A bag contains only red, green, brown and yellow marbles. The probabilities of selecting each colour are shown below. red=5x green=2x brown=3x yellow=4x Find the probability of selecting a yellow marble. P(Yellow)=?

28.57%

Step-by-step explanation:

In order to find the probability of selecting a yellow marble we first need to calculate the total number of marbles in the bag. We do this by adding the number of individual colored marbles together.

5 + 2 + 3 + 4 = 14 total marbles

Now that we have the total number of marbles in the bag we need to divide the number of yellow marbles by this total to get the probability in decimal form.

4 (yellow) / 14 (total) =  0.2857

Now we need to multiply this decimal by 100 to get the percentage probability.

0.2857 * 100 = 28.57%

Finally, we can see that the probability of selecting a yellow marble is 28.57%

∠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.