Explanation Given, Urbandelphia General Hospital has three emergency clinics throughout the city. Statistics have been gathered regarding the number of patients seen on night shift for each clinic, and there are 23 emergency physicians available. Clinic Center City South Street West Side Number of Patients 213 65 300 Now total number of physicians in three types of clinics = 213 + 65 + 300 = 578 . Now Center City is entitled to 213 578 = 0.368 = 36.8 % of 23 emergency physicians. Now South Street is entitled to 65 578 = 0.112 = 11.2 % of 23 emergency physicians. Now West Side is entitled to 300 578 = 0.52 = 52 % of 23 emergency physicians. From the table, Clinic Number of Patients Patients in clinic deserved Assign internal parts Examine Fractional part Assign additional member Center City 36.8% 0.368 × 23 = 8.464 8 0.464 8 South Street 11.2% 0.112 × 23 = 2.576 2 0.576 2+1 = 3 West Side 52% 0.52 × 23 = 11.96 11 0.96 11+1 = 12 Total 100% 23 21 23 So we need to apportion two more, according to Hamilton method the group which has the highest fraction will get the additional representatives i.e., from the table South Street and West Side has the highest fraction of 0.576 and 0.96 so both gets the additional representatives. Therefore Center City has 8 physicians, South Street has 3 physicians and West Side has 12 physicians. Center City has 8 physicians, South Street has 3 physicians and West Side has 12 physicians. Given. Urbandelphia General Hospital has three emergency clinics throughout the city. Statistics have been gathered regarding the number of patients seen on night shift for each clinic, and there are 24 emergency physicians available. Clinic Center City South Street West Side Number of Patients 213 65 300 Now total number of physicians in three types of clinics = 213 + 65 + 300 = 578 . Now Center City is entitled to 213 578 = 0.368 = 36.8 % of 23 emergency physicians. Now South Street is entitled to 65 578 = 0.112 = 11.2 % of 23 emergency physicians. Now West Side is entitled to 300 578 = 0.52 = 52 % of 23 emergency physicians. From the table, Clinic Number of Patients Patients in clinic deserved Assign internal parts Examine Fractional part Assign additional member Center City 36.8% 0.368 × 24 = 8.832 8 0.832 8+1 = 9 South Street 11.2% 0.112 × 24 = 2.688 2 0.688 2+1 = 3 West Side 52% 0.52 × 24 = 12.48 12 0.48 12 Total 100% 24 22 24 So we need to apportion two more, according to Hamilton method the group which has the highest fraction will get the additional representatives i.e., from the table South Street and Center City has the highest fraction of 0.688 and 0.832 so both gets the additional representatives. Therefore Center City has 9 physicians, South Street has 3 physicians and West Side has 12 physicians. Given, Urbandelphia General Hospital has three emergency clinics throughout the city. Statistics have been gathered regarding the number of patients seen on night shift for each clinic, and there are 25 emergency physicians available. Clinic Center City South Street West Side Number of Patients 213 65 300 Now total number of physicians in three types of clinics = 213 + 65 + 300 = 578 . Now Center City is entitled to 213 578 = 0.368 = 36.8 % of 23 emergency physicians. Now South Street is entitled to 65 578 = 0.112 = 11.2 % of 23 emergency physicians. Now West Side is entitled to 300 578 = 0.52 = 52 % of 23 emergency physicians. From the table, Clinic Number of Patients Patients in clinic deserved Assign internal parts Examine Fractional part Assign additional member Center City 36.8% 0.368 × 25 = 9.2 9 0.2 9 South Street 11.2% 0.112 × 25 = 2.8 2 0.8 2+1 = 3 West Side 52% 0.52 × 25 = 13 13 0 13 Total 100% 25 24 25 So we need to apportion one more, according to Hamilton method the group which has the highest fraction will get the additional representatives i.e., from the table South Street has the highest fraction of 0.8 so it gets the additional representatives. Therefore Center City has 9 physicians, South Street has 3 physicians and West Side has 13 physicians. Given, Urbandelphia General Hospital has three emergency clinics throughout the city. Statistics have been gathered regarding the number of patients seen on night shift for each clinic, and there are 26 emergency physicians available. Clinic Center City South Street West Side Number of Patients 213 65 300 Now total number of physicians in three types of clinics = 213 + 65 + 300 = 578 . Now Center City is entitled to 213 578 = 0.368 = 36.8 % of 23 emergency physicians. Now South Street is entitled to 65 578 = 0.112 = 11.2 % of 23 emergency physicians. Now West Side is entitled to 300 578 = 0.52 = 52 % of 23 emergency physicians. From the table, Clinic Number of Patients Patients in clinic deserved Assign internal parts Examine Fractional part Assign additional member Center City 36.8% 0.368 × 26 = 9.568 9 0.568 9+1 = 10 South Street 11.2% 0.112 × 26 = 2.912 2 0.912 2+1 = 3 West Side 52% 0.52 × 26 = 13.52 13 0.52 13 Total 100% 26 24 26 So we need to apportion two more, according to Hamilton method the group which has the highest fraction will get the additional representatives i.e., from the table South Street and Center City has the highest fraction of 0.912 and 0.568 so both gets the additional representatives. Therefore Center City has 10 physicians, South Street has 3 physicians and West Side has 13 physicians. Given, Urbandelphia General Hospital has three emergency clinics throughout the city. Statistics have been gathered regarding the number of patients seen on night shift for each clinic, and there are 27 emergency physicians available. Clinic Center City South Street West Side Number of Patients 213 65 300 Now total number of physicians in three types of clinics = 213 + 65 + 300 = 578 . Now Center City is entitled to 213 578 = 0.368 = 36.8 % of 23 emergency physicians. Now South Street is entitled to 65 578 = 0.112 = 11.2 % of 23 emergency physicians. Now West Side is entitled to 300 578 = 0.52 = 52 % of 23 emergency physicians. From the table, Clinic Number of Patients Patients in clinic deserved Assign internal parts Examine Fractional part Assign additional member Center City 36.8% 0.368 × 27 = 9.936 9 0.936 9+1 = 10 South Street 11.2% 0.112 × 27 = 3.024 3 0.024 3 West Side 52% 0.52 × 27 = 14.04 14 0.04 14 Total 100% 27 26 27 So we need to apportion one more, according to Hamilton method the group which has the highest fraction will get the additional representatives i.e., from the table Center City has the highest fraction of 0.936, so it gets the additional representatives. Therefore Center City has 10 physicians, South Street has 3 physicians and West Side has 14 physicians. Given, Urbandelphia General Hospital has three emergency clinics throughout the city

Mathematics All Around, Books a la carte edition (6th Edition)

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ISBN: 9780134462448

Author: Pirnot, Tom

Publisher: PEARSON

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Chapter 10.1, Problem 21E

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Chapter 10.1, Problem 20E

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The apportionment using Hamilton method with the given information that, there are 23 emergency physicians available.

Solution Summary: The author explains that states with small populations generally will lose a representative at some point.

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The apportionment using Hamilton method with the given information that, there are 23 emergency physicians available.