Amathematician decided to throw a party. when all the guests arrived, she joined the party with her husband. including the mathematician and her husband, there were five couples, making the total number of people in attendance 10. after several minutes of mingling and introductions the mathematician asked each of the nine others in attendance how many people they shook hands with. each person gave her a different answer from 0 to8. if couples did not shake hands with each other, how many people did the mathematician's husband shake hands with?

Nthe opening scene of the movie raiders of the lost ark, indiana jones replaces a golden statue with a bag of sand. the platform on which the statue is placed is designed to detect the mass of the statue. if the bag of sand has a different mass than the statue, then a mechanism triggers and destruction ensues. the density of gold is about 20\text{ g/cm}^320 g/cm 3 20, space, g, slash, c, m, start superscript, 3, end superscript. the density of sand can be estimated at 2.5\text{ g/cm}^32.5 g/cm 3 2, point, 5, space, g, slash, c, m, start superscript, 3, end superscript. the gold statue can be modeled as a cylinder with height 25\text{ cm}25 cm25, space, c, m and radius 8\text{ cm}8 cm8, space, c, m. in terms of \piπpi, what is the mass of sand indiana jones needs to avoid triggering the mechanism?