a leprechaun places a magic penny under a girl's pillow. the next night there are 2 magic pennies under her pillow. each night the number of magic pennies doubles. how much money will the girl have after 25 nights?

(a) (8%) compute the probability of an even integer among the 100 integers 1! , 2! , 3! , until 100! (here n! is n factorial or n*(n-1)*(n-2) *… 1) (b) (16%) compute the probability of an even integer among the 100 integers: 1, 1+2, 1+2+3, 1+2+3+4, …., 1+2+3+… + 99, and 1+2+3+… + 100

Sketch the region enclosed by the given curves. decide whether to integrate with respect to x or y. draw a typical approximating rectangle and label its height and width. y= 5x, y=7x^2then find the area s of the region.

Sally deposited money into a savings account paying 4% simple interest per year. the first year, she earned $75 in interest. how much interest will she earn during the following year?