True or False. The two functions f and g defined by f(x) = 3x + 3 for x real and g(t) = 3t + 3 for t real and positive
False. Two functions are equal if their rules are equal and their domains are the same.
How to Create a Fair and Equitable Partnership From Day One?
You should certainly register your business with your state's labor department. As for the type of entity you select, that will depend on a variety of factors that I cannot address without knowing more information from you. For instance, a sole proprietorship would not be an option if both you and your partner intend on owning equity in the business. From what you describe, the more suitable option would likely be a partnership or S Corporation. This decision will impact how profits are distributed and accounted for in the company books. In terms of allocating profits, it is still possible for two partners to have equal ownership in the business even if one contributes capital and the other does not. Specifically, the other partner can gain equity by contributing labor (i.e. sweat equity) and property.
Explain what regularization is and why it is useful.
Regularization is the process of adding a tuning parameter to a model to induce smoothness to prevent overfitting. (see also KDnuggets posts on Overfitting) This is most often done by adding a constant multiple to an existing weight vector. This constant is often either the L1 (Lasso) or L2 (ridge), but can in actuality be any norm. The model predictions should then minimize the mean of the loss function calculated on the regularized training set.