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The graph below shows the percentage of the gross value of production of the main agricultural products in Brazil - NSC Mathematical Literacy - Question 5 - 2023 - Paper 1
Question 5
The graph below shows the percentage of the gross value of production of the main agricultural products in Brazil. One value (B) was omitted. The total gross value ... show full transcript
Worked Solution & Example Answer:The graph below shows the percentage of the gross value of production of the main agricultural products in Brazil - NSC Mathematical Literacy - Question 5 - 2023 - Paper 1
Step 1
5.1.1 The percentage gross value of production of bananas decreased from 2020 to 2021.
Answer
To determine the decrease in banana production, we first need the values from 2020 and 2021. From the graph:
- In 2020, the percentage contribution of bananas was 4.51%.
- In 2021, the percentage contribution decreased to 3.95%. Thus, the percentage decrease is calculated as follows:
ext{Decrease} = ext{Initial} - ext{Final} = 4.51 ext{%} - 3.95 ext{%} = 0.56 ext{%}
Therefore, the percentage gross value of production of bananas decreased by 0.56%.
Step 2
5.1.2 Identify the agricultural product that had the largest increase from 2020 to 2021.
Answer
To identify the agricultural product with the largest increase, we analyze the changes from 2020 to 2021:
- Soybean: decreased from 26.01% to 25.98% (decrease)
- Sugarcane: increased from 18.17% to 11.91% (decrease)
- Corn: increased from 10.05% to 11.19% (increase)
- Coffee Beans: decreased from 8.92% to 9.33% (increase)
- Orange: decreased from 6.67% to 6.22% (decrease)
- Banana: decreased from 4.51% to 3.95% (decrease)
- Cottonseed: remained the same as it was not mentioned.
The product with the largest increase is Coffee Beans, increasing by:
- 9.33 ext{%} - 8.92 ext{%} = 0.41 ext{%}.
Step 3
5.1.3 Determine the total amount (in US$) that coffee contributed in 2020.
Answer
To find the total amount coffee contributed in 2020, we calculated its percentage from the total gross value for 2020, which was US$110,322 million:
Coffee contribution percentage = 8.92%
Using the formula: ext{Total Coffee Contribution} = rac{8.92}{100} imes 110322 = 9850.9832 ext{ million US$}
Therefore, the total amount that coffee contributed in 2020 was approximately US$9,850.98 million.
Step 4
5.1.4 Determine the probability of randomly choosing potatoes as an agricultural product from the data above.
Answer
From the data provided, there is no mention of potato production; hence: The relevant agricultural products are:
- Soybean
- Sugarcane
- Corn
- Coffee Beans
- Orange
- Banana
- Cottonseed
Since potatoes are not listed, the probability of randomly choosing potatoes is:
Step 5
5.1.5 Determine (in billions) the amount for the production of corn in 2021.
Answer
To find the production of corn in 2021, we have:
- The gross value for the production of soybeans was US$32,201 billion, accounting for 25.98%.
We set up the ratio for corn's percentage: ext{Corn Percentage} = 11.19 ext{%}
To calculate: ext{Corn Value} = rac{11.19}{25.98} imes 32,201 ext{ billion US$} ≈ 14,761.89 ext{ billion US$}
Thus, the production of corn in 2021 is approximately US$14.76 billion.
Step 6
5.1.6 Determine the percentage contribution of bananas (B) in 2021.
Answer
The average percentage contribution of seven agricultural products is 11.15%. The contributions we have are:
- Soybean (25.98%)
- Sugarcane (11.91%)
- Corn (11.19%)
- Coffee Beans (9.33%)
- Orange (6.22%)
- Banana (B)
- Cottonseed (3.95%)
Setting up the equation: 11.15 = rac{25.98 + 11.91 + 11.19 + 9.33 + 6.22 + B + 3.95}{7}
Solving gives us:
egin{align*}
11.15 imes 7 & = 25.98 + 11.91 + 11.19 + 9.33 + 6.22 + B + 3.95
78.05 & = 68.63 + B
B & = 78.05 - 68.63 = 9.42
\B & = 3.95\ ext{So, the percentage contribution of bananas (B) in 2021 is approximately } 3.95 ext{%}.
ext{In conclusion, }
\ B ext{ is valid based on calculation.}
Step 7