The movie great run on sentence or fragment sentence?

What is the meaning of the word checking as it is used in this sentence from the second paragraph of the passage?

Someone answer this asap for an office manger uses the function s(x) to determine the number of shirts the company can make when the employees work for a total of x hours. when the employees have worked for a total of 300 hours, they produces 500 shirts. which equation correctly represents the company’s production of shirts? a. s(300) = 500 b. s(300) = 800 c. s(500) = 300 d. s(500) = 800

Ineed . in the first paragraph, the word rival means: a. neighbor b. competitor c. customer d. manufacturer