The table shows the soil density of several soil samples at different depths. Depth (m) 1 5 6 8 10 12 14 21 23 24 28 Soil density ( ) 1045 1063 1102 1140 1191 1232 1249 1254 1265 1268 1273 (a) Using technology (graphing calculator or Excel spreadsheet), Write the quadratic regression equation that models the data. Let x = depth below the surface and let y = soil density. (b) Use the equation to estimate the soil density of a sample at a depth of 20 m. Show your work.

(a)

(b) The soil density of a sample at a depth of 20 m is 1266.43 kg/m³.

Step-by-step explanation:

The data provided is:

Depth (m): {1, 5, 6, 8, 10, 12, 14, 21, 23, 24, 28}

Soil density (kg/m³): {1045, 1063, 1102, 1140, 1191, 1232, 1249, 1254, 1265, 1268, 1273}

(a)

Use Excel to form the quadratic regression equation.

Enter the data in Excel.

Compute the value of X².

Go to Data → Data Analysis → Regression

Select the values accordingly.

In the X range select both values of X and X².

Click OK.

The output is attached below.

The quadratic regression equation is:

(b)

Compute the value of y if x = 20 m as follows:

Thus, the soil density of a sample at a depth of 20 m is 1266.43 kg/m³.

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step-by-step explanation:

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