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Answer :
To solve this question, we're considering the domain of the situation in which a monogramming company charges customers for each letter in a monogramming project. The cost is calculated using the formula [tex]\( c = 3.75x \)[/tex], where [tex]\( x \)[/tex] is the number of letters.
Let's analyze the options to determine which type of number is most reasonable for the domain:
1. All integers (Option A): Integers include both positive and negative numbers, as well as zero. While numbers of letters can be zero, having a negative number of letters doesn't make sense in this context.
2. All whole numbers (Option B): Whole numbers are non-negative integers, which include zero and all positive integers. This is reasonable because you can't have a fraction of a letter or a negative number of letters in a monogramming project. You start counting from zero letters up to as many as needed, and they must be whole, complete letters.
3. All real numbers (Option C): Real numbers include all possible numbers, including fractions and decimals. Since you can't have a fractional part of a letter in this context (like 2.5 letters), this option wouldn't be reasonable.
4. All of the above (Option D): Given that not all the listed types (specifically, real numbers and negative integers) are suitable for this situation, this option isn't appropriate.
Based on this analysis, the most reasonable domain is all whole numbers because they represent non-negative, complete counts of letters. Therefore, the correct answer is:
B. All whole numbers
Let's analyze the options to determine which type of number is most reasonable for the domain:
1. All integers (Option A): Integers include both positive and negative numbers, as well as zero. While numbers of letters can be zero, having a negative number of letters doesn't make sense in this context.
2. All whole numbers (Option B): Whole numbers are non-negative integers, which include zero and all positive integers. This is reasonable because you can't have a fraction of a letter or a negative number of letters in a monogramming project. You start counting from zero letters up to as many as needed, and they must be whole, complete letters.
3. All real numbers (Option C): Real numbers include all possible numbers, including fractions and decimals. Since you can't have a fractional part of a letter in this context (like 2.5 letters), this option wouldn't be reasonable.
4. All of the above (Option D): Given that not all the listed types (specifically, real numbers and negative integers) are suitable for this situation, this option isn't appropriate.
Based on this analysis, the most reasonable domain is all whole numbers because they represent non-negative, complete counts of letters. Therefore, the correct answer is:
B. All whole numbers
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