The Transportation Safety Authority (TSA) has developed a new test to detect large amounts of liquid in luggage bags. Based on many test runs, the TSA determines that if a bag does contain large amounts of liquid, there is a probability of 0.97 the test will detect it. If a bag does not contain large amounts of liquid, there is a 0.1 probability the test will conclude that it does (a false positive). Suppose that in reality only 1 in 100 bags actually contain large amounts of liquid. a. What is the probability a randomly selected bag will have a positive test?

the probability is 0.1087 (10.87%)

Step-by-step explanation:

defining the random variable T= the test is positive , then the probability that the test is positive given that a bag is chosen at random is

P(T)= probability of choosing a bag with large amounts of liquid * probability that the test is positive given that that the bag have excess liquid + probability of choosing a bag that does not have not large amounts of liquid * probability that the test is positive given that that the bag does not have not have excess liquid = 1/100 * 0.97 + 99/100 * 0.1 = 0.1087 (10.87%)

∠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.

c 1 hour

step-by-step explanation:

m = 2e

m = 2 so 2 = 2e

1 = e