Prove: if n is a natural number, then 2^2n − 1 must be divisible by 3.

Find the actual dimensions of the box. the side length are in meters and integers. the surface area of the box is 104 m2 and volume of the box is 60 m3.

Over the course of the school year, you keep track of how much snow falls on a given day and whether it was a snow day. your data indicates that of twenty-one days with less than three inches of snow, five were snow days, while of the eight days with more than three inches of snow, six were snow days. if all you know about a day is that it is snowing, what is the probability that it will be a snow day?

Match each whole number with a rational, exponential expression 3 square root 27^2find the domain and range of the exponential function h(x)=125^x. explain your findings. as x decreases does h increase or decrease? explain. as x increases does h increase or decrease? explain.