John is watching an old game show rerun on television called let's make a deal in which the contestant chooses a prize behind one of two curtains. behind one of the curtains is a gag prize worth $150, and behind the other is a round-the-world trip worth $7,200. the producer of the game show has placed a subliminal message on the curtain containing the gag prize, which makes the probability of choosing the gag prize equal to 75 percent. what is the expected value of the selection, and what is the standard deviation of that selection?

Which expression is equivalent to 16 in exponential form? a) 4 × 4 b) 8 × 2 c) 23 d) 24

X/y + 4y/x divided by x/y - 2y/x explain as in depth as you can how you simplfied the fractions. i don't know where to start on this : /

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