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The phrase "and the second class" is correct and usable in written English.
It can be used when referring to a specific category or group that is being discussed, often in comparison to another class or category.
Example: "In our study, we analyzed the first class of data and the second class to determine the differences in outcomes."
Alternatives: "and the second category" or "as well as the second group".
Exact(17)
The first class graduated 84 officers in 2009, and the second class graduated 212 officers in 2010.
"I know that the first-class passengers got off first, and the second class got off second, and they made the third class wait for the lifeboats, but then there were no more lifeboats and everybody just panicked".
The program will launch at the end of November, with the first class graduating at the end of January and the second class beginning in March.
The first class contains Lax Friedrichs-like methods which aLax Friedrichs-likee stable, and the second class contains Godunov-like methods.
This first class consists of at most weakly unstable agents (i.e. agents have all eigenvalues in the closed left half plane) and the second class consists of at most weakly non-minimum-phase agents (i.e. agents have all zeros in the closed left half plane).
The first class includes the PDGFs, cystine-knot containing growth factors that are homologous and the second class comprises MCSF, SCF, and Flt3-ligand (Flt3-L), proteins that belong to the family of four-helix cytokines, a fold that is unrelated to VEGF.
Similar(42)
Three-dimensional islands may also result in well-ordered surface structures and represent the second class.
Second class children could read the children's books provided in the library or play deck quoits and shuffleboard on the second class promenade.
We must underline, that y for two-class selections is coded as a vector with value 1 for the first class and −1 for the second class.
Twenty-four students from the first class and 28 students from the second class were invited.
A total of 43 providers participated in the first class and 45 providers attended the second class.
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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