questios are based on the following circle graph.the represents the results of a survey in wich 400 people were asked to identify the the tv channel on wich they preferred to watch the evening news.
wkod 13 percent.
WCLM 24 percent.
WANR 22 PERCENT.
WWCN 41 PERCENT.
Wich channel is the most popular one for the evening news?
how many people preferred WCLM ?
How many more people preferred WWCN than WANR ?
write a ratio to express the number of people who preferred WANR to those who preferred WCLM.
The correct answer and explanation is:
Answers and Explanation:
1. Which channel is the most popular one for the evening news?
The most popular channel is WWCN, as it received the highest percentage of votes, 41%.
2. How many people preferred WCLM?
To find the number of people who preferred WCLM, calculate 24% of 400: Number of people=400×24100=96\text{Number of people} = 400 \times \frac{24}{100} = 96
So, 96 people preferred WCLM.
3. How many more people preferred WWCN than WANR?
First, calculate the number of people who preferred each channel:
- WWCN: 400×41100=164400 \times \frac{41}{100} = 164
- WANR: 400×22100=88400 \times \frac{22}{100} = 88
Next, find the difference between the two: Difference=164−88=76\text{Difference} = 164 – 88 = 76
So, 76 more people preferred WWCN than WANR.
4. Write a ratio to express the number of people who preferred WANR to those who preferred WCLM.
From earlier calculations:
- WANR: 88 people
- WCLM: 96 people
The ratio of WANR to WCLM is: Ratio=8896=1112\text{Ratio} = \frac{88}{96} = \frac{11}{12}
So, the ratio is 11:12.
Explanation:
The circle graph represents the preferences of 400 individuals regarding their favorite TV channel for evening news. To solve the given questions, we use percentages and basic arithmetic.
First, WWCN is the most popular channel since it has the highest percentage of votes (41%). Percentages directly indicate preference levels, making WWCN the clear leader.
Second, to determine how many people preferred WCLM, we calculate 24% of 400. Percentages are portions of a total, so multiplying 24%24\% by the total number of respondents (400) gives us 96 people.
Third, to compare WWCN and WANR, we calculate the number of people for each channel based on their respective percentages, 41% and 22%. Subtracting WANR’s total (88) from WWCN’s total (164) shows a difference of 76 people, emphasizing WWCN’s popularity.
Finally, the ratio of WANR to WCLM is derived by comparing the number of people who preferred each channel (88 and 96, respectively). Ratios represent comparative quantities and can be simplified like fractions. Dividing both numbers by their greatest common divisor (8) gives the simplest form, 11:12.
These calculations demonstrate how percentages from a graph can be translated into actual values, facilitating comparisons, rankings, and ratio analysis.