To solve this, we need to break down the expression \( 1.95(0.4d) \) and understand what it represents.
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The term \( 0.4d \) indicates a decrease of 40% from the original price \( d \) because:
- 40% of \( d \) is \( 0.4d \), meaning that the new price after this decrease is \( d - 0.4d = 0.6d \).
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The term \( 1.95(0.4d) \) represents 195% of \( 0.4d \), which is an increase after the decrease:
- \( 1.95(0.4d) = 0.78d \), meaning that the stock price after both events results in a price equal to \( 0.78d \).
Now let's analyze the price changes:
- The price originally was \( d \).
- After a decrease of 40%, the price becomes \( 0.6d \).
- The expression \( 1.95(0.4d) \) suggests that after that decrease, we're calculating a new price based on \( 0.4d \), which technically represents another price evaluation rather than a direct rise from the previous decrement.
Given this, let's analyze the options:
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The price decreased by 60% and then increased by 95%: This is incorrect because it states a 60% decrease, which does not happen.
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The price increased by 0.95% and then decreased by 0.6%: This is incorrect based on our findings.
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The price decreased by 40% and then increased by 0.95%: This also does not align with our findings.
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The price decreased by 40% and then increased by 95%: This is correct since the expression indicates that after a 40% decrease (resulting in \( 0.6d \)), we find 195% of some portion of the original value.
Since \( 1.95(0.4d) \) mathematically indicates an increase after the decrease (a complex combination but leading to a variant decrease), the correct interpretation based on given decreasing and increasing rates should support this.
Thus, the choice is:
The price decreased by 40% and then increased by 95%.