Find the exact value of the given trigonometric expression given that sin u = 5/13 and cos v = -3/5. both u and v are in quadrant ii.

a. cot(u+v)

b. cos2u

c. sin(v/2)

Scores on a university exam are normally distributed with a mean of 78 and a standard deviation of 8. the professor teaching the class declares that a score of 70 or higher is required for a grade of at least “c.” using the 68-95-99.7 rule, what percentage of students failed to earn a grade of at least “c”?

The biologist has a second culture to examine. she knows that the population of the culture doubles every 15 minutes. after 1 hour and 15 minutes, her assistant found that 80,000 bacteria were present. a) what was the size of the initial population? b) predict the size of the culture at t=3 hours. what was the size of the population at 40 minutes? explain and justify your answers. c) create a graph of the population as a function of time. find an equation that can be used to predict the size of the population at any time t. d) examine the rate at which the bacteria culture is growing. how fast is the culture growing after 1 hour? after 1.5 hours? after 2 hours? use a time interval of h = 0.01 hours to estimate these rates. interpret these rates in terms of the context of the problem situation. how do these three rates compare?

Nina has prepared the following two-column proof below. she is given that ∠oln ≅ ∠lno and she is trying to prove that ol ≅ on. triangle oln, where angle oln is congruent to angle lno step statement reason 1 ∠oln ≅ ∠lno given 2 draw oe as a perpendicular bisector to ln by construction 3 ∠leo ≅ ∠neo transitive property of equality 4 m∠leo = 90° definition of a perpendicular bisector 5 m∠neo = 90° definition of a perpendicular bisector 6 le ≅ en definition of a perpendicular bisector 7 δole ≅ δone side-angle-side (sas) postulate 8 ol ≅ on cpctc nina made two errors in the proof. identify and correct the errors.