On a field trip, there is a 55% chance of kids having pizza for lunch, a 20% chance of kids having tacos for lunch and a 11% chance of kids having pizza and tacos together for lunch. Are the two events "kids eating pizza" and "kids eating tacos" independent? Justify your answer.

Event A is having pizza for lunch and B having tacos for lunch. Since , these two events are independent.

Step-by-step explanation:

Two events, A and B are independent, if:

In this problem:

Event A: having pizza for lunch.

Event B: having tacos for lunch.

55% chance of kids having pizza for lunch

This means that

20% chance of kids having tacos for lunch

This means that

11% chance of kids having pizza and tacos together for lunch.

This means that

So

Event A is having pizza for lunch and B having tacos for lunch. Since , these two events are independent.

∠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.

x = 17

step-by-step explanation:

1st step: isolate x.

24 - 3x = -27

-24         -24

-3x   =   -51

2nd step: divide.

-3x     =   -51

  3             3

  x       =     17

hope this