1. A university football stadium has 81,500 seats. The stadium is at full capacity on game day. Layla believes only 79,000 seats are occupied. Find the percent error of Layla’s prediction. Round your answer to the nearest hundredth of a percent.(1 point)
Responses
0.0307%
0.0307%
−3.07%
negative 3.07 percent
3.07%
3.07%
90.3067%
2.Aatikah plans to buy books at a book fair. She thinks she will need $30.00 to purchase the books. She only spends $19.75. Find the percent error in her prediction. Round your answer to the nearest whole number.(1 point)
Responses
1%
1%
58%
58%
2%
2%
52%
52%
3.Julian and Brittany mailed 275 wedding invitations to family and friends and predicted that they would all attend. Only 265 out of 275 people committed to attending the wedding. Calculate the percent error in their prediction. Round your answer to the nearest hundredth percent.(1 point)
Responses
0.038%
0.038%
3.77%
3.77%
3.63%
3.63%
−4.00%
To solve these percent error problems, you will need to use the formula:
Percent Error = |(Observed Value - Predicted Value) / Predicted Value| * 100
Let's go through each question and calculate the percent error.
1. Layla believed that only 79,000 seats are occupied, but the stadium is at full capacity with 81,500 seats.
The formula will be: |(81,500 - 79,000) / 79,000| * 100 = 3.1646%
Rounded to the nearest hundredth of a percent, the percent error is 3.07%.
2. Aatikah predicted she would need $30.00 to purchase books, but she only spent $19.75.
The formula will be: |(19.75 - 30) / 30| * 100 = 34.1667%
Rounded to the nearest whole number, the percent error is 34%.
3. Julian and Brittany predicted that all 275 people they invited would attend their wedding, but only 265 committed.
The formula will be: |(265 - 275) / 275| * 100 = 3.6364%
Rounded to the nearest hundredth of a percent, the percent error is 3.63%.
So, the answers to the questions are:
1. 3.07%
2. 34%
3. 3.63%
1. To find the percent error of Layla's prediction, we need to calculate the difference between the actual number of occupied seats and Layla's prediction, and then divide that difference by the actual number of occupied seats:
Actual occupied seats = 81,500
Layla's predicted occupied seats = 79,000
Difference = 81,500 - 79,000 = 2,500
Percent error = (Difference / Actual occupied seats) * 100
Percent error = (2,500 / 81,500) * 100
Rounding to the nearest hundredth of a percent, the percent error is 3.07%. Therefore, the correct answer is 3.07%.
2. To find the percent error in Aatikah's prediction, we need to calculate the difference between the predicted amount and the actual amount, and then divide that difference by the actual amount:
Actual amount = $19.75
Aatikah's predicted amount = $30.00
Difference = $30.00 - $19.75 = $10.25
Percent error = (Difference / Actual amount) * 100
Percent error = ($10.25 / $30.00) * 100
Rounding to the nearest whole number, the percent error is 58%. Therefore, the correct answer is 58%.
3. To calculate the percent error in Julian and Brittany's prediction, we need to calculate the difference between the predicted number of attendees and the actual number of attendees, and then divide that difference by the actual number of attendees:
Actual attendees = 265
Predicted attendees = 275
Difference = 275 - 265 = 10
Percent error = (Difference / Actual attendees) * 100
Percent error = (10 / 265) * 100
Rounding to the nearest hundredth percent, the percent error is 3.77%. Therefore, the correct answer is 3.77%.
1. The percent error can be calculated as follows:
Percent error = (Actual value - Predicted value) / Actual value * 100
In this case, the actual value is 81,500 and the predicted value is 79,000.
Percent error = (81,500 - 79,000) / 81,500 * 100
Percent error = 2,500 / 81,500 * 100
Percent error = 0.0307
Therefore, the percent error of Layla's prediction is 0.0307%.
2. The percent error can be calculated as follows:
Percent error = (Actual value - Predicted value) / Actual value * 100
In this case, the actual value is $30.00 and the predicted value is $19.75.
Percent error = ($30.00 - $19.75) / $30.00 * 100
Percent error = $10.25 / $30.00 * 100
Percent error = 0.3417 * 100
Therefore, the percent error in Aatikah's prediction is 34.17%.