p5. Find the number of three-digit integers that contain at least one 0 or 5. The leading digit of the three-digit integer cannot be zero.
p6. What is the sum of the solutions to 5x+7x+8=7x+5x+8
p7. Let BC be a diameter of a circle with center O and radius 4. Point A is on the circle such that ∠AOB=45o. Point D is on the circle such that line segmentOD intersects line segment AC at E and OD bisects ∠AOC. Compute the area of ADE, which is enclosed by line segments AE and ED and minor arc AD.
p8. William is a bacteria farmer. He would like to give his fiance2021 bacteria as a wedding gift. Since he is an intelligent and frugal bacteria farmer, he would like to add the least amount of bacteria on his favorite infinite plane petri dish to produce those 2021 bacteria.
The infinite plane petri dish starts off empty and William can add as many bacteria as he wants each day. Each night, all the bacteria reproduce through binary fission, splitting into two. If he has infinite amount of time before his wedding day, how many bacteria should he add to the dish in total to use the least number of bacteria to accomplish his nuptial goals?
PS. You should use hide for answers Collected [url=https://artofproblemsolving.com/community/c5h2760506p24143309]here. algebrageometrycombinatoricsnumber theoryStanford Math TournamentSMT