Question

In Exercises 29–36, answer the given questions, which are related to percentages.

Marriage Proposals In a survey conducted by TheKnot.com, 1165 engaged or married women were asked about the importance of a bended knee when making a marriage proposal. Among the 1165 respondents, 48% said that the bended knee was essential.

a. What is the exact value that is 48% of 1165 survey respondents?

b. Could the result from part (a) be the actual number of survey subjects who said that a bended knee is essential? Why or why not?

c. What is the actual number of survey respondents saying that the bended knee is essential?

d. Among the 1165 respondents, 93 said that a bended knee is corny and outdated. What percentage of respondents said that a bended knee is corny and outdated?

Short answer

a. 559.2 respondents

b. No

c. 559 respondents

d. Approximately 8%

Step-by-step solution

Given information

TheKnot.com surveyed 1165 women who were either engaged or married. Of all the subjects, 48% responded that bended knee was essential for making a marriage proposal.

Finding the percent equivalent value

a.

Mathematically, x% sign means$\frac{x}{100}$.

Then 48% of 1165 respondents are:

$$\begin{gathered} 48\%\times 1165=\frac{48}{100}\times 1165 \\ =559.2 \end{gathered}$$

Thus, the exact value is 559.2 respondents.

Criteria for determining the actual count of responses

b.

The actual count in part (a) is 559.2, which is in decimal form.

However, the count of subjects who think that bended knee is essential should be a whole number.

Thus, the value of 559.2 cannot be the actual count of responses.

Determining the actual count of responses

c.

The decimal values can be converted to whole numbers using therounding-offrules.

Thus, the actual count of responses in the survey should be 559.

Computing the percentage 

d.

It is known that 93 subjects responded that bending the knee is corny and outdated.

The fraction of 1165 women who consider bending the knee as corny and outdated is equivalent to $\frac{93}{1165}$.

The formula for determining the percentage from the fraction is:

$$\begin{gathered} \frac{93}{1165}\times 100=7.9828\% \\ \approx 8\% \end{gathered}$$

Thus, approximately 8% of the women responded that bending the knee is corny and outdated.