Circonferenza non centrata

Prove that the value of the expression 7^8–7^7+7^6 is divisible by 43.

Acafeteria manager can choose from among six side dishes for the lunch menu: applesauce, broccoli, corn, dumplings, egg rolls, or french fries. he used a computer program to randomly select three dishes for monday's lunch. what is the theoretical probability the applesauce and broccoli will both be offered monday?

Among the most famous of all meteor showers are the perseids, which occur each year in early august. in some areas the frequency of visible perseids can be as high as 40 per hour. given that such sightings are poisson events, calculate the probability that an observer who has just seen a meteor will have to wait at least five minutes before seeing another.