Zara has a collection of 4 marbles: an Aggie, a Bumblebee, a Steelie, and a Tiger. She wants to display them in a row on a shelf
, but does not want to put the Steelie and the Tiger next to one another. In how many ways can she do this? Akash's birthday cake is in the form of a $4\times 4\times 4$ inch cube. The cake has icing on the top and the four side faces, and no icing on the bottom. Suppose the cake is cut into 64 smaller cubes, each measuring $1\times 1\times 1$ inch, as shown below. How many of the small pieces will have icing on exactly two sides?
After school, Maya and Naomi headed to the beach, 6 miles away. Maya decided to bike while Naomi took a bus. The graph below shows their journeys, indicating the time and distance traveled. What was the difference, in miles per hour, between Naomi's and Maya's average speeds?
Finding an equation of a tangent line to that function requires that we find the derivative of the function at that point. Since this is an absolute value function with its cusp at (2, 5), the function is not differentiable here.
