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...
Melrose’s hot air balloon is a sphere of diameter 100 feet. How many cubic feet of air will Melrose’s hot air balloon hold when completely filled? Express your answer as a decimal to the nearest tenth...
For the following problems, assume that the snowballs are perfect spheres. Chiquita and Rhonda are each building a snowman. Rhonda tells Chiquita that she is making each of her 3 balls of snow 20%...
Environmental engineers work with other engineers, scientists and experts to control water and air pollution, as well as its impact on public health, waste disposal, recycling and more. Environmental...
Final exams often accompany the final days of school. Sherry has had four tests so far in her science class, each worth 1/6 of her final grade. She scored 87%, 89%, 92% and 91% on these tests. Her...
Now that 2024 is finally here, let’s see what we can do with this new number! If the perimeter of a particular square is 2024 inches, what is the area of the square, in square inches? Express your...
Cara was born on January 1, 2010, and her mother, Sydney, was born on January 1, 1982. In what year will Sydney’s age be twice Cara’s age? If we let Cara’s age be C, then Sydney’s age is S = C + 28...
According to “A History of Valentine’s Day Cards in America” by T.M. Wilson, in 1847 Esther Howland was the first to mass-produce Valentine’s Day cards. She made them out of lace, paint and expensive...
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...