Question

Introduce [select], look for relationships among the variables, and construct a mathematical [select] of the form maximize (or minimize) on the interval. Find the [select] of [select]. Use the procedures developed in section 11.5 to find the [select] of [select] on the interval and the numbers where this occurs. Use the solution to the mathematical model to answer all the questions asked in the problem.

A) variables, model, relationships, maximum, maximum
B) variables, model, relationships, minimum, minimum
C) equations, model, relationships, maximum, minimum
D) equations, analysis, parameters, minimum, maximum

Answer 1

In this question, students are introduced to variables and asked to find relationships among them and construct mathematical models to maximize or minimize values. They are also asked to find the correlation coefficient and estimated maximum values using the mathematical model. Students should carefully analyze the relationship between the variables, draw a scatter plot, calculate the least-squares line, and use the solution to answer all the questions in the problem.

Step-by-step explanation:

a. In this question, variables are being introduced and relationships among them are being sought. Students are asked to construct a mathematical model of the form maximize (or minimize) on the interval and find the values of the maximum (or minimum).

b. To find the relationships among the variables, students should decide which variable should be the independent variable and which should be the dependent variable. They can then draw a scatter plot of the ordered pairs to visually analyze the relationship between the variables.

c. After drawing the scatter plot, students should calculate the least-squares line by finding the equation in the form ý = a + bx.

d. To find the correlation coefficient, students can use the procedures taught in section 11.5. They should determine whether the correlation coefficient is significant or not.

e. Some questions also ask students to find the estimated maximum values for certain variables on specific pages or intervals. Students should use the solution to the mathematical model to answer all the questions asked in the problem.

f. For example, if the question asks about the maximum value for a restaurant on page 10, students can substitute the appropriate values into the mathematical model to find the maximum value. Similarly, if the question asks about the maximum value for a restaurant on page 70, students can use the same procedure to find the answer.

Keywords: variables, relationships, mathematical model, maximize, minimize, interval, least-squares line, correlation coefficient, significant, estimated maximum values