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Define x @ y as (x3 − y)/x, for distinct positive integers x and y. What is the value of 5 @ 10? Evaluating 5 @ 10 yields (53 − 10)/5 = (125 − 10)/5 = 115/5 = 23. Define a # b as a2 − b2 − ab, for...

The Washington Monument in Washington, D.C. is an obelisk. An obelisk is a tall monument with four gently sloping sides and a pyramid shape on top. The obelisk structure first appeared in Ancient...

Ariel, Ollie and Eden are going trick-or-treating for Halloween, but first their parents are taking them to a costume store to pick out costumes. The store has 9 different costume options available –...

The holidays are here, and it’s not uncommon for offices and classrooms to do a gift exchange. These often work as follows: the names of all participants are put into a hat, and everyone draws a name...

The weekend has just begun, and Derek wants to build a snowman either on Saturday or Sunday, but he can only build a snowman if it snows. There is a 1/2 probability that it snows on Saturday, and a 1...

Troy, Elliott and Shaun are three contestants on a game show. In one of the rounds of the game show, the 3 contestants have a chance to spin a wheel up to two times in a row to try to get the highest...

Sun City earned its name because it rarely rains there. In fact, it rains only 54 days each year there, on average. What percent of the days in 2023 is it expected to rain in Sun City? Express your...

The Walton and the Brady families plan to vacation together in an 8-bedroom vacation home. John and Olivia will bring six children — boys, Jason, Ben and Jim-Bob, and girls, Mary Ellen, Erin and...

The date of the beginning of the school year has long been a topic of debate in many areas across the United States, but the trend is leaning towards starting school earlier rather than later...