Atest to determine whether a certain antibody is present is 99.7% effective. this means that the test will accurately come back negative if the antibody is not present (in the test subject). the probability of a test coming back positive when the antibody is not present (a false positive) is 0.003. suppose the test is given to seven randomly selected people who do not have the antibody.

1) prove that 731^3−631^3 is divisible by 100 2) prove that 99^3−74^3 is divisible by 25

Solve 17= -13 - 8x and show your work.

Ican interpret and represent the remainder in division calculations sensibly for the context (eg if we wont to know how many 40 seat buses will be needed to transport 170 students for on excursion, we divide 170 by 40 and realise buses and another smaller vehicle to that we need 4 transport 10 more students) solve the following questions. show your work! 11) the zoo had 420 butterflies that needed to be transported to a new enclosure. the boxes that the butterflies would be moved in only hold 80 butterflies in each. how many boxes would they need? 2 12) each classroom in the school can have exactly 25 students, if there are 345 students in the school how many full classrooms are there?