Which sentence below is properly punctuated?
a.
bertie had several people working for him; a private secretary, an administrative assistant, and a research aide.
b.
bertie had several people working for him, a private secretary, an administrative assistant, and a research aide.
c.
bertie had several people working for him: a private secretary, an administrative assistant, and a research aide

Option C is correctly punctuation. The colon is used because you're listing off the different types of employees Bertie has working for him. The types of a people are dependent clauses (that is, by themselves, they don't make a completely sentence). Had there been a bridging word or phrase like "including" or "for example" then you wouldn't need a colon because those words would serve the same function. A semicolon does not work in this case because that would be used to connect two independent clauses without a conjunction between them (i.e. "and", "or", "but" etc.).

The slope of a linear equation is equal to the change in the value of the dependent variable divided by the change in the value of the independent variable. in this problem, the dependent variable is the profit while the independent variable is the worker's average pay. if the profit is said to increase by 1500 when worker's average pay decrease by 450, the slope is equal to 1500/(-450)=-3.33