Question

three parties, l, c, and k, are running for the election in a town of 8,000 residents. the results of a survey conducted by the local newspaper are shown in the circle graph below. based on this information, which statement is true? a. the expected difference in votes between the l party and the k party is 1,760. b. 2,000 people are expected to vote the k party. c. the c party expects to obtain 600 more votes than the k party. d. 5,280 people are expected to vote the l party or the k party.

Explanation:

Step1: Calculate the number of votes for each party

The total number of residents is \(n = 8000\).

• For party \(L\): The percentage of votes is \(47\%\), so the number of votes \(V_L=8000\times0.47 = 3760\)
• For party \(K\): The percentage of votes is \(19\%\), so the number of votes \(V_K=8000\times0.19 = 1520\)
• For party \(C\): The percentage of votes is \(25\%\), so the number of votes \(V_C=8000\times0.25 = 2000\)

Step2: Analyze each option

• Option A

The difference between \(L\) and \(K\) is \(V_L - V_K=8000\times(0.47 - 0.19)=8000\times0.28 = 2240
eq1760\)

• Option B

\(V_K = 8000\times0.19=1520
eq2000\)

• Option C

\(V_C-V_K=8000\times(0.25 - 0.19)=8000\times0.06 = 480
eq600\)

• Option D

\(V_L + V_K=8000\times(0.47 + 0.19)=8000\times0.66 = 5280\)

Answer:

D. 5,280 people are expected to vote the L party or the K party.