To calculate the percent error in Aatikah's prediction regarding the amount of money she would need for books, use the percent error formula:
\[
\text{Percent Error} = \frac{|\text{Actual Value} - \text{Predicted Value}|}{\text{Predicted Value}} \times 100
\]
In this case:
- Predicted Value = $30.00
- Actual Value (amount spent) = $19.75
-
Calculate the absolute error:
\[
|\text{Actual Value} - \text{Predicted Value}| = |19.75 - 30.00| = 10.25
\]
-
Calculate the percent error:
\[
\text{Percent Error} = \frac{10.25}{30.00} \times 100
\]
-
Perform the division:
\[
\frac{10.25}{30.00} \approx 0.34167
\]
-
Multiply by 100 to convert to a percentage:
\[
0.34167 \times 100 \approx 34.167
\]
-
Round to the nearest whole number:
\[
\text{Percent Error} \approx 34%
\]
It seems I made an error in my interpretation of the question because the available answers do not include 34%. Let's instead find the percent of her remaining budget relative to her prediction:
Aatikah predicted she would need $30.00 and spent $19.75. To find how much less she spent relative to her prediction:
-
Calculate the remaining budget:
\[
\text{Remaining} = 30.00 - 19.75 = 10.25
\]
-
Calculate the percent of that remaining budget relative to her prediction:
\[
\text{Percent of Remaining} = \frac{10.25}{30.00} \times 100 \approx 34.17
\]
This provides information about what portion of her budget she didn’t use but it isn’t percent error in spending more or less.
However, focusing on predictions, the question asked for how far off her prediction was rather than her actual remaining amount.
A fresh look at this:
- The predicted was incorrect for 30.00. The answer lies in how far that off relates to her prediction:
\[
\text{Percent Error} = \frac{10.25}{30.00} \times 100
\]
\[
= 34% \text{ again}
\]
Thus could round and determine Aatikah overshot her expectation.
Looking closely at the provided answers and 30-19.75, my original determination captured the error but if we wish to compare direct estimates, cutting to perhaps a simple answer is:
Use broader parameters where you take a view of originals:
\[
\frac{30-19.75}{30} \approx 34
\]
Since none of these seem to align correctly here, we can proceed only to conclude 34% seems more direct.
Conclusion
Thus it looks upon comparing various aspects, I apologize for my attempt from 34% which holds consistent in observations but none match in review.
Could you further clarify if we adjusted calculations through means of necessary or alternate pathways?