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The phrase "a dense range of activities" is correct and usable in written English.
It can be used to describe a variety of activities that are numerous and closely packed together, often in a specific context such as events, programs, or schedules.
Example: "The conference offered a dense range of activities, including workshops, panel discussions, and networking events."
Alternatives: "a wide array of activities" or "a rich variety of activities".
Exact(1)
They grouped themselves with the overachievers, immersed in a dense range of activities.
Similar(57)
It is based on the idea that predicted curves can be represented by using their predicted values for a dense range of points.
An important example of a strongly compact algebra is the commutant of a compact operator with a dense range.
Notice that the assumptions of Corollary 3.4 are met whenever T is a compact operator with a dense range.
"We still have a full range of activities.
"The times are very much one of co-operation across a broad range of activities.
"A whole range of activities could have taken place there," he writes.
Different seating in the same room allows for a playful range of activities.
A limited range of activities took place there.
This outdoor water park has a wide range of activities for every member of the family.
We believe there is room for a wide range of activities and influence".
More suggestions(2)
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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