Question

Question was provided via image upload.

Explanation:

Identify given values and conversion factors

We are given:

• Length of the soccer field: \(L = 125\text{ m}\)
• Width of the soccer field: \(W = 95\text{ m}\)
• Conversion factor: \(1\text{ meter} = 3.281\text{ feet}\)
• We also need to convert to inches using \(1\text{ foot} = 12\text{ inches}\).

Convert the length to feet and inches

Calculate the length in feet:

$$ L_{\text{ft}} = 125 \times 3.281 = 410.125\text{ ft} $$

Rounding to four significant figures (or matching the options):

$$ L_{\text{ft}} \approx 410.1\text{ ft} $$

Calculate the length in inches:

$$ L_{\text{in}} = 410.125 \times 12 = 4921.5\text{ in} $$

Expressing this in scientific notation with appropriate significant figures:

• With two significant figures (matching the precision of \(95\text{ m}\)): \(4.9 \times 10^3\text{ in}\)
• The value \(4921.5\text{ in}\) is also written as \(4.9215 \times 10^3\text{ in}\).
• Let's check the options:
• \(4.9215\text{ in long}\) (written as \(4.9215\text{ in long}\) or \(4.9215\text{ m long}\)? The image shows "\(4.9215\text{ in long}\)" or "\(4.9215\text{ m long}\)"? It says "\(4.921\ 5\text{ in long}\)" or similar. Let's look closely: "\(4.921\ 5\text{ in long}\)" is \(4921.5\) written with a space as a thousands separator, or it is \(4.9215 \times 10^3\). Actually, \(4921.5\text{ in}\) is exactly \(4.9215 \times 10^3\text{ in}\).
• Let's check \(4.9 \times 10^3\text{ in long}\).

Convert the width to feet and inches

Calculate the width in feet:

$$ W_{\text{ft}} = 95 \times 3.281 = 311.695\text{ ft} $$

Rounding to four significant figures:

$$ W_{\text{ft}} \approx 311.7\text{ ft} $$

Calculate the width in inches:

$$ W_{\text{in}} = 311.695 \times 12 = 3740.34\text{ in} $$

Expressing this in scientific notation with two significant figures:

$$ W_{\text{in}} \approx 3.7 \times 10^3\text{ in} $$

Select the four correct responses

Based on our calculations, the correct dimensions are:

1. \(410.1\text{ ft long}\) (from \(125 \times 3.281 = 410.125\))
2. \(311.7\text{ ft wide}\) (from \(95 \times 3.281 = 311.695\))
3. \(4.9 \times 10^3\text{ in long}\) (from \(4921.5\text{ in}\) rounded to 2 significant figures)
4. \(3.7 \times 10^3\text{ in long}\) (from \(3740.34\text{ in}\) rounded to 2 significant figures)

Answer:

• 38.1 ft wide
• 410.1 ft long (Correct answer)
• 4.921 5 m long
• *4.9 10^3 in long (Correct answer)**
• 311.7 ft wide (Correct answer)
• *3.7 10^3 in long (Correct answer)**
• 3.7 * 10^2 in long