Chapter 3.2, Problem 18AYU

a

To determine

Draw a scatter diagram of the data treating weight as the independent variable.

Answer to Problem 18AYU

  

Explanation of Solution

Given information:

The following data represents the weight (in grams) of a box of raisins and the number of raisins in the box.

  $\begin{array}{cc}Weight\left(ingrams\right)W& NumberofRai\sin s,N\\ 42.3& 87\\ 42.7& 91\\ 42.8& 93\\ 42.4& 87\\ 42.6& 89\\ 42.4& 90\\ 42.3& 82\\ 42.5& 86\\ 42.7& 86\\ 42.5& 86\end{array}$

Draw a scatter diagram of the data treating weight as the independent variable.

Calculation:

Draw a scatter diagram of the data treating weight as the independent variable.

  

Hence, the result shown in scatter plot.

b.

To determine

What type of relation appears to exist between the weight of a candy bar and the number of calories?

Answer to Problem 18AYU

The reletion defind by the set of order pairs $\left(w.n\right)$ does not represent a function.

Explanation of Solution

Given information:

The following data represents the weight (in grams) of a box of raisins and the number of raisins in the box.

  $\begin{array}{cc}Weight\left(ingrams\right)W& NumberofRai\sin s,N\\ 42.3& 87\\ 42.7& 91\\ 42.8& 93\\ 42.4& 87\\ 42.6& 89\\ 42.4& 90\\ 42.3& 82\\ 42.5& 86\\ 42.7& 86\\ 42.5& 86\end{array}$

What type of relation appears to exist between the weight of box of raisins and the number of raisins in the box.

Calculation:

t

A relation is aid to be a function if no first element in the set of ordered pairs is paired with two different second elements

On observing the given table .we can see that for the same weight w, there are diffirent n- valve . that is same of the w-valve have more than one N-valve

Thus the reletion defind by the set of order pairs $\left(w.n\right)$ does not represent a function.

Hence, the reletion defind by the set of order pairs $\left(w.n\right)$ does not represent a function.

c.

To determine

Find a linear model that contains the points.

Answer to Problem 18AYU

  $\boxed{y=10x-341}$

Explanation of Solution

Given information:

The following data represents the weight (in grams) of a box of raisins and the number of raisins in the box.

  $\begin{array}{cc}Weight\left(ingrams\right)W& NumberofRai\sin s,N\\ 42.3& 87\\ 42.7& 91\\ 42.8& 93\\ 42.4& 87\\ 42.6& 89\\ 42.4& 90\\ 42.3& 82\\ 42.5& 86\\ 42.7& 86\\ 42.5& 86\end{array}$

Select two points and find a linear model that contains the points.

Calculation:

Consider points, $\left(42,3,82\right)$ and $\left(42,7,86\right)$ now find the slope of line that contains the same points.

Slope $m$ of line containing points $P\left(x_1,y_1\right)$ and $Q\left(x_2,y_2\right)$ is obtained by the formula,

  $m=\frac{y_2-y_1}{x_2-x_1}=\frac{\Delta y}{\Delta x}$

So,

  $m=\frac{86-82}{42.7-42.3}=\frac{4}{0.4}=10$

Now find the equation of line that contains the points using point-slope form.

  $y-y_1=m\left(x-x_1\right)$

Now substitute $m=10,x_1=42.3,y_1=82$

  $\begin{array}{l}y-82=10\left(x-42.3\right)\\ y-82=10x-423\\ y=10x-423+82\\ y=10x-341\end{array}$

Hence, the equation of line is, $\boxed{y=10x-341}$

d.

To determine

Graph the line on scatter plot.

Answer to Problem 18AYU

  

Explanation of Solution

Given information:

The following data represents the weight (in grams) of a box of raisins and the number of raisins in the box.

  $\begin{array}{cc}Weight\left(ingrams\right)W& NumberofRai\sin s,N\\ 42.3& 87\\ 42.7& 91\\ 42.8& 93\\ 42.4& 87\\ 42.6& 89\\ 42.4& 90\\ 42.3& 82\\ 42.5& 86\\ 42.7& 86\\ 42.5& 86\end{array}$

Graph the line on scatter plot drawn in part $\left(a\right)$ .

Calculation:

In order to graph the line $y=10x-341$ on scatter plot, find the point $y$ .

  $\begin{array}{l}y=10\times 42.5-341\\ y=84\end{array}$

Similarly other points are,

  $\begin{array}{ccccc}x& 42.2& 42.5& 42.9& 43\\ y& 81& 84& 88& 89\end{array}$

Let Graph the line on scatter plot. $y=10x-341$

  

Hence, the graph of line is plotted.

e.

To determine

Use the linear model to predict the number of calories in a candy bar.

Answer to Problem 18AYU

  $\boxed{f\left(x\right)=10x-341}$

Explanation of Solution

Given information:

The following data represents the weight (in grams) of various candy bars and the corresponding number of calories.

  $\begin{array}{ccc}CandyBar& Weight,X& CaloriesY\\ Hershey\text{'}sMilkChocolate& 44.28& 230\\ Nestle\text{'}sCrunch& 44.84& 230\\ Butterfinger& 61.30& 270\\ BabyRuth& 66.45& 280\\ AlmondJoy& 47.33& 220\\ Twix& 58.00& 280\\ Snic\ker s& 61.12& 280\\ Heath& 39.52& 210\end{array}$

Use the linear model to predict the resin in the box weight $42.5$ grams.

Calculation:

Use the linear model to predict the resin in the box weight $42.5$ grams.

  $y=10x-341$

Function is $f\left(x\right)=10x-341$

Hence, $\boxed{f\left(x\right)=10x-341}$

f.

To determine

Interpret the slope of the line.

Answer to Problem 18AYU

  $\boxed{10}$

Explanation of Solution

Given information:

The following data represents the weight (in grams) of various candy bars and the corresponding number of calories.

  $\begin{array}{ccc}CandyBar& Weight,X& CaloriesY\\ Hershey\text{'}sMilkChocolate& 44.28& 230\\ Nestle\text{'}sCrunch& 44.84& 230\\ Butterfinger& 61.30& 270\\ BabyRuth& 66.45& 280\\ AlmondJoy& 47.33& 220\\ Twix& 58.00& 280\\ Snic\ker s& 61.12& 280\\ Heath& 39.52& 210\end{array}$

Interpret the slope of the line found in part $\left(c\right)$ .

Calculation:

Interpret the slope of the line.

  $m=\frac{y_2-y_1}{x_2-x_1}=\frac{\Delta y}{\Delta x}$ is average rate of change of $y$ with respect $x$ .which is equal to $42.5$ .

If the weight of is increased by $1gm$ then number of resins increased by $10$

Hence, the number of resins increased by $\boxed{10}$