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An unknown metal has been found and the following experimental results have been tabulated in the table below. The table contains the grams of the unknown metal and the volume in milliliters of water displacement. Find a linear model that express volume as a function of the mass. Round your answers to 3 decimal places grams Volume in ml 18 141.3 19.5 153.1 21 168.1 22.5 178.4 24 184.6 25.5 202.2 27 214.1 Volume = ◻ x+ ◻ where x is the grams of the unknown metal Question Help: ◻ Message instructor

An unknown metal has been found and the following experimental results have been tabulated in the table below. The table contains the grams of the unknown metal and the volume in milliliters of water displacement. Find a linear model that express volume as a function of the mass.\newlineRound your answers to 33 decimal places\newline\begin{tabular}{|r|r|}\newline\hline grams & Volume in ml \mathrm{ml} \\\newline\hline 1818 & 141141.33 \\\newline\hline 1919.55 & 153153.11 \\\newline\hline 2121 & 168168.11 \\\newline\hline 2222.55 & 178178.44 \\\newline\hline 2424 & 184184.66 \\\newline\hline 2525.55 & 202202.22 \\\newline\hline 2727 & 214214.11 \\\newline\hline\newline\end{tabular}\newlineVolume = = □ \square x+ x+ □ \square where x x is the grams of the unknown metal\newlineQuestion Help: □ \square Message instructor

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Q. An unknown metal has been found and the following experimental results have been tabulated in the table below. The table contains the grams of the unknown metal and the volume in milliliters of water displacement. Find a linear model that express volume as a function of the mass.\newlineRound your answers to 33 decimal places\newline\begin{tabular}{|r|r|}\newline\hline grams & Volume in ml \mathrm{ml} \\\newline\hline 1818 & 141141.33 \\\newline\hline 1919.55 & 153153.11 \\\newline\hline 2121 & 168168.11 \\\newline\hline 2222.55 & 178178.44 \\\newline\hline 2424 & 184184.66 \\\newline\hline 2525.55 & 202202.22 \\\newline\hline 2727 & 214214.11 \\\newline\hline\newline\end{tabular}\newlineVolume = = □ \square x+ x+ □ \square where x x is the grams of the unknown metal\newlineQuestion Help: □ \square Message instructor
  1. Plot Data Points: First, let's plot the data points to see if they form a linear relationship. We'll use the grams as the xx-values and the volume in milliliters as the yy-values.
  2. Calculate Slope: Next, we calculate the slope mm of the line using the formula m=y2−y1x2−x1m = \frac{y_2 - y_1}{x_2 - x_1}. We'll use the first and last data points for this calculation: (18,141.3)(18, 141.3) and (27,214.1)(27, 214.1). So, m=214.1−141.327−18=72.89=8.089m = \frac{214.1 - 141.3}{27 - 18} = \frac{72.8}{9} = 8.089.
  3. Find Y-Intercept: Now, we find the y-intercept bb using the equation of the line y=mx+by = mx + b. Substituting one point (18,141.3)(18, 141.3) into the equation and the slope we just calculated, 141.3=8.089×18+b141.3 = 8.089 \times 18 + b. Solving for bb gives b=141.3−145.602=−4.302b = 141.3 - 145.602 = -4.302.
  4. Linear Model Equation: With the slope and y-intercept calculated, the linear model is Volume=8.089x−4.302Volume = 8.089x - 4.302. We round these to three decimal places as instructed.

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