Lucas has five buttons in a container. each button is a different shape. there is a star, an oval, a hexagon, a circle, and a heart. he picks one button, replaces it, and then picks another button. the sample size for this compound event is suppose one square-shaped button is added to the container. if lucas repeats the same picking process, then the sample size would be

Part A: There are five buttons in all in all in the given item. The item above can be answered through the fundamental principles of counting. 

There are 5 items to choose from during the first pick. Because the shape can be returned and picked again, there are also 5 items to choose from in the second pick. Multiplying them,
                               n = 5 x 5 = 25
Therefore, the sample size for the compound event is equal to 25.

Part B: The same concept can be used in this part of the item; however, instead of 5 there are 6 buttons to choose from.
                              n = 6 x 6 = 36

Hence, the sample size of this picking process is 36. 

It's like discovering the answer to a puzzle. the purpose in solving an equation is to find the value or values of the variable that makes it a true statement. any value of the variable that makes the equation true is called a solution to the equation.