Show that each of these conditional statements is a tautology by using truth tables: (a) ¬p→(p→q)

Suppose that the price p (in dollars) and the weekly sales x (in thousands of units) of a certain commodity satisfy the demand equation 4p cubedplusx squaredequals38 comma 400. determine the rate at which sales are changing at a time when xequals80, pequals20, and the price is falling at the rate of $.20 per week.

Mr. brettler is hanging up a 5-foot tall rectangular welcome sign in the gym. he has drawn a sketch on a coordinate grid. he has the lower vertices of the sign at (9, –3) and (–6, –3). where would the upper vertices be on the grid?

Ican interpret and represent the remainder in division calculations sensibly for the context (eg 27.4 in calculating average height in cm: $27.44 if it represents an amount of money) solve the following problems. 15) the wildlife park charges $25.50 dollars per person to enter their park if the park made $15096 dollars today, how many people entered the park? 16) ms adams plus 2,230 other keen runners ran a marathon: between them they ran 94817.5km. how many km did each competitor run?