Suppose the n$-$vector x is sparse, i$.$e$.,$ has only a few nonzero entries. Give a short sentence or two explaining what this means in each of the following contexts. $($a$)$ x represents the daily cash flow of some business over n days. $($b$)$ x represents the annual dollar value purchases by a customer of n products or services. $($c$)$ x represents a portfolio, say, the dollar value holdings of n stocks. $($d$)$ x represents a bill of materials for a project, i$.$e$.,$ the amounts of n materials needed. $($e$)$ x represents a monochrome image, i$.$e$.,$ the brightness values of n pixels. $($f$)$ x is the daily rainfall in a location over one year.