4. Suppose you decide to arrange tables in a square configuration with only a single row of tables on the ed square. As the arrangements increase in size, a square on the inside. Chairs will not be set in this space. ge of the square. Chairs will be set on only the outside of the there will be open space in the shape of a. Study the first two possible arrangements and then draw the next two in the sequence b. Generalize the number of chairs needed for n tables. Consider using an approach e the one shown in the section in which we determined how many chairs are needed for tables of a certain type. In this problem, there are corner tables and the interior tables are between the corner tables. Write an expression for the number of chairs and simplify it

Ryan is building a triangle sequence so that one triangle is added to the right each time, as shown below. How many matchsticks will he use for the nth figure and for the figure one before the nth? Click the icon to view the matchstick square figures. The nth figure will take matchsticks to build. (Type an expression using n as the variable. Simplify your answer.) The figure one before the nth figure will take matchsticks to build. (Type an expression using n as the variable. Simplify your answer.)

You are a thief overhearing someone's safe combination, which consists of a 5-digit number sequence. You are sure that the combination code contains at least two 6. How many codes would you have to potentially check to open the safe?

A problem in Mrs. Schrader's geometry class has seven steps in the proof. She writes the steps, one per card, and gives them to a student to put in proper sequence. How many different sequences of steps are possible?