Chapter 4.4, Problem 10PPS

(a)

To determine

To make: a scatter plot comparing the weight in pounds to the amount of milk needed in ounces.

Explanation of Solution

Given information:

The table shows the amount of milk, in ounces that a baby goat needs based on its weight, in pounds.

  

Calculation:

Consider the given table,

  

Now, plot the scatter diagram corresponding to the table as shown,

  

(b)

To determine

To draw: a line of fit for the data.

Explanation of Solution

Given information:

The table shows the amount of milk, in ounces that a baby goat needs based on its weight, in pounds.

  

Calculation:

Consider the given table,

  

Now, draw a line for fit the date as shown,

  

(c)

To determine

To write: the slope intercepts form of an equation for the line of fit.

Answer to Problem 10PPS

The equation is $y=1.6x+4$ .

Explanation of Solution

Given information:

The table shows the amount of milk, in ounces that a baby goat needs based on its weight, in pounds.

  

Calculation:

Consider the given table,

  

Answers will vary depending on which points the student picks. Sample answer: Choose two points on the best fit line: $\left(10,20\right)$ and $\left(15,28\right)$ . Calculate the slope

  $\begin{array}{l}m=\frac{y_2-y_1}{x_2-x_1}\\ m=\frac{28-20}{15-10}\\ m=\frac{8}{5}\\ m=1.6\end{array}$

Now, use the slope and either of the two points, to find the $y$ intercept.

  $\begin{array}{c}y=mx+b\\ 28=1.6\left(15\right)+b\\ 28=24+b\\ b=4\end{array}$

So, the equation is $y=1.6x+4$ .

(d)

To determine

To predict: the amount of milk needed for a baby goat that weighs 55 pounds.

Answer to Problem 10PPS

The 92 ounce milk is needed for a baby goat that weighs 55 pounds.

Explanation of Solution

Given information:

The table shows the amount of milk, in ounces that a baby goat needs based on its weight, in pounds.

  

Calculation:

Consider the given table,

  

Let, $x=55$ pounds

So, substitute this into the equation,

  $\begin{array}{c}y=1.6x+4\\ y=1.6\times 55+4\\ =88+4\\ =92\end{array}$

So, the 92 ounce milk is needed for a baby goat that weighs 55 pounds.

(e)

To determine

To predict: the weight of a baby goat that needs 38 ounce of milk.

Answer to Problem 10PPS

The weight of a baby goat that needs 38 ounces of milk is 21.25 pounds.

Explanation of Solution

Given information:

The table shows the amount of milk, in ounces that a baby goat needs based on its weight, in pounds.

  

Calculation:

Consider the given table,

  

Let, $y=38$ ounces

So, substitute this into the equation,

  $\begin{array}{c}y=1.6x+4\\ 38=1.6\times x+4\\ 38-4=1.6x\\ x=\frac{34}{1.6}\\ =21.25\end{array}$

So, the weight of a baby goat that needs 38 ounces of milk is 21.25 pounds.