Final answer:
There would be 10,000,000 possible phone numbers in the 828 area code, as each of the seven unrestricted digits can be any value from 0 to 9, which is calculated as 10 to the power of 7.
Step-by-step explanation:
The question asks how many phone numbers would be possible in the 828 area code if there were no restrictions on the remaining seven digits. Since a standard North American phone number consists of 10 digits, with the first three being the area code and the next seven being the local number, we will calculate the possibilities for the seven-digit local number.
Each digit of a phone number can be any digit from 0 to 9, which gives us 10 possible values for each digit spot. For seven unrestricted digits, we calculate the total number of combinations by using the principle of multiplication, raising the number of possibilities for each digit to the power of the number of digits.Therefore, 10^7 (10 to the power of 7) is the number of possible phone numbers. This results in 10,000,000 possible combinations.In the 828 area code of western North Carolina, there are no restrictions on the remaining seven digits of a phone number. To determine how many phone numbers are possible, we need to consider that each digit can be one of ten possible numbers (0-9). Since there are seven digits, we multiply 10 by itself seven times (10^7) to get the total number of combinations. This gives us a total of 10,000,000 possible phone numbers in the 828 area code.