A gambler has 4 packs of cards, each of which is well shuffled and has equal numbers of red, green and blue cards. For each turn he pays 2$ and draws a card from each pack. He wins 3$ if he gets 2 red cards, 5$ if he gets 3 red cards and 10$ if he gets 4 red cards. Let the random variable X represent how much the gambler earned and Y represent the number of blue cards chosen. Find the joint distribution of X and Y.

Polygon abcde is reflected to produce polygon a′b′c′d′e′. what is the equation for the line of reflection?

0if x and y vary inversely and y=6 as x=7, what is the constant of variation?

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