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"cost is given" is a grammatically correct and usable phrase in written English.
It can be used to indicate that the cost of something has been previously stated or provided. Example: The cost is given on the price tag for each item in the store. In this sentence, "cost is given" means that the price for each item has already been provided and is displayed on the price tag.
Exact(26)
No estimate of cost is given.
Thus the total serial cost is given by the geometric sum.
The water cost is given out to appreciate the economic performance of the solar desalination system.
A rigorous analysis (independent of heuristic arguments) of its error and cost is given.
Next, a detailed account of energy-efficient unicast routing alternatives, with a particular focus on those based on additive link cost is given.
A "total cost" is given by Ryanair at the penultimate stage of the booking with a note in red which says: "Excluding administration fee (if applicable)." The £6 is only added at the final stage when the customer identifies their debit or credit card.
Similar(34)
No cost was given for the new rocket programme, but much of the research is already complete.
More than £5.5 million was spent in the present financial year, including £1.3 million on "timber extraction", although no explanation for this cost was given.
Historical examples of runtime, problem size, and estimated cost are given for actual and hypothetical Navier Stokes flow cases from the past 40 years.
That is why cargo time window was given the name soft time window, and penalty cost was given the name inconvenience cost.
(12), (13), (15), (16), (17), and (18), the new form of the expectation and variance of the total cost are given in Eqs.
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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