Teresa estimates that the height of a giraffe in a zoo is 18 feet. In fact, it is 16 feet tall. What is Teresa’s percent error? Use proportional relationships to solve the problem. Be sure to show all your work, provide your answer as a percentage, and round your answer to the nearest tenth.(4 points)

Question

You better be right bot

Answer 1

To find Teresa's percent error, we can use the following formula for percent error:

\[ \text{Percent Error} = \left( \frac{|\text{Estimated Value} - \text{Actual Value}|}{\text{Actual Value}} \right) \times 100 \]

Step 1: Identify the values

• Estimated Value = 18 feet
• Actual Value = 16 feet

Step 2: Calculate the absolute error

\[ |\text{Estimated Value} - \text{Actual Value}| = |18 - 16| = 2 \text{ feet} \]

Step 3: Calculate the percent error

Now, substitute the values into the percent error formula:

\[ \text{Percent Error} = \left( \frac{2}{16} \right) \times 100 \]

Step 4: Perform the division

\[ \frac{2}{16} = 0.125 \]

Step 5: Multiply by 100 to convert to percentage

\[ \text{Percent Error} = 0.125 \times 100 = 12.5% \]

Final Answer

Teresa’s percent error is 12.5%.

This rounds to the nearest tenth as 12.5%.

Answer 2

Now write it into a summary

Answer 3

To calculate Teresa's percent error in estimating the height of a giraffe, we first identified the estimated height (18 feet) and the actual height (16 feet). We calculated the absolute error by finding the difference between the estimated and actual values, which was 2 feet. Using the percent error formula, we substituted our values:

\[ \text{Percent Error} = \left( \frac{|\text{Estimated Value} - \text{Actual Value}|}{\text{Actual Value}} \right) \times 100 \]

This led to:

\[ \text{Percent Error} = \left( \frac{2}{16} \right) \times 100 = 12.5% \]

Thus, Teresa's percent error in her estimation of the giraffe's height is 12.5%.

Answer 4

Write a summary with the equation in the summary

Answer 5

In calculating Teresa's percent error in estimating the height of a giraffe, we started with her estimated height of 18 feet and the actual height of 16 feet. To determine the percent error, we used the formula:

\[ \text{Percent Error} = \left( \frac{|\text{Estimated Value} - \text{Actual Value}|}{\text{Actual Value}} \right) \times 100 \]

We first found the absolute error:

\[ |\text{Estimated Value} - \text{Actual Value}| = |18 - 16| = 2 \text{ feet} \]

Next, we substituted this value into the percent error formula:

\[ \text{Percent Error} = \left( \frac{2}{16} \right) \times 100 \]

Calculating the division, we got:

\[ \frac{2}{16} = 0.125 \]

Finally, multiplying by 100, we determined that:

\[ \text{Percent Error} = 0.125 \times 100 = 12.5% \]

Therefore, Teresa's percent error in her estimation of the giraffe's height is 12.5%.

Answer 6

Simplify the formula

Answer 7

The formula for percent error can be simplified by breaking it down into a more straightforward expression. The original formula is:

\[ \text{Percent Error} = \left( \frac{|\text{Estimated Value} - \text{Actual Value}|}{\text{Actual Value}} \right) \times 100 \]

We can denote the estimated value as \(E\) and the actual value as \(A\). Thus, the formula can be simplified to:

\[ \text{Percent Error} = \left( \frac{|E - A|}{A} \right) \times 100 \]

In a more concise form, the calculation can be expressed as:

\[ \text{Percent Error} = \frac{|E - A| \times 100}{A} \]

Final Summary with Simplified Formula

To find Teresa's percent error in estimating the height of a giraffe, we used the simplified formula for percent error:

\[ \text{Percent Error} = \frac{|E - A| \times 100}{A} \]

Where \(E\) is her estimated height (18 feet) and \(A\) is the actual height (16 feet).

Calculating the absolute error gives us:

\[ |E - A| = |18 - 16| = 2 \text{ feet} \]

Substituting into the simplified formula:

\[ \text{Percent Error} = \frac{2 \times 100}{16} \]

This calculates to:

\[ \text{Percent Error} = \frac{200}{16} = 12.5% \]

Therefore, Teresa's percent error in her estimation of the giraffe's height is 12.5%.

Answer 8

That is not simplfied

Answer 9

I apologize for the misunderstanding. Let's simplify the percent error formula step-by-step without additional notation or unnecessary complexity.

The original formula for percent error is:

\[ \text{Percent Error} = \left( \frac{|\text{Estimated Value} - \text{Actual Value}|}{\text{Actual Value}} \right) \times 100 \]

We can represent the estimated value as \( E \) and the actual value as \( A \):

\[ \text{Percent Error} = \left( \frac{|E - A|}{A} \right) \times 100 \]

Now, this can be directly simplified to focus just on the value of the absolute difference:

\[ \text{Percent Error} = \frac{|E - A| \times 100}{A} \]

This is the simplest way to express the percent error in relation to the actual value.

To summarize:

1. Estimate (E) = 18 feet
2. Actual (A) = 16 feet

Using the formula:

\[ \text{Percent Error} = \frac{|E - A| \times 100}{A} = \frac{|18 - 16| \times 100}{16} = \frac{2 \times 100}{16} = \frac{200}{16} = 12.5% \]

Thus, the simplified formula for percent error is \( \frac{|E - A| \times 100}{A} \), and Teresa's percent error in her estimation of the giraffe's height is 12.5%. Thank you for your patience.

Answer 10

Please don’t use number and just articulate the formula into a summary

Answer 11

The formula for percent error is articulated as follows:

\[ \text{Percent Error} = \left( \frac{|\text{Estimated Value} - \text{Actual Value}|}{\text{Actual Value}} \right) \times 100 \]

In this formula, the numerator represents the absolute difference between the estimated value and the actual value, while the denominator is the actual value. The result is then multiplied by 100 to express the error as a percentage.

To summarize the calculation:

1. Identify the Estimated Value and Actual Value: The process begins by defining the values being compared.

2. Calculate the Absolute Difference: The absolute difference between the estimated and actual values is determined.

3. Substitute into the Formula: The absolute difference is divided by the actual value.

4. Multiply by 100: Finally, the result is multiplied by 100 to convert it to a percentage.

This concise process provides a clear method for calculating the percent error in any estimation, helping to quantify the accuracy of the estimate relative to the actual value.