The angle of a tapered groove is checked using a 20mm diameter roller as shown in the above figure. If the roller lies 2.12mm below the top of the groove, determine the value of angle θ.

Two language majors, anna and megan, took exams in two languages. anna scored 85 on both exams. megan scored 74 on the first exam and 85 on the second exam. overall, student scores on the first exam had a mean of 82 and a standard deviation of 4, and the second exam scores had a mean of 71 and a standard deviation of 13. a) to qualify for language honors, a major must maintain at least an 85 average across all language courses taken. so far, which of anna and megan qualify? b) which student's overall performance was better?

In need of in the diagram, ∠abc is a right angle. ∠dbc = 30°27'40". find the measure of ∠abd.

George is putting trim around his rectangular deck, including the gate. he will need 44 feet of trim to do the entire deck. if the deck is 13 feet long, how wide is the deck?