Question

The members of a high school band asked a number of students whether they would like blue, gold, or both for the uniforms for the band. The results are given in the Venn diagram. A circle labeled blue 32 overlaps a circle labeled gold 25. Overlap is labeled 12. 4-column table with 3 rows. First column is labeled band uniforms with entries gold, not gold, total. Second column is blue with entries 16%, b, blank. Third column is not blue with entries a, 8%, blank. Fourth column is labeled total with entries blank, blank, 100%. What are the values of a and b in the relative frequency table for the survey results? Round answers to the nearest percent. a = 33%, b = 73% a = 68%, b = 43% a = 25%, b = 32% a = 33%, b = 43%

Answer 1

Answer:

its D or option 4

Step-by-step explanation:

Answer 2

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

∴ $\frac{16}{100}$ × 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 = $\frac{32}{75}$ × 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 = $\frac{25}{75}$ × 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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