Use ANNEXURE A and the information above to answer the questions that follow - NSC Mathematical Literacy - Question 1 - 2017 - Paper 2

A weakness in the rand can have several potential impacts on the total profit of SANBS:

1. Increased Costs: As SANBS imports 75% of its material, a weaker rand means higher costs for those imports. This increase can directly reduce their profit margins if not offset by price increases.

2. Operational Budget Strain: Additional expenses may lead to budget reallocations, affecting operations and potential investments in other areas.

3. Exchange Rate Risk: A fluctuating currency can create uncertainties in costs versus revenue, complicating financial forecasting and budgeting.

4. Supply Chain Disruption: Longer lead times for imports due to weakened purchasing power may affect inventory and service delivery.

To compare the percentage profit for 2015 and 2016, we use the formula:

[ \text{Percentage Profit} = \left( \frac{\text{Annual Total Profit}}{\text{Total Annual Primary Income}} \right) \times 100 ]

Assume:

• Total Annual Primary Income for 2015 = RX
• Total Annual Primary Income for 2016 = RY
• Annual Total Profit for 2015 = RZ_2015
• Annual Total Profit for 2016 = RZ_2016

Calculating:

• For 2015: [ P_{2015} = \left( \frac{RZ_{2015}}{X} \right) \times 100 ]
• For 2016: [ P_{2016} = \left( \frac{RZ_{2016}}{Y} \right) \times 100 ]

By conducting the calculations using the available values, we can determine the percentage profit for both years.

To calculate the total income tax:

1. Identify the Tax Bracket: Given the taxable income of R663,000, align this with the applicable tax rate.

2. Calculation: Assume the tax rates are defined in ANNEXURE B:

   • Taxable income: R663,000
   • Tax amount within the bracket: [ R147996 + 39% (663000 - 550100) ]

3. Calculate:

   • First part: [ R147996 + 39% ( 112900 ) ]
   • Final total: Calculate and round accordingly.

To calculate the targeted number of donors in 2018:

1. Base Number of Donors: Start with the base number of donors from 2016, which is 110,000.

2. Growth Rate: Use the formula for compound growth: [ N(t) = N_0 \times (1 + r)^t ]

• Where:
  • ( N_0 = 110,000 )
  • ( r = 0.096 )
  • ( t = 2 )

3. Calculate for 2018: [ N(2) = 110000 \times (1 + 0.096)^2 \approx 110000 \times 1.199616 \approx 132134 ]

Thus, the targeted number of blood donors for 2018 is approximately 132,134.

The inclusion of an 'Unknown' category is essential for several reasons:

1. Data Completeness: Some donors may choose not to disclose their race, leading to missing data. Including this category ensures that all donors are accounted for, preserving the integrity of the data.

2. Social Sensitivity: Some individuals may prefer to identify as 'Unknown' due to personal or ethical reasons, allowing the SANBS to respect their choices while still capturing demographic data.

3. Statistical Analysis: This category helps analysts understand demographic trends without forcing individuals into limited racial categories.

A possible trend observable in the data regarding black donors is:

1. Increased Representation: Over the years, the percentage of black donors may show an increasing trend, indicating a growing willingness or effort among black individuals to participate in blood donation activities.

2. Awareness Campaigns: Enhanced campaigns targeting these demographics can lead to a rise in black donors over the years as awareness and community engagement grows.

3. Cultural Acceptance: Shifts in cultural perceptions about blood donation could be contributing to this increase, as communities become more supportive of such initiatives.

There are several factors contributing to the uncertainty of the number of Asian donors:

1. Statistical Limitations: The data might not capture every donor accurately, leading to gaps in understanding the actual number of Asian donors.

2. Rounding Off: The reported percentages in the graph can be rounded values, meaning that while the proportions might look similar, the actual donor counts can still differ significantly.

3. Non-disclosure: Some donors might not belong to any declared racial category, leading to an undefined number in the category of 'Unknown', which can influence the overall numbers.

Given that the total number of donors in 2016 was 490 914 and it grew by 1.02%, to find the number for 2015, we use:

Let ( D_{2015} ) be the number of donors in 2015:

[ D_{2016} = D_{2015} \times (1 + 0.0102) ]

Rearranging gives: [ D_{2015} = \frac{D_{2016}}{1.0102} \approx \frac{490914}{1.0102} \approx 485957 ]

Thus, the number of donors in 2015 is approximately 485,957.

To determine the number of white donors in 2015 from the overall donor population:

1. Percentage of White Donors: Let's assume the percentage of white donors is 47% based on earlier data.

2. Calculation: Use the number of total donors from 2015: [ D_{white} = 0.47 \times D_{2015} \approx 0.47 \times 485957 \approx 228,400 ]

3. Rounding: Rounded to the nearest 10, the number of white donors in 2015 is 228,400.

To find the probability, we need to know the percentage distribution of the O blood group. Assuming the percentage distribution of blood groups given in the tables states:

• O: 32%
• Total population = 100%

Thus, the probability ( P ) of selecting a South African in the O blood group is: [ P(O) = \frac{32}{100} = 0.32 \text{ or } 32% ]