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Calculate the attack rate for rice and swallow given the number of people who ate each and the number who got diarrhea, using a constant k=250.

Mathematics

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Answer

27.52
38.29
58.33

Step-by-step solution

3 steps

The formula for attack rate is:

Attack Rate=Number of people who got sick after eating a specific food itemTotal number of people who ate that specific food item×k\text{Attack Rate} = \frac{\text{Number of people who got sick after eating a specific food item}}{\text{Total number of people who ate that specific food item}} \times k

where kk is the given constant. In this case, k=250k = 250.

Given data:

  • People who ate rice = 109
  • People who ate swallow = 111
  • People who ate beans porridge = 30
  • People who ate rice and had diarrhea = 12
  • People who ate swallow and had diarrhea = 17
  • People who ate beans and had diarrhea = 7
  • Constant k=250k = 250

  1. Calculate the attack rate for Rice.

    Attack Rate (Rice)=People who ate rice and had diarrheaPeople who ate rice×k\text{Attack Rate (Rice)} = \frac{\text{People who ate rice and had diarrhea}}{\text{People who ate rice}} \times k Attack Rate (Rice)=12109×250\text{Attack Rate (Rice)} = \frac{12}{109} \times 250 Attack Rate (Rice)=3000109\text{Attack Rate (Rice)} = \frac{3000}{109} Attack Rate (Rice)≈27.5229\text{Attack Rate (Rice)} \approx 27.5229

    Rounding to two decimal places:

    Attack Rate (Rice)≈27.52\text{Attack Rate (Rice)} \approx 27.52

    The attack rate for rice is 27.52\boxed{27.52}.

  2. Calculate the attack rate for Swallow.

    Attack Rate (Swallow)=People who ate swallow and had diarrheaPeople who ate swallow×k\text{Attack Rate (Swallow)} = \frac{\text{People who ate swallow and had diarrhea}}{\text{People who ate swallow}} \times k Attack Rate (Swallow)=17111×250\text{Attack Rate (Swallow)} = \frac{17}{111} \times 250 Attack Rate (Swallow)=4250111\text{Attack Rate (Swallow)} = \frac{4250}{111} Attack Rate (Swallow)≈38.2883\text{Attack Rate (Swallow)} \approx 38.2883

    Rounding to two decimal places:

    Attack Rate (Swallow)≈38.29\text{Attack Rate (Swallow)} \approx 38.29

    The attack rate for swallow is 38.29\boxed{38.29}.

  3. Calculate the attack rate for Beans Porridge.

    Attack Rate (Beans Porridge)=People who ate beans and had diarrheaPeople who ate beans×k\text{Attack Rate (Beans Porridge)} = \frac{\text{People who ate beans and had diarrhea}}{\text{People who ate beans}} \times k Attack Rate (Beans Porridge)=730×250\text{Attack Rate (Beans Porridge)} = \frac{7}{30} \times 250 Attack Rate (Beans Porridge)=175030\text{Attack Rate (Beans Porridge)} = \frac{1750}{30} Attack Rate (Beans Porridge)≈58.3333\text{Attack Rate (Beans Porridge)} \approx 58.3333

    Rounding to two decimal places:

    Attack Rate (Beans Porridge)≈58.33\text{Attack Rate (Beans Porridge)} \approx 58.33

    The attack rate for beans porridge is 58.33\boxed{58.33}.

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