18. A simple telephone system consists of two end offices and a single toll office to which each end office is connected by a 1-MHz full-duplex trunk. The average telephone is used to make four calls per 8-hour workday. The mean call duration is 6 min. Ten percent of the calls are long distance (i. e., pass through the toll office). What is the maximum number of telephones an end office can support

The maximum number of telephones an end office can support is 51200.

Step-by-step explanation:

It is provided that each telephone user makes 4 calls. The average duration of a call is 6 minutes.

Total times of the 4 calls = 4 × 6 = 24 minutes.

It is also provided that 10% of the calls are long-distance.

The time duration for long distance calls is, 10% × 24 = 2.4 minutes.

Assume that each user has a 4kHz connection.

The number of calls that can be made is:

It is also provided that the working hour per day is 8.

Then  the maximum number of telephones an end office can support is:

Max. Number of phone calls =

Thus, the maximum number of telephones an end office can support is 51200.

75 tickets have been sold so far.

step-by-step explanation:

in this question it is clearly mentioned that 45 children's tickets have been sold and this number is 60% of the total tickets sold.

now let's assume the total number of tickets sold be x.

then 60% of x = 45

⇒

⇒ x(.6) = 45

by dividing with .6 on both the sides of the equation

⇒ x = 75

therefore 75 tickets have been sold so far.