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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...

Speedy Delivery charges $20.00 to send a 1-pound package via two-day service and an additional $2.00 for every 4 ounces of package weight over 1 pound. How much will it cost to ship a package that...

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...

The tangram is an ancient Chinese puzzle consisting of seven flat geometric shapes. These shapes, called tans, include one square, one parallelogram and five right isosceles triangles which are all...

March 23 is National Puppy Day! Solve the problems below about two of the best things, math and puppies. Rufus the poodle is 1 year old and currently eats 1 dog biscuit per day. Every year, the number...

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...

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...