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Answer :
To solve the problem, let's calculate the total number of seconds Jim's playlist will play:
1. Determine the total number of songs: Jim has a total of 1,900 songs in his music library.
2. Average duration of each song: Each song has an average playing time of 3.5 minutes.
3. Convert the average time from minutes to seconds: There are 60 seconds in a minute, so we need to convert the time for each song into seconds:
[tex]\[
3.5 \text{ minutes} \times 60 \text{ seconds/minute} = 210 \text{ seconds}
\][/tex]
4. Calculate the total playing time in seconds: Multiply the number of songs by the average song duration in seconds:
[tex]\[
1,900 \text{ songs} \times 210 \text{ seconds/song} = 399,000 \text{ seconds}
\][/tex]
5. Express the total playing time in scientific notation: The number 399,000 can be expressed as:
[tex]\[
3.99 \times 10^5
\][/tex]
So, the total number of seconds the playlist will play, expressed in scientific notation, is [tex]\(3.99 \times 10^5\)[/tex] seconds. Therefore, the correct answer is:
- [tex]\(3.99 \times 10^5\)[/tex] seconds.
1. Determine the total number of songs: Jim has a total of 1,900 songs in his music library.
2. Average duration of each song: Each song has an average playing time of 3.5 minutes.
3. Convert the average time from minutes to seconds: There are 60 seconds in a minute, so we need to convert the time for each song into seconds:
[tex]\[
3.5 \text{ minutes} \times 60 \text{ seconds/minute} = 210 \text{ seconds}
\][/tex]
4. Calculate the total playing time in seconds: Multiply the number of songs by the average song duration in seconds:
[tex]\[
1,900 \text{ songs} \times 210 \text{ seconds/song} = 399,000 \text{ seconds}
\][/tex]
5. Express the total playing time in scientific notation: The number 399,000 can be expressed as:
[tex]\[
3.99 \times 10^5
\][/tex]
So, the total number of seconds the playlist will play, expressed in scientific notation, is [tex]\(3.99 \times 10^5\)[/tex] seconds. Therefore, the correct answer is:
- [tex]\(3.99 \times 10^5\)[/tex] seconds.
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