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According to the North American Numbering Plan Administration (NANPA) standards, U. S. phone numbers contain a 3-digit area code, followed by a 3-digit exchange code and end in a 4­digit subscriber number. The first digit of both the area code and exchange code cannot be 0 or 1. How many different combinations of area code and exchange code are possible? Express your answer in scientific notation.

In the state of Maryland, the 301 area code took effect in 1947, and by 1991 every possible phone number with a 301 area code had been assigned to a Maryland phone subscriber. At that time, the state instituted the 410 area code. Just six years later the state had exhausted its pool of available phone numbers with a 410 area code. So in 1997, the 240 and 443 area codes took effect in the state. In 2012, once again on the verge of running out of phone numbers, the state of Maryland introduced a new 667 area code to expand its pool of available phone numbers. What is the total number of unique phone numbers possible (in compliance with NANPA standards) using the 301, 410, 240, 443 and 667 area codes?

It took 44 years (1947 to 1991) to deplete the pool of available numbers with a 301 area code in the state of Maryland, but only 6 years (1991 to 1997) to exhaust all possible numbers with a 410 area code. The proliferation of cell phone use is the main cause for the drastic increase in the rate at which phone numbers were assigned. What is the percent increase from the rate at which 301 area code phone numbers were assigned to the rate at which numbers with a 410 area code were assigned? Express your answer to the nearest whole number.

1) 6.4 × 10^5 combinations

2) 40,000,000phone numbers

3) 633%

Step-by-step explanation:

1) U.S. phone numbers:

area code = 3-digit, exchange code= 3-digit, subscriber code at the end= 4­digit

and exchange code cannot be 0 or 1

Since number system is from 0-9:

For 3 digit area code:

The first digit of area code cannot be 0 or 1, the numbers would be between 2-9. When you count 2-9 =8 numbers

The 2 and 3 digit would be between 0-9. When you count 0-9 = 10 numbers for both

Combinations of area code = 8 × 10 × 10 = 800 different combinations.

For exchange code:

The first digit of exchange code cannot be 0 or 1, the numbers would be between 2-9. When you count 2-9 = 8 numbers

The 2 and 3 digit would be between 0-9. When you count 0-9 = 10 numbers for both

Combinations of exchange code = 8 × 10 × 10 = 800 different combinations.

The number of different combinations of area code and exchange code that is possible = 800 × 800

= 640,000 = 6.4 × 10^5 combinations.

2) Area code (3digit): 1st digit falls between 2-9 = 8numbers, 2 others are 10 numbers each.

Exchange code (3 digit): 1st digit falls between 2-9 = 8numbers, 2 others are 10 numbers each.

Subscriber number (4 digit) falls between 0-9 = 10 numbers each

For each of the five area codes combination(exchange code, subscriber number),

we have 8 × 10 × 10 = 800 possible exchange codes

10 × 10 × 10 × 10 = 10,000 possible subscriber numbers.

The total number of unique phone numbers possible (in compliance with NANPA standards) using the 301, 410, 240, 443 and 667 area codes:

= 5 × 800 × 10,000 = 40,000,000 phone numbers.

3) There are 8,000,000 unique phone numbers for the 301 area code.

If these numbers were exhausted in 44 years, then number of phone numbers assigned yearly:

= 8,000,000 ÷ 44 = 181,818.18

There are 8,000,000 unique phone numbers for the 410 area code.

If these numbers were exhausted in 6 years, then number of phone numbers assigned yearly:

= 8,000,000 ÷ 6 = 1,333,333.33

For the 410 area code, difference in numbers assigned yearly:

= 1,333,333.33 - 181,818.18 = 1,151,515.15

phone numbers assigned per year. Percentage increase = (increase/number of 301code assigned yearly)×100

(1,151,515.15 ÷ 181,818.18) ×100 = 633.33 ≈ 633%

The percent increase from the rate at which 301 area code phone numbers were assigned to the rate at which numbers with a 410 area code were assigned = 633%

step-by-step explanation:

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step-by-step explanation: