15 points! Make sure everything is correct!

These all start the same way:

1. AD ≅ CD  Given

2. BD ⊥ AC  Given

ok, now we're aiming for congruent triangles using SAS

3. BD ≅ BD    Reflexive property

4. ∠ADB and ∠CDB are right        Def perpendicular lines

5. ∠ADB ≅ ∠CDB are right        Right angle congruence theorem (!)

6. ΔADB ≅ ΔCDB                       SAS

7. ∠ABD ≅ ∠CBD                      CPCTC

0.1373 = 13.73% probability that the lines are occupied for exactly 5 calls

Step-by-step explanation:

For each call, there are only two possible outcomes. Either the lines are occupied, or they are not. The events that the lines are occupied on successive calls are independent. This means that we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

In which is the number of different combinations of x objects from a set of n elements, given by the following formula.

And p is the probability of X happening.

The phone lines to an airline reservation system are occupied 61% of the time.

This means that

If 11 calls are placed, what is the probability that the lines are occupied for exactly 5 calls

This is P(X = 5) when n = 11. So

0.1373 = 13.73% probability that the lines are occupied for exactly 5 calls