Question

27 to get a special deal at the bookstore, a customer must spend more than $40. sean is planning on buying a movie for $16 and some books, b, that cost $8 each. the inequality he wants to use to see how many books he needs to buy is 8b + 16 > 40. which number of books will not allow sean to get the special deal? a 3 books b 4 books c 6 books d 7 books 28 the scatter plot below was graphed from a data set containing five data points. scatter plot image which is closest to the linear correlation coefficient of the relationship shown in the graph? a -0.12 b 0.03 c 0.35 d 0.52

Explanation:

Question 27

Step1: Substitute b=3 into inequality

Substitute \( b = 3 \) into \( 8b + 16 \). We get \( 8\times3 + 16 = 24 + 16 = 40 \). The inequality is \( 8b + 16>40 \), and \( 40\) is not greater than \( 40 \), so \( 3 \) books do not satisfy the inequality.

Step2: Substitute b=4 into inequality

Substitute \( b = 4 \) into \( 8b + 16 \). We get \( 8\times4 + 16 = 32 + 16 = 48 \). Since \( 48>40 \), \( 4 \) books satisfy the inequality.

Step3: Substitute b=6 into inequality

Substitute \( b = 6 \) into \( 8b + 16 \). We get \( 8\times6 + 16 = 48 + 16 = 64 \). Since \( 64>40 \), \( 6 \) books satisfy the inequality.

Step4: Substitute b=7 into inequality

Substitute \( b = 7 \) into \( 8b + 16 \). We get \( 8\times7 + 16 = 56 + 16 = 72 \). Since \( 72>40 \), \( 7 \) books satisfy the inequality.

Step1: Analyze the scatter plot trend

The scatter plot shows a positive but weak linear relationship. A correlation coefficient close to 0 means a very weak relationship, but here there is a slight positive trend. Among the options, \( 0.35 \) is a positive value indicating a weak positive correlation, which matches the scatter plot's trend (points have a slight upward trend but are spread out). \( - 0.12 \) is negative (no negative trend here), \( 0.03 \) is almost no correlation (but the points show a bit more of a positive trend than that), and \( 0.52 \) is a stronger positive correlation than the plot shows.

Answer:

A. 3 books

Question 28