paul a dentist determined that the number of cavities that develops in his patients mouth each year varies inversely to the number of seconds spent brushing each night.

Answer:Lori will have [tex]1[/tex] cavity if she brushed for [tex]120\ sec[/tex] each night.Step-by-step explanation:As the question suggests cavities developed varies inversely with the number of seconds spent on brushing.Lets take the terms as [tex]c=\frac{k}{t}[/tex],where [tex]k[/tex] is the constant of proportionality.Andc = Number of cavities developed each year t = Number of minutes spent on brushing per nightNow we will plugging the values of the given terms and find the value of [tex]k[/tex],for this we can re-arrange it as...[tex]k=c\times( t)[/tex][tex]t=30\ sec=\frac{30}{60} =0.5\ min[/tex] and [tex]c=4[/tex][tex]k=0.5\times 4=2[/tex]Now as Lori will increase her brushing time so as the cavity will decrease.So for this we have been given,[tex]t=120\ sec=\frac{120}{60} = 2\ min[/tex] and [tex]k=2[/tex].As [tex]c=\frac{k}{t} =\frac{2}{2} =1[/tex]So as per Paul's observation if Lori brushed for [tex]2\ mins[/tex] at night she will have [tex]1[/tex] cavity on that year.