Question set 1: one instructor believes that students take more than 2 classes per quarter on average. he randomly interviewed a class of 24 students and found out the mean number of classes per quarter is 2.3 classes and standard deviation of 0.8. assume alpha is 0.05. (a) set up the hypothesis..

Given: ad¯¯¯¯¯ is an altitude. prove: ab2+ac2=cb2 right triangle a b c with right angle a. point d lies on side b c and segment a d is drawn. angle a d c is a right angle. drag and drop a reason into each box to correctly complete the two-column proof. statement reason ad¯¯¯¯¯ is an altitude, and ∠bac is a right angle. given ∠adb and ∠adc are right angles. definition of altitude ∠bac≅∠bda ? ∠bac≅∠adc ? ∠b≅∠b ? ∠c≅∠c reflexive property of congruence △abc∼△dba ? △abc∼△dac aa similarity postulate abbd=cbab ? ab2=(cb)(bd) cross multiply and simplify. acdc=cbac polygon similarity postulate ac2=(cb)(dc) cross multiply and simplify. ab2+ac2=ab2+(cb)(dc) addition property of equality ab2+ac2=(cb)(bd)+(cb)(dc) substitution property of equality ab2+ac2=(cb)(bd+dc) ? bd+dc=cb segment addition postulate ab2+ac2=cb2 substitution property of equality

Problem 2. find the exact value of the remaining trigonometric functions. sketch theangle 8 for each problem. (3 points each)(a) tan 0 =o is in quadrant 2

The measures of the angles in △abc are given by the expressions in the table. angle measure angle a 65° angle b (3x−10)° angle c (2x)∘ find the value of x. then find the m∠b and m∠c.