Respuesta :
Answer:
See Below
Step-by-step explanation:
Let total number of people be "n"
Since 53% believe their high school, that would be "0.53n"
Since 0.5% fall in error margin, that would be ± 0.005n
Hence,
Greatest number of people would be:
[tex](\frac{0.53n+0.005n}{n})*100=0.535[/tex]
That is 53.5% of people
and
Least nnumber of people would be:
[tex](\frac{0.53n-0.005n}{n})*100=0.525[/tex]
That is 52.5% of people
Thus, the absolute value equation would be:
0.525n ≤ absolute number of people who think their team will win ≤ 0.535n
Where "n" is the total number of spectators
Answer:
The required inequality is: [tex]|x-53|\leq 0.5[/tex]
The least and the greatest percent of people that think their team will win the state championship is 52.5% and 53.5% respectively.
Step-by-step explanation:
Consider the provided information.
In a sports poll, 53% of those surveyed believe their high school football team will win the state championship.
The poll shows a margin of error of 0.5 percentage points.
Let x is the actual number of percent of people that think their team will win the state championship.
The absolute difference of x and 53 should be less than or equal to 0.5
Therefore, the required inequality is:
[tex]|x-53|\leq 0.5[/tex]
[tex]\mathrm{Apply\:absolute\:rule}:\quad \mathrm{If}\:|u|\:\le \:a,\:a\:>\:0\:\mathrm{then}\:-a\:\le \:u\:\le \:a[/tex]
By using the above rule we can solve the inequality as shown:
[tex]-0.5\le \:x-53\le \:0.5[/tex]
Add 53 as shown:
[tex]-0.5+53\le \:x\le \:0.5+53[/tex]
[tex]52.5\le \:x\le \:53.5[/tex]
Hence, the least and the greatest percent of people that think their team will win the state championship is 52.5% and 53.5% respectively.
