Question

1. sugar level in patient’s bloodstream a doctor measured the blood sugar levels of one of her patients shortly after giving the patient a candy bar to eat. the graph below shows the patient’s blood sugar level (y) x hours after she ate the candy bar. how long after eating the candy bar was the patient’s blood sugar level the highest? (a) 20 minutes (b) 30 minutes (c) 40 minutes (d) 1 hour ten students took a math quiz that consisted of 10 questions. the median score was 5.5. the modal score was 6. the teacher recorded the results of the first nine students in the following line plot. 20. what was the average score of the first nine students whose scores were represented on the line plot? give your answer to one decimal place. (a) 4.9 (b) 5.4 (c) 5.5 (d) 5.7 21. what score did the tenth student get in the quiz? (a) 4 (b) 5 (c) 6 (d) 7

Explanation:

19.

Step1: Analyze the graph

The \(y\) - axis represents the sugar level and the \(x\) - axis represents the time. The highest point on the graph (maximum \(y\) - value) occurs at \(x = 0.5\) hours.

Step2: Convert hours to minutes

Since \(1\) hour \(=60\) minutes, then \(x=0.5\) hours. Using the conversion formula \(t = 60x\), where \(x = 0.5\). So \(t=60\times0.5=30\) minutes.

Step1: Calculate the sum of the first - nine scores

From the line - plot:
The scores are \(2,3,3,4,5,5,8,9,10\)
The sum \(S=2 + 3+3+4+5+5+8+9+10=\sum_{i = 1}^{9}x_{i}=49\)

Step2: Calculate the average

The average \(\bar{x}=\frac{S}{n}\), where \(n = 9\) (the number of students). So \(\bar{x}=\frac{49}{9}\approx5.4\)

Step1: Recall the formula for the median

For \(n = 10\) (even number of data points), the median \(M=\frac{x_{5}+x_{6}}{2}\). Given \(M = 5.5\).
The first nine scores in ascending order: \(2,3,3,4,5,5,8,9,10\)
Let the tenth score be \(x\). The data set with the tenth score (in ascending order) is \(2,3,3,4,5,5,x,8,9,10\) (assuming \(x\geq5\)).
Since \(M=\frac{5 + 6}{2}=5.5\) (to make the median \(5.5\)), the data set should be \(2,3,3,4,5,6,8,9,10\) (after re - ordering when \(x = 6\)) and the mode (most frequent value) is \(6\) (appears twice, and other non - repeated values).

Answer:

B. 30 minutes

20.