The true proportion p of people who give a favorable rating to Congress is 8% with a margin of error of 1.5%. Describe this statement using an absolute value equation.

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Alicia Washington · Accepted Answer

Given:  People p votes 8% with an error of 1.5%  Calculation:  Given that people votes 8% =8100=0.08  The margin error is 1.5% =1.5100=0.015  So, the given statement is expressed as  |p−0.08|≤0.015  Conclusion:  Thus, the absolute value notation for the given statement is |p−0.08|≤0.015

xleb123 · Accepted Answer

The absolute value equation that represents the given statement is:|p−0.08|=0.015Explanation:- p represents the true proportion of people who give a favorable rating to Congress.- The value 0.08 represents the assumed proportion of people who give a favorable rating to Congress.- The absolute value equation |p−0.08|=0.015 states that the difference between the true proportion p and the assumed proportion 0.08 is equal to 0.015, which represents the margin of error.- By taking the absolute value of the difference, we disregard the direction of the difference and focus on its magnitude.- The equation ensures that the true proportion p lies within a range of 0.08±0.015, meaning that the true proportion of people who give a favorable rating to Congress is estimated to be between 6.5% and 9.5%, with 95% confidence.

fudzisako · Accepted Answer

Answer:0.065≤p≤0.095Solution:p - The true proportion of people who give a favorable rating to Congress.M - The margin of error.The given statement states that the true proportion p is 8% with a margin of error of 1.5%. We can express this using an absolute value equation as:|p−0.08|≤0.015In this equation, |p−0.08| represents the absolute difference between the true proportion p and the value 0.08, which is the given proportion of 8%. The equation states that this absolute difference is less than or equal to the margin of error 0.015.To solve this absolute value equation, we can split it into two separate cases and solve for each case separately.Case 1: (p−0.08)≤0.015In this case, the positive difference between p and 0.08 is less than or equal to the margin of error. Solving for p, we have:p−0.08≤0.015Adding 0.08 to both sides of the inequality:p≤0.095Case 2: −(p−0.08)≤0.015In this case, the negative difference between p and 0.08 is less than or equal to the margin of error. Solving for p, we have:−p+0.08≤0.015Subtracting 0.08 from both sides of the inequality:−p≤−0.065Since we multiplied both sides of the inequality by -1, we need to reverse the inequality:p≥0.065Combining the results from both cases, we can conclude that the true proportion p of people who give a favorable rating to Congress lies between 0.065 and 0.095, inclusive.Therefore, the absolute value equation that describes the statement is:|p−0.08|≤0.015And the solution to this equation is:0.065≤p≤0.095

Jazz Frenia · Accepted Answer

Let x represent the true proportion of people who give a favorable rating to Congress. The given information states that x is 8% with a margin of error of 1.5%.The margin of error can be interpreted as the maximum deviation from the true proportion. In this case, it is 1.5% or 0.015.Using the absolute value equation, we can express the statement as:|x−0.08|≤0.015This equation represents that the absolute difference between the true proportion x and the known proportion 0.08 (which corresponds to 8%) is less than or equal to the margin of error 0.015.This equation ensures that the true proportion lies within the given range, accounting for the margin of error.

The true proportion p of people who give a favorable

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