In a group of 50 patrons, 8 patrons like lattes and espressos, 12 patrons like espressos and cappuccinos, 9 patrons like lattes and cappuccinos, and 5 patrons like all 3 coffee drinks. altogether, 20 patrons like lattes, 28 patrons like espressos, and 19 patrons like cappuccinos. how many patrons don't like any of these coffee drinks?

1. are the triangles similar and if so why? what is the value of x? show your work.

Apinhole camera is made out of a light-tight box with a piece of film attached to one side and pinhole on the opposite side. the optimum diameter d(in millimeters) of the pinhole can be modeled by d=1.9[ (5.5 x 10^-4) l) ] ^1/2, where l is the length of the camera box (in millimeters). what is the optimum diameter for a pinhole camera if the camera box has a length of 10 centimeters

In a two-digit number the units' digit is 7 more than the tens' digit. the number with digits reversed is three times as large as the sum of the original number and the two digits. find the number.