Ralph lauren can make at most 30 knit sweaters and 20 trademark polo shirts in a week. it takes a worker 10 hours to make a sweater and 20 hours to make a polo shirt. The total number a worker 10 hours to make a sweater and 20 hours to make a polo shirt. The total number of hours worked by all of the empolyees can be no more than 500 hours per week. If the profit on a sweater is $10 and the profit for a polo shirt is also $10 hpw many of each should ralph lauren make to maximize profit? Hpw many of each should be made if the profit on a polo shirt is $30 and the profit on a sweater is $10?

The chart below shows the distribution of weeds in yard

The american academy of pediatrics wants to conduct a survey of recently graduated family practitioners to assess why they did not choose pediatrics for their specialization. provide a definition of the population, suggest a sampling frame, and indicate the appropriate sampling unit.

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