Question

You conduct a random survey of your small town about having a townwide garage sale. Of those surveyed, 56% are in favor and 44% are opposed. The actual percent could be 5% more or 5% less than the acquired results.
A. Write and solve an absolute value equation to find the least and greatest percents of your twin population that could be opposed to a townwide garage sale.

B. A friend claims that half the town is actually opposed to a townwide garage sale. Does this statement conflict with the survey data? Explain.

Answer 1

Using the absolute value function, we have that:

A. The least percentage and the greatest are, respectively, of 39% and 49%.

B. The statement conflicts with the survey data, as the greatest percentage is below 50%.

What is the absolute value function?

The absolute function is defined by:

• |x| = x, x ≥ 0.

• |x| = -x, x < 0.

It measures the distance of a point x to the origin.

For this problem, the difference between the percentage of opposed and 44% can be of at most 5%, hence the absolute value equation is:

|x - 44| = 5.

Hence the least and greatest percentages are given as follows:

• x - 44 = -5 -> x = 39%.

• x - 44 = 5 -> x = 49%.

Thus the statement conflicts with the survey data, as the greatest percentage is below 50%.

More can be learned about the absolute value function at brainly.com/question/24837065

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