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The phrase "activities were based" is correct and usable in written English.
You can use it to describe the foundation or origin of certain activities, often in a context where you are explaining what those activities rely on or are derived from.
Example: "The activities were based on the principles of teamwork and collaboration, ensuring that everyone contributed equally."
Alternatives: "activities were grounded" or "activities were founded".
Exact(23)
In reviewing our program against the new standards, we noted that while our targeted nosocomial infection surveillance activities were based on a formal risk assessment, the assessment for our other routine IC rounding activities was less formal.
The equivalent activities were based on the activity of pure rutin.
The administered activities were based on the package insert for the treatment device: ~120 Gy to treatment volume for glass microspheres.
Mr Hayes's trading activities were based around movements in the Libor rate - an interest rate used by banks around the world to set the price of financial products worth trillions of pounds.
The initial guided group activities were based on exam questions, clicker questions, and problems for informal group work that one of the authors (SF) had used in several previous iterations of the course.
Most of his activities were based in the areas of Tulkarm, Nablus and Jenin (modern-day northern West Bank).
Similar(37)
Other significant economic activities are based on farming and cattle breeding in the surrounding area.
We find that KT activities are based on relational rather than commercial activities.
The instructional design of such learning activities is based on a constructivist approach of learning.
This account of his activities is based on interviews with American military and intelligence officials and businessmen in the region.
Its activities are based around an understanding that military force alone cannot solve the complexity of challenges facing individual nations and regional alliances.
More suggestions(15)
organization were based
campaign were based
activity were based
initiative were based
activities were lost
activities were investigated
activities were measured
activities were shown
activities were initiated
activities were invigorated
activities were organized
activities were perceived
activities were dropped
activities were limited
activities were practiced
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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