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Deirdre is buying plastic mugs to send to her cousin. She made a table of the various heights of stacks of different numbers of mugs.

Number of Plastic Mugs
Stack Height (in inches)

1
6

2
6.75

3
7.5

4
8.25

5
9

6
9.75

Which equation represents the height,
h, of a stack of mugs in terms of the number of mugs,
t, in the stack?
a.
h=6+0.75(t-1)
b.
h=6+0.75 t
c.
h=0.75+t(t-1)
d.
h=0.75 t-6

$7$ . Deirdre is buying plastic mugs to send to her cousin. She made a table of the various heights of stacks of different numbers of mugs. $\newline$ \begin{tabular}{|c|c|} $\newline$ \hline Number of Plastic Mugs & Stack Height (in inches) \\ $\newline$ \hline $1$ & $6$ \\ $\newline$ \hline $2$ & $6$ . $75$ \\ $\newline$ \hline $3$ & $7$ . $5$ \\ $\newline$ \hline $4$ & $8$ . $25$ \\ $\newline$ \hline $5$ & $9$ \\ $\newline$ \hline $6$ & $9$ . $75$ \\ $\newline$ \hline $\newline$ \end{tabular} $\newline$ Which equation represents the height, $h$ , of a stack of mugs in terms of the number of mugs, $t$ , in the stack? $\newline$ a. $h=6+0.75(t-1)$ $\newline$ b. $h=6+0.75 t$ $\newline$ c. $h=0.75+t(t-1)$ $\newline$ d. $h=0.75 t-6$

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Interpret stem-and-leaf plots

Full solution

Q.

7

. Deirdre is buying plastic mugs to send to her cousin. She made a table of the various heights of stacks of different numbers of mugs.

\newline

\begin{tabular}{|c|c|}

\newline

\hline Number of Plastic Mugs & Stack Height (in inches) \\

\newline

\hline

1

&

6

\\

\newline

\hline

2

&

6

.

75

\\

\newline

\hline

3

&

7

.

5

\\

\newline

\hline

4

&

8

.

25

\\

\newline

\hline

5

&

9

\\

\newline

\hline

6

&

9

.

75

\\

\newline

\hline

\newline

\end{tabular}

\newline

Which equation represents the height,

h

, of a stack of mugs in terms of the number of mugs,

t

, in the stack?

\newline

a.

h=6+0.75(t-1)

\newline

b.

h=6+0.75 t

\newline

c.

h=0.75+t(t-1)

\newline

d.

h=0.75 t-6

Find Height Difference: Look at the first two rows of the table to find the difference in height when one mug is added. $\newline$ Calculation: $6.75 - 6 = 0.75$ inches.
Check Height Increase: Check if the height increases by $0.75$ inches for each additional mug by comparing the height for $2$ mugs and $3$ mugs. $\newline$ Calculation: $7.5 - 6.75 = 0.75$ inches.
Confirm Pattern: Confirm the pattern by checking the height increase for $3$ mugs to $4$ mugs. $\newline$ Calculation: $8.25 - 7.5 = 0.75$ inches.
Identify Equation Pattern: Since the height increases by $0.75$ inches for each additional mug, the equation must include a term $0.75t$ . Check the options to see which one fits this pattern.
Verify Option a: Option a has the term $0.75(t-1)$ , which accounts for the initial height of $6$ inches for the first mug and adds $0.75$ inches for each additional mug. $\newline$ Check if this equation gives the correct height for $1$ mug. $\newline$ Calculation: $h = 6 + 0.75(1-1) = 6$ inches.
Verify $1$ Mug Height: Verify the equation for $2$ mugs. $\newline$ Calculation: $h = 6 + 0.75(2-1) = 6.75$ inches.
Verify $2$ Mugs Height: Check the equation for $3$ mugs. $\newline$ Calculation: $h = 6 + 0.75(3-1) = 7.5$ inches.
Verify $3$ Mugs Height: Since the equation $h=6+0.75(t-1)$ gives the correct height for $1$ , $2$ , and $3$ mugs, it seems to be the correct equation.

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