5. Translate each of these statements into logical expressions using predicates, quantifiers, and logical connectives. The domain is all people on Earth. a) No one is perfect. b) Not everyone is perfect. c) All your friends are perfect. d) At least one of your friends is perfect. e) Everyone is your friend and is perfect. f) Not everybody is your friend or someone is not perfect.

Acable company wants to provide cell phone service for residents on an island. the function for the cost of laying the cable from the island to the mainland is c(x)= 6.500 square root x2+4, where x represents the length of the cable in feet. what are the domain and range of the function? a) domain: all real numbers range: all real numbers greater than or equal to 17,000 b) domain: all real numbers greater than or equal to 0 range: all real numbers greater than or equal to 17,000 c) domain: all real numbers greater than or equal to 0 range: all real numbers greater than or equal to 13,000 d) domain: all real numbers greater than or equal to 13,000 range: all real numbers greater than or equal to 0

Find the area of the region that is inside r=3cos(theta) and outside r=2-cos(theta). sketch the curves.

Agrid shows the positions of a subway stop and your house. the subway stop is located at (-5,2) and your house is located at (-9,9). what is the distance, to the nearest unit, between your house and the subway stop?