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"a cost involved" is correct and can be used in written English.
You can use it to refer to the expense associated with something, either literal or figurative. For example, "The team was aware of the cost involved in travelling to the championship match."
Exact(33)
However, since there is a cost involved, optimisation is required.
"project cost" means a cost involved in carrying out a project.
"Because there is a cost involved, the retailers aren't too enthusiastic about it," he said.
"I think there is a cost involved, but there is always a cost," Oren said.
There is a cost involved: pain to my family and stress on my career.
But there's a cost involved in managing them, and the savings may be more than offset by those costs".
Similar(27)
For many lenders, there is still a notable cost involved in initiating a reverse mortgage, though these upfront costs have been reduced in recent years and some smaller lenders now offer very low upfront costs.
There's also a financial cost involved in travelling to get an abortion, does this create a class divide in who can and cannot have an abortion?
But within the news is a very interesting point: It's the idea that Amazon was selling ebooks "below cost" at $9.99 and that there was a real cost involved in selling access to a conglomeration of bits.
The ferry does fortunately provide an alternative, even though there is a minor cost involved.
There is also an entropic cost involved in maintaining a regulatory system, stemming from random mutations that tend to destroy transcription factors and binding sites.
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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