My score: \( 82 / 122 \) pts ( \( 67.21 \% \) ) A set of plans shows that an opening in a bulkhead is needed for a section of pipe to pass through. The plans show metric values, but the only tape measure available is marked in inches. The pipe is shown as a - size DN80 (a European pipe-sizing standard), and a chart indicates the outside diameter of DN80 pipe is 88 millimeters ( mm ). According. to the plans, all openings must be 40 mm larger than the pipe. You know that 25.4 mm is equal to one inch. What is the diameter of the needed opening in inches? Round your answer to the nearest whole inch.

To find the diameter of the needed opening in inches, we can follow these steps: 1. **Determine the outside diameter of the pipe in millimeters.** - The outside diameter of DN80 pipe is given as \( 88 \, \text{mm} \). 2. **Calculate the required diameter of the opening in millimeters.** - According to the plans, the opening must be \( 40 \, \text{mm} \) larger than the pipe's diameter. - Therefore, the diameter of the opening \( D \) in millimeters can be calculated as: \[ D = 88 \, \text{mm} + 40 \, \text{mm} \] 3. **Convert the diameter from millimeters to inches.** - We know that \( 1 \, \text{inch} = 25.4 \, \text{mm} \). - To convert the diameter \( D \) from millimeters to inches, we use the formula: \[ D_{\text{inches}} = \frac{D}{25.4} \] 4. **Round the result to the nearest whole inch.** Now, let's perform the calculations step by step. First, calculate the diameter of the opening in millimeters: \[ D = 88 + 40 \] Next, convert this diameter to inches: \[ D_{\text{inches}} = \frac{D}{25.4} \] Let's calculate these values. Calculate the value by following steps: - step0: Calculate: \(88+40\) - step1: Add the numbers: \(128\) Calculate or simplify the expression \( (128 / 25.4) \). Calculate the value by following steps: - step0: Calculate: \(\frac{128}{25.4}\) - step1: Convert the expressions: \(\frac{128}{\frac{127}{5}}\) - step2: Multiply by the reciprocal: \(128\times \frac{5}{127}\) - step3: Multiply: \(\frac{128\times 5}{127}\) - step4: Multiply: \(\frac{640}{127}\) 1. The diameter of the opening in millimeters is calculated as: \[ D = 88 + 40 = 128 \, \text{mm} \] 2. Now, we convert this diameter to inches: \[ D_{\text{inches}} = \frac{128}{25.4} \approx 5.03937 \, \text{inches} \] 3. Rounding \( 5.03937 \) to the nearest whole inch gives us \( 5 \, \text{inches} \). Thus, the diameter of the needed opening is approximately **5 inches**.