**Experiment Analysis on Unknown Metal's Mass and Volume**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 expresses mass as a function of the volume.| Grams | Volume in mL ||-------|--------------|| 14 | 267.8 || 15.5 | 293.5 || 17 | 335 || 18.5 | 364.6 || 20 | 378.7 || 21.5 | 419.5 || 23 | 435.5 |A) **Task: Write the Linear Regression Equation**- Determine the linear regression equation for the data in the chart.- The equation is in the form: \[ \text{Volume} = mx + c \] where $ x $ is the grams of the unknown metal. Round your answers to 3 decimal places.B) **Task: Calculate Predicted Volume**- If the mass of an unknown metal is 12 grams, using your un-rounded regression equation, find its predicted volume.- Round your answer to 1 decimal place.**Submit your answer using the form provided.**### Explanation of Data Table:- **Columns and Units:** The table consists of two columns. The first column lists the mass of the metal samples in grams, while the second column provides the corresponding volume in milliliters.- **Linear Relationship:** The task involves finding a linear relationship (volume as a function of mass) using linear regression techniques to aid in predictions of volume based on given mass values.**Interactive Element:**- A form to submit your linear regression equation and the predicted volume for a metal mass of 12 grams, rounding as specified.

A).The table below shows the required calculation- Where, x=14+15.5+17+18.5+....+237=129.57=18.5…

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 expresses mass as a function of the volume.

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 expresses mass as a function of the volume.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Concept explainers

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

Question

**Experiment Analysis on Unknown Metal's Mass and Volume**

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 expresses mass as a function of the volume.

| Grams | Volume in mL |
|-------|--------------|
| 14 | 267.8 |
| 15.5 | 293.5 |
| 17 | 335 |
| 18.5 | 364.6 |
| 20 | 378.7 |
| 21.5 | 419.5 |
| 23 | 435.5 |

A) **Task: Write the Linear Regression Equation**
- Determine the linear regression equation for the data in the chart.
- The equation is in the form:
\[
\text{Volume} = mx + c
\]
where $ x $ is the grams of the unknown metal. Round your answers to 3 decimal places.

B) **Task: Calculate Predicted Volume**
- If the mass of an unknown metal is 12 grams, using your un-rounded regression equation, find its predicted volume.
- Round your answer to 1 decimal place.

**Submit your answer using the form provided.**

### Explanation of Data Table:
- **Columns and Units:** The table consists of two columns. The first column lists the mass of the metal samples in grams, while the second column provides the corresponding volume in milliliters.
- **Linear Relationship:** The task involves finding a linear relationship (volume as a function of mass) using linear regression techniques to aid in predictions of volume based on given mass values.

**Interactive Element:**
- A form to submit your linear regression equation and the predicted volume for a metal mass of 12 grams, rounding as specified.

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