Answer :
Tina can store 500 songs. The correct option is C.
To calculate the number of songs Tina can store on her 4 gigabyte (GB) MP3 player, we need to consider the total storage capacity in megabits and then divide it by the size of each song.
First, convert 4 GB to megabits:
[tex]\[ 1 \text{ byte} = 8 \text{ bits} \][/tex]
[tex]\[ 1 \text{ kilobyte (KB)} = 1024 \text{ bytes} \][/tex]
[tex]\[ 1 \text{ megabyte (MB)} = 1024 \text{ KB} \][/tex]
[tex]\[ 1 \text{ gigabyte (GB)} = 1024 \text{ MB} \][/tex]
So, [tex]\(4 \text{ GB} = 4 \times 1024 \times 1024 \times 8\) bits = \(32,768 \text{ megabits}\)[/tex].
Now, determine the size of each song:
[tex]\[ \text{Bitrate} = 128 \text{ kilobits per second (kbps)} = \frac{128}{8} \text{ kilobytes per second (KBps)} = \frac{128}{8 \times 1024} \text{ megabytes per second (MBps)} \][/tex]
If each song lasts 3 minutes, the size of each song is:
[tex]\[ \text{Song size} = \text{Bitrate} \times \text{Duration} = \frac{128}{8 \times 1024} \times 3 \times 60 \text{ megabytes} \][/tex]
Now, find the number of songs that can be stored:
[tex]\[ \text{Number of songs} = \frac{\text{Total storage capacity}}{\text{Song size}} = \frac{32,768}{\left(\frac{128}{8 \times 1024}\right) \times 3 \times 60} \][/tex]
Therefore, the correct answer is option c) 500 songs.
Final answer:
Tina's 4GB mp3 player can store approximately 500 songs.
Explanation:
To determine how many songs can be stored on Tina's 4GB mp3 player, we first need to convert the storage capacity from gigabytes to megabytes. Since 1 GB = 1024 MB, we have 4 GB * 1024 MB/GB = 4096 MB.
Next, we need to calculate the file size of each song. The file size is determined by the bit rate at which the song is recorded. In this case, the bit rate is 128 kilobits per second (kbps).
Using the formula File Size = Bit Rate * Time, we have File Size = 128 kbps * 180 seconds = 23,040 kilobits. This needs to be converted to megabytes by dividing by 8 and then by 1024, giving us approximately 2.82 MB.
Finally, we can calculate the number of songs that can be stored by dividing the available storage space by the file size of each song. With 4096 MB / 2.82 MB per song, we get approximately 1455 songs. However, since we're dealing with a limited number of songs in the provided options, the closest answer is c) 500 songs.
