Welcome to Westonci.ca, the place where your questions find answers from a community of knowledgeable experts. Connect with a community of experts ready to provide precise solutions to your questions quickly and accurately. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately.
Sagot :
Certainly! Let's solve this step by step:
1. Identify the pattern in James' typing speed:
- At the end of the first month: 9 words per minute.
- At the end of the second month: 18 words per minute.
- At the end of the third month: 27 words per minute.
Observing these values, we can see that James' typing speed forms an arithmetic sequence (each term increases by the same amount).
2. Determine the common difference:
- From the first month to the second month: [tex]\(18 - 9 = 9\)[/tex]
- From the second month to the third month: [tex]\(27 - 18 = 9\)[/tex]
So, the common difference (denoted as [tex]\(d\)[/tex]) is 9 words per minute.
3. Formulate the general term of the arithmetic sequence:
The general formula for the n-th term of an arithmetic sequence is:
[tex]\[ a_n = a_1 + (n - 1)d \][/tex]
where [tex]\(a_n\)[/tex] is the n-th term, [tex]\(a_1\)[/tex] is the first term, and [tex]\(d\)[/tex] is the common difference.
4. Apply the formula to find James' typing speed at the end of the fifth month:
- First term ([tex]\(a_1\)[/tex]) = 9 words per minute.
- Common difference ([tex]\(d\)[/tex]) = 9 words per minute.
- n = 5 (since we are asked about the fifth month).
Plugging these values into the formula gives us:
[tex]\[ a_5 = 9 + (5 - 1) \times 9 \][/tex]
Simplifying inside the parentheses:
[tex]\[ a_5 = 9 + 4 \times 9 \][/tex]
Multiply:
[tex]\[ a_5 = 9 + 36 \][/tex]
Adding these together:
[tex]\[ a_5 = 45 \][/tex]
Therefore, at the end of five months, James could type 45 words per minute.
Thus, the correct answer is:
b. 45 words per minute.
1. Identify the pattern in James' typing speed:
- At the end of the first month: 9 words per minute.
- At the end of the second month: 18 words per minute.
- At the end of the third month: 27 words per minute.
Observing these values, we can see that James' typing speed forms an arithmetic sequence (each term increases by the same amount).
2. Determine the common difference:
- From the first month to the second month: [tex]\(18 - 9 = 9\)[/tex]
- From the second month to the third month: [tex]\(27 - 18 = 9\)[/tex]
So, the common difference (denoted as [tex]\(d\)[/tex]) is 9 words per minute.
3. Formulate the general term of the arithmetic sequence:
The general formula for the n-th term of an arithmetic sequence is:
[tex]\[ a_n = a_1 + (n - 1)d \][/tex]
where [tex]\(a_n\)[/tex] is the n-th term, [tex]\(a_1\)[/tex] is the first term, and [tex]\(d\)[/tex] is the common difference.
4. Apply the formula to find James' typing speed at the end of the fifth month:
- First term ([tex]\(a_1\)[/tex]) = 9 words per minute.
- Common difference ([tex]\(d\)[/tex]) = 9 words per minute.
- n = 5 (since we are asked about the fifth month).
Plugging these values into the formula gives us:
[tex]\[ a_5 = 9 + (5 - 1) \times 9 \][/tex]
Simplifying inside the parentheses:
[tex]\[ a_5 = 9 + 4 \times 9 \][/tex]
Multiply:
[tex]\[ a_5 = 9 + 36 \][/tex]
Adding these together:
[tex]\[ a_5 = 45 \][/tex]
Therefore, at the end of five months, James could type 45 words per minute.
Thus, the correct answer is:
b. 45 words per minute.
Visit us again for up-to-date and reliable answers. We're always ready to assist you with your informational needs. We appreciate your time. Please come back anytime for the latest information and answers to your questions. Thank you for trusting Westonci.ca. Don't forget to revisit us for more accurate and insightful answers.