The values of a and b are a = 33% and b = 43% ⇒ last answer
Step-by-step explanation:
The venn-diagram contains:
- A circle labeled blue 32
- A circle labeled gold 25
- The two circles are overlap with label 12 on the overlap
The table:
→ Band  :  blue  :  N.b  : total
→ gold   :  16%   :  a      :  49%
→ N.g     :  b       :  8%   :  51%
→ Total  :  59%  :  41%  :  100%
We need to find the values of a and b
From the table 
16% represents the percentage of blue and gold uniforms (2nd row with 2nd column)
From venn-diagram 
The common part of blue and gold label with 12 (overlap of two circles)
∴ 16% of the total number of students = 12
∵ 16% × x = 12
∴  × x = 12
 × x = 12
∴ 0.16 x = 12
- Divide both sides by 0.16
∴ x = 75
∵ x represents the total number of students
∴ The total number of students were asked is 75
From the table
b represents the percentage of blue but not gold uniforms (3rd row and 2nd column)
From venn-diagram 
The part that has blue and not gold labeled with 32 (the part of the blue circle not in the gold circle)
∴ 32 of the total number of students like the blue but not gold
- Divide 32 by the total 75 , then multiply the quotient by 100% 
    to find the percentage of blue but not gold
∴ b =  × 100% = 42.6666%
 × 100% = 42.6666% 
∴ b ≅ 43%
From the table
a represents the percentage of gold nut not blue uniforms (2nd row and 3rd column)
From venn-diagram
The part that has gold and not blue labeled with 25 (the part of the gold circle not in the blue circle)
∴ 25 of the total number of students like the gold but not blue
- Divide 25 by the total 75 , then multiply the quotient by 100% 
    to find the percentage of gold but not blue
∴ a =  × 100% = 33.3333%
 × 100% = 33.3333% 
∴ a ≅ 33%
The values of a and b are a = 33% and b = 43%
To check your answer complete the table you will find the total of it is 100% ( for the columns 16% + 43% = 59% , 33% + 8% = 41% , then 59% + 41% = 100%, for the rows 16% + 33% = 49% , 43% + 8% = 51% , then 49% + 51% = 100%)
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You can learn more about the probability in brainly.com/question/3756853
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