Economists often track employment trends by measuring the proportion of people who are "underemployed," meaning they are either unemployed or would like to work full time but are only working part-time. In the summer of 2013, 17.6% of Americans were "underemployed." The mayor of Thicksburg wants to show the voters that the situation is not as bad in his town as it is in the rest of the country. His staff takes a simple random sample of 300 Thicksburg residents and finds that 45 of them are underemployed. Do the data give convincing evidence that the proportion of underemployed in Thicksburg is lower than elsewhere in the country?

no

Step-by-step explanation:

Take 45 and divide by 300 to find the percent that are underemployed

45/ 300 =.15

Changing to percent form

15%

The sample is fairly small.  Depending on the population of Thicksburg, this could be too small to give an accurate representation.  Less than 3% difference between the national average and the population of Thicksburg is not enough to convince the people that their population has significantly lower underemployment

the direct variation says that:

then the equation is of the form is given by:

            where k is the constant variation.

from the given table:

consider any value of x and m(x)=y

x = 2 and m(x)=y = 3

substitute these value in [1]; we have;

divide both sides by 2 we get;

⇒

check:

put x = -1 and m(x) = -1.5

substitute in the equation:

-1.5 = -1.5                   true

therefore, the function m(x) represents a direct variation

graph of this function as shown below: