that the latent disengagement variable represents two groups of test-takers, those who are mostly engaged (by far the majority of the sample) and those who are mostly disengaged.
Similar(58)
As I said, things start out pretty interesting, and I was mostly engaged by the "alternate history" approach.
In the GCs, it seems that the PD-1 on TFH cells is mostly engaged by PD-L2 expressed on GC B cells, and this interaction would probably modulate in situ the GC reaction.
Workers are mostly engaged in informal economic activities.
Russians and Kazakhs are mostly engaged in agriculture and livestock raising or in mining.
But Mrs. Logan's students are mostly engaged, trading thoughts and relishing the assignment.
They are mostly engaged in the informal sector to earn income for their day to day life (Central Statistical Agency 2008).
Workers are mostly engaged in their work; this explains why performance goals are frequently achieved.
The estimated 30 million population are mostly engaged in subsistence agriculture.
In terms of the clutch model, adhesions at the front are mostly engaged whereas adhesions at the sides are mostly disengaged.
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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