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Answer :
We are given that the stock increases by
[tex]$$14\frac{2}{3}$$[/tex]
points on two days and decreases by 10,
[tex]$$8\frac{1}{3}$$[/tex]
, and
[tex]$$12\frac{2}{3}$$[/tex]
points on the other three days. We will compute the net change step by step.
1. Convert Mixed Numbers to Improper Fractions:
The increase of
[tex]$$14\frac{2}{3}$$[/tex]
points can be written as
[tex]$$14\frac{2}{3} = \frac{14 \times 3 + 2}{3} = \frac{42 + 2}{3} = \frac{44}{3}.$$[/tex]
Similarly, for the decreases:
- For
[tex]$$8\frac{1}{3},$$[/tex]
we have
[tex]$$8\frac{1}{3} = \frac{8 \times 3 + 1}{3} = \frac{24 + 1}{3} = \frac{25}{3}.$$[/tex]
- For
[tex]$$12\frac{2}{3},$$[/tex]
it becomes
[tex]$$12\frac{2}{3} = \frac{12 \times 3 + 2}{3} = \frac{36 + 2}{3} = \frac{38}{3}.$$[/tex]
2. Calculate Total Increase:
The stock increases by
[tex]$$\frac{44}{3}$$[/tex]
points on two days. Therefore, the total increase is:
[tex]$$\text{Total Increase} = 2 \times \frac{44}{3} = \frac{88}{3}.$$[/tex]
3. Calculate Total Decrease:
The decreases occur as follows:
- First day: 10 points.
- Second day:
[tex]$$\frac{25}{3}$$[/tex]
points.
- Third day:
[tex]$$\frac{38}{3}$$[/tex]
points.
To combine these, express 10 as a fraction with denominator 3:
[tex]$$10 = \frac{30}{3}.$$[/tex]
Now, add them together:
[tex]$$\text{Total Decrease} = \frac{30}{3} + \frac{25}{3} + \frac{38}{3} = \frac{30+25+38}{3} = \frac{93}{3} = 31.$$[/tex]
4. Compute the Net Change:
The net change in the stock’s value is the total increase minus the total decrease:
[tex]$$\text{Net Change} = \frac{88}{3} - 31.$$[/tex]
Rewrite 31 with denominator 3:
[tex]$$31 = \frac{93}{3}.$$[/tex]
Then,
[tex]$$\text{Net Change} = \frac{88}{3} - \frac{93}{3} = \frac{88 - 93}{3} = \frac{-5}{3}.$$[/tex]
Expressing [tex]$\frac{-5}{3}$[/tex] as a mixed number:
[tex]$$\frac{-5}{3} = -1\frac{2}{3}.$$[/tex]
Thus, the value of the stock changed by
[tex]$$-1\frac{2}{3}$$[/tex]
points that week.
The correct answer is:
(D) [tex]$-1 \frac{2}{3}$[/tex] points.
[tex]$$14\frac{2}{3}$$[/tex]
points on two days and decreases by 10,
[tex]$$8\frac{1}{3}$$[/tex]
, and
[tex]$$12\frac{2}{3}$$[/tex]
points on the other three days. We will compute the net change step by step.
1. Convert Mixed Numbers to Improper Fractions:
The increase of
[tex]$$14\frac{2}{3}$$[/tex]
points can be written as
[tex]$$14\frac{2}{3} = \frac{14 \times 3 + 2}{3} = \frac{42 + 2}{3} = \frac{44}{3}.$$[/tex]
Similarly, for the decreases:
- For
[tex]$$8\frac{1}{3},$$[/tex]
we have
[tex]$$8\frac{1}{3} = \frac{8 \times 3 + 1}{3} = \frac{24 + 1}{3} = \frac{25}{3}.$$[/tex]
- For
[tex]$$12\frac{2}{3},$$[/tex]
it becomes
[tex]$$12\frac{2}{3} = \frac{12 \times 3 + 2}{3} = \frac{36 + 2}{3} = \frac{38}{3}.$$[/tex]
2. Calculate Total Increase:
The stock increases by
[tex]$$\frac{44}{3}$$[/tex]
points on two days. Therefore, the total increase is:
[tex]$$\text{Total Increase} = 2 \times \frac{44}{3} = \frac{88}{3}.$$[/tex]
3. Calculate Total Decrease:
The decreases occur as follows:
- First day: 10 points.
- Second day:
[tex]$$\frac{25}{3}$$[/tex]
points.
- Third day:
[tex]$$\frac{38}{3}$$[/tex]
points.
To combine these, express 10 as a fraction with denominator 3:
[tex]$$10 = \frac{30}{3}.$$[/tex]
Now, add them together:
[tex]$$\text{Total Decrease} = \frac{30}{3} + \frac{25}{3} + \frac{38}{3} = \frac{30+25+38}{3} = \frac{93}{3} = 31.$$[/tex]
4. Compute the Net Change:
The net change in the stock’s value is the total increase minus the total decrease:
[tex]$$\text{Net Change} = \frac{88}{3} - 31.$$[/tex]
Rewrite 31 with denominator 3:
[tex]$$31 = \frac{93}{3}.$$[/tex]
Then,
[tex]$$\text{Net Change} = \frac{88}{3} - \frac{93}{3} = \frac{88 - 93}{3} = \frac{-5}{3}.$$[/tex]
Expressing [tex]$\frac{-5}{3}$[/tex] as a mixed number:
[tex]$$\frac{-5}{3} = -1\frac{2}{3}.$$[/tex]
Thus, the value of the stock changed by
[tex]$$-1\frac{2}{3}$$[/tex]
points that week.
The correct answer is:
(D) [tex]$-1 \frac{2}{3}$[/tex] points.
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