Answer :
To determine how many points the value of the stock changed over the week, let's break down the changes day by day and then sum them up.
1. Days of Increase:
- On two occasions, the value of the stock increases by [tex]\(14 \frac{2}{3}\)[/tex] points.
- First increase: [tex]\(14 \frac{2}{3} = 14 + \frac{2}{3} = 14.6666...\)[/tex] points.
- Second increase: again, [tex]\(14 \frac{2}{3} = 14.6666...\)[/tex] points.
2. Days of Decrease:
- First decrease: 10 points.
- Second decrease: [tex]\(8 \frac{1}{3}\)[/tex] points, which is [tex]\(8 + \frac{1}{3} = 8.3333...\)[/tex] points.
- Third decrease: [tex]\(12 \frac{2}{3}\)[/tex] points, which is [tex]\(12 + \frac{2}{3} = 12.6666...\)[/tex] points.
3. Calculating Total Change:
- Total increase over two days: [tex]\(14.6666... + 14.6666... = 29.3333...\)[/tex] points.
- Total decrease over three days: [tex]\(10 + 8.3333... + 12.6666... = 31\)[/tex] points.
4. Net Change for the Week:
- The overall change in the stock's value is the total increase minus the total decrease.
- Net Change = Total Increase - Total Decrease = [tex]\(29.3333...\)[/tex] points - [tex]\(31\)[/tex] points = [tex]\(-1.6666...\)[/tex] points.
Thus, during the week, the stock's value changed by approximately [tex]\(-1 \frac{2}{3}\)[/tex] points. The correct answer to the problem is [tex]\(-1 \frac{2}{3}\)[/tex] points.
1. Days of Increase:
- On two occasions, the value of the stock increases by [tex]\(14 \frac{2}{3}\)[/tex] points.
- First increase: [tex]\(14 \frac{2}{3} = 14 + \frac{2}{3} = 14.6666...\)[/tex] points.
- Second increase: again, [tex]\(14 \frac{2}{3} = 14.6666...\)[/tex] points.
2. Days of Decrease:
- First decrease: 10 points.
- Second decrease: [tex]\(8 \frac{1}{3}\)[/tex] points, which is [tex]\(8 + \frac{1}{3} = 8.3333...\)[/tex] points.
- Third decrease: [tex]\(12 \frac{2}{3}\)[/tex] points, which is [tex]\(12 + \frac{2}{3} = 12.6666...\)[/tex] points.
3. Calculating Total Change:
- Total increase over two days: [tex]\(14.6666... + 14.6666... = 29.3333...\)[/tex] points.
- Total decrease over three days: [tex]\(10 + 8.3333... + 12.6666... = 31\)[/tex] points.
4. Net Change for the Week:
- The overall change in the stock's value is the total increase minus the total decrease.
- Net Change = Total Increase - Total Decrease = [tex]\(29.3333...\)[/tex] points - [tex]\(31\)[/tex] points = [tex]\(-1.6666...\)[/tex] points.
Thus, during the week, the stock's value changed by approximately [tex]\(-1 \frac{2}{3}\)[/tex] points. The correct answer to the problem is [tex]\(-1 \frac{2}{3}\)[/tex] points.
