Rafeal’s family dinner costs $56.25. His dad wants him to leave a 35% tip. How much money should Rafeal provide as a tip? Round your answer to the nearest hundredth.(1 point)

Question

Responses

$1.97
$1.97

$35.00
$35.00

$19.69
$19.69

$75.94

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

90.3067%
90.3067%

3.07%
3.07%

0.0307%
0.0307%

−3.07%

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

2%
2%

1%
1%

52%
52%

58%

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

3.63%
3.63%

−4.00%
negative 4 point 0 0 percent

3.77%
3.77%

0.038%

Answer 1

Let's solve each problem step by step.

1. Rafeal's Family Dinner Tip

To calculate the tip amount, we can use the formula: \[ \text{Tip} = \text{Dinner Cost} \times \text{Tip Percentage} \]

Dinner cost = $56.25
Tip percentage = 35% = 0.35

Calculating the tip: \[ \text{Tip} = 56.25 \times 0.35 = 19.6875 \] Rounding to the nearest hundredth: \[ \text{Tip} \approx 19.69 \] Answer: $19.69

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2. Percent Error of Layla’s Prediction

Percent error formula: \[ \text{Percent Error} = \left|\frac{\text{Actual Value} - \text{Predicted Value}}{\text{Actual Value}}\right| \times 100% \]

Actual value = 81,500
Predicted value = 79,000

Calculating percent error: \[ \text{Percent Error} = \left|\frac{81,500 - 79,000}{81,500}\right| \times 100% \] \[ = \left|\frac{2,500}{81,500}\right| \times 100% \approx 3.07% \] Answer: 3.07%

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3. Percent Error in Aatikah's Prediction

Use the same percent error formula: \[ \text{Percent Error} = \left|\frac{\text{Actual Value} - \text{Predicted Value}}{\text{Predicted Value}}\right| \times 100% \]

Predicted value = $30.00
Actual value = $19.75

Calculating percent error: \[ \text{Percent Error} = \left|\frac{30.00 - 19.75}{30.00}\right| \times 100% \] \[ = \left|\frac{10.25}{30.00}\right| \times 100% \approx 34.17% \] Rounding to the nearest whole number: \[ \approx 34% \] Answer: None of the options seem to match the calculation. The closest option would be 34%, but it seems there may be an error in the options provided.

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4. Percent Error in Julian and Brittany's Prediction

Calculating percent error: \[ \text{Percent Error} = \left|\frac{275 - 265}{275}\right| \times 100% \] \[ = \left|\frac{10}{275}\right| \times 100% \approx 3.6364% \] Rounding to the nearest hundredth: \[ \approx 3.64% \] Answer: 3.63%

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Summary of Answers:

1. Tip: $19.69
2. Layla's Percent Error: 3.07%
3. Aatikah's Percent Error: 34% (not one of the listed options)
4. Julian and Brittany's Percent Error: 3.63%