Question

Tyler is bored in history class, so he is staring at the ceiling tiles. He notices that some tiles are perfect squares, while others are long rectangles. He also notices that some of the tiles are bright white, while others are off-white. He makes detailed notes on how often each of these tiles occurs. Tragically, Tyler crumpled up his notes when the teacher looked in his direction, and now he can't read all the numbers. The absolute and relative frequency tables below show the numbers that Tyler is able to read. Can you help him figure out the rest? Fill in the missing values from each table.
Fill in the missing values from each table.
Square Rectangle Row total
Bright white 252525 101010 353535
Off-white
101010
Column total
202020
Square Rectangle Row total
Bright white Row %Column %Total % \begin{aligned} &\text{71.43} \\ &\text{52.08} \\ &\text{36.76} \end{aligned}
​

71.43
52.08
36.76
​
\begin{aligned} &\text{28.57} \\ &\text{50.00} \\ &\text{14.71} \end{aligned}
​

28.57
50.00
14.71
​
\begin{aligned} &\text{100} \\ &\text{------} \\ &\text{51.47} \end{aligned}
​

100
——
51.47
​

Off-white Row %Column %Total % \begin{aligned} &\text{69.70} \\ &\text{47.92} \\ &\text{33.83} \end{aligned}
​

69.70
47.92
33.83
​
\begin{aligned} &\text{30.30} \\ &\text{50.00} \\ &\text{14.71} \end{aligned}
​

30.30
50.00
14.71
​
\begin{aligned} &\text{100} \\ &\text{-----} \\ &\text{48.53} \end{aligned}
​

100
—–
48.53
​

Column total Row %Column %Total % \begin{aligned} &\text{-----} \\ &\text{100} \\ &\large \text{$x$} \end{aligned}
​

—–
100
x
​
\begin{aligned} &\text{-----} \\ &\text{100} \\ &{\text{29.41}} \end{aligned}
​

—–
100
29.41
​
\begin{aligned} &\text{100} \\ &\text{100} \\ &\text{100} \end{aligned}
​

100
100
100
​

x=x=x, equals

Answer 1

Answer:

The complete tables are shown below.

The value of x is 70.59%.

Step-by-step explanation:

Absolute frequency table:

         Square   Rectangle Row Total

Bright            25         10              35

Off White    23         10              33

Column Total    48         20              68

Relative frequency table

                                   Square Rectangle Row total

                 Row%      71.43%  28.57%          100.00%

Bright Column%     52.08%  50.00%             ____

                 Total%      36.76%    14.71%            51.47%

                   Row%      69.70%  30.30%          100.00%

Off White  Column%   47.92%  50.00%              ___

                   Total%      33.83%    14.71%           48.53%

                   Row%          ____                  ____            100.00%

Column  Column%       100.00%           100.00%  100.00%

                  Total%       x  = 70.59%     29.41%  100.00%

$\text{Value of}\ x=100.00\%-29.41\%=70.59\%$