Afarmer estimates that he has 9,000 bees producing honey on his farm. the farmer becomes concerned when he realizes the population of bees seems to be decreasing steadily at a rate of 5% per year. if the number of bees in the population after x years is represented by f(x), which statements about the situation are true? check all that apply.

the function f(x) = 9,000(1.05)x represents the situation.

the function f(x) = 9,000(0.95)x represents the situation.

after 2 years, the farmer can estimate that there will be about 8,120 bees remaining.

after 4 years, the farmer can estimate that there will be about 1,800 bees remaining.

the domain values, in the context of the situation, are limited to whole numbers.

the range values, in the context of the situation, are limited to whole numbers.

Part of the total score for each program is the sum of five program component scores. on the free program, the sum of these five program component scores is multiplied by a factor of 2.0. yuzuru hanyu, of japan, earned scores of 9.07, 8.96, 8.89, 9.21, and 9.36 for the program components portion of his free program. how many total points did he receive for this portion?

Monthly water bills for a city have a mean of $108.43 and a standard deviation of $32.09. find the probability that a randomly selected bill will have an amount greater than $155, which the city believes might indicate that someone is wasting water. would a bill that size be considered unusual?

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