The probability that Maria succeeds at any given free-throw is 75 % 75%75, percent. She was curious how many free-throws she can expect to succeed in a sample of 10 1010 free-throws. She simulated 25 2525 samples of 10 1010 free-throws where each free-throw had a 0.75 0.750, point, 75 probability of being a success. Maria counted how many free-throws were successes in each simulated sample. Here are her results: 5 5 6 6 7 7 8 8 9 9 10 10# of free-throw successes Use her results to estimate the probability that she succeeds at fewer than 7 77 free-throws in a sample of 10 1010 free-throws. Give your answer as either a fraction or a decimal. P ( fewer than 7 successes ) ≈

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