Question

Mr. Jones has taken a survey of college students and found that 40 out of 47 students are liberal arts majors. If a college has 10,827 students, what is the number of students who are liberal arts majors, rounded to the nearest whole number?

Answer 1

To find the number of liberal arts majors in a college with 10,827 students, based on the survey result where 40 out of 47 students are liberal arts majors, a proportion is used and the resulting equation 40/47 = X/10,827 is solved for X, which is then rounded to the nearest whole number.

Step-by-step explanation:

The subject of this question is Mathematics, specifically it relates to the application of proportions and statistical estimation to make a prediction based on sample data. In the scenario presented, Mr. Jones has conducted a survey and found that 40 out of 47 students are liberal arts majors. To estimate the number of liberal arts majors in a college of 10,827 students, we would set up a proportion based on the sample data and solve for the unknown total number of liberal arts majors in the college.

The proportion is as follows:
(Number of liberal arts majors in the sample) / (Total number of students in the sample) = (Number of liberal arts majors in the college) / (Total number of students in the college)

Using this formula, we calculate:
40 / 47 = X / 10,827

Cross-multiply and divide to find the value of X, which will provide us with the estimated number of liberal arts majors in the college, rounding to the nearest whole number.