To determine the number of minutes Sidney plans to study on day 7, we need to identify the pattern in the amount of time he studies each day.
Let's look at the given data:
[tex]\[
\begin{array}{|c|c|c|c|}
\hline & \text{Day} & & \text{Minutes} \\
\hline & 1 & III & 11 \\
\hline & 2 & II & 18 \\
\hline & 3 & II & 25 \\
\hline & 4 & III & 32 \\
\hline & 5 & III & 39 \\
\hline & 6 & I & 46 \\
\hline & 7 & II & ? \\
\hline
\end{array}
\][/tex]
We can see the minutes he spends studying each day:
- Day 1: 11 minutes
- Day 2: 18 minutes
- Day 3: 25 minutes
- Day 4: 32 minutes
- Day 5: 39 minutes
- Day 6: 46 minutes
Observing the pattern, we find that each day's study time increases by 7 minutes compared to the previous day. To check:
- From day 1 to day 2: [tex]\( 18 - 11 = 7 \)[/tex]
- From day 2 to day 3: [tex]\( 25 - 18 = 7 \)[/tex]
- From day 3 to day 4: [tex]\( 32 - 25 = 7 \)[/tex]
- From day 4 to day 5: [tex]\( 39 - 32 = 7 \)[/tex]
- From day 5 to day 6: [tex]\( 46 - 39 = 7 \)[/tex]
This consistent increase indicates that the pattern is an increase of 7 minutes every day.
To find the minutes Sidney plans to study on day 7, we add this increment of 7 minutes to the time he studied on day 6:
Minutes on day 6: 46 minutes
Adding the increment for day 7:
[tex]\[
46 + 7 = 53
\][/tex]
Therefore, Sidney plans to study for 53 minutes on day 7.
The correct answer is:
[tex]\[
53
\][/tex]
