a table has the points: (1, 40) (1, 35) (1, 30) (3, 110) (3, 105) (3, 90) (5, 170) (5, 160) (5, 180) (10, 400) (10, 390) (10, 420)
Gary saw a video on the internet in which dropping mint candies into bottles of soda pop caused the soda pop to spurt immediately from the bottle. He wondered if the height of the spurt was linearly related to the number of mint candies used. He collected data using 1, 3, 5, and 10 mint candies dropped into two-liter bottles of soda pop. The height of the spurt was measured in centimeters. Each quantity of mint candies was tried three times. The data is shown in the table.
Using the mean of the data points for 3 and 10, what is the BEST interpretation of the slope in context of this problem?
To find the mean of the data points for 3 and 10 mint candies, we need to calculate the average height for both quantities separately and then find the mean of those averages.
For 3 mint candies:
(3, 110) (3, 105) (3, 90)
Average height for 3 mint candies = (110 + 105 + 90) / 3 = 305 / 3 = 101.67 cm
For 10 mint candies:
(10, 400) (10, 390) (10, 420)
Average height for 10 mint candies = (400 + 390 + 420) / 3 = 1210 / 3 = 403.33 cm
Now, let's find the mean of these averages:
Mean of the averages = (101.67 + 403.33) / 2 = 505 / 2 = 252.5 cm
The slope in this context represents the change in height (in centimeters) for every additional mint candy used.
Based on the mean of the data points for 3 and 10 mint candies, we can interpret the slope as follows: On average, for every additional mint candy dropped into a two-liter bottle of soda pop, the spurt height increases by 252.5 centimeters.
thats not one of the answers, the answers are A: The slope is 40, which means that for every mint candy dropped into the bottle of soda pop the minimum height of the spurt increase is 40 cm. B: The slope is 47.1, which means that for every mint candy dropped into the bottle of soda pop the maximum height of spurt increase is 47.1 cm. C: The slope is 43.1, which means that for every mint candy dropped into the bottle of soda pop the height of the spurt increases by 43.1 cm. D: The slope is 47.1, which means that for every mint candy dropped into the bottle of soda pop the height of the spurt increases by 47.1 cm.
Apologies for the confusion. Based on the given data, the mean of the data points for 3 and 10 mint candies is approximately 252.5 cm, not one of the options provided.
However, we can still make an interpretation based on the available options.
Option C states that the slope is 43.1, which means that for every mint candy dropped into the bottle of soda pop, the height of the spurt increases by 43.1 cm. Although this value is not the exact mean of the data points, it is closest to the range of values in the given options.
Therefore, the BEST interpretation of the slope based on the available options is option C: The slope is 43.1, which means that for every mint candy dropped into the bottle of soda pop, the height of the spurt increases by 43.1 cm.