In a game, a die is thrown and has the following probability distribution. the game is free to play. the payoff for some of the values was randomly generated: outcome 1 2 3 4 5 6 probability 1 6 1 6 1 6 1 6 1 6 1 6 payoff $3 $5 -$10 $11 $3 ? what would the payoff of the outcome of 6 have to be for this to be a fair distribution? (hint: expected value = $0

∠1≅∠2 by the alternate exterior angles theorem.

step-by-step explanation:

given, a ∥ b and ∠1 ≅ ∠3 .we have to prove that e ∥ f

we know that ∠1≅∠3 and that a || b because they are given. we see that by the alternate exterior angles theorem. therefore, ∠2≅∠3 by the transitive property. so, we can conclude that e || f by the converse alternate exterior angles theorem.

we have to fill the missing statement.

transitivity property states that if a = b and b = c, then a = c.

now, given ∠1≅∠3 and by transitivity property ∠2≅∠3 .

hence, to apply transitivity property one angle must be common which is not in result after applying this property which is ∠1.

the only options in which ∠1 is present are ∠1 and ∠2, ∠1 and ∠4

∠1 and ∠4 is not possible ∵ after applying transitivity we didn't get ∠4.

hence, the missing statement is ∠1≅∠2.

so, ∠1≅∠2 by the alternate exterior angles theorem.

answer: a) 56% women

b)44% men

step-by-step explanation:

you divide them and then you get the answer i took this class this year

step-by-step explanation: