Question

the relationship between temperature and cones sold is positive or negative linear or nonlinear strong or weak. use a trend line to predict the temperature if 14 ice cream cones were sold. are there any outliers? if so, list which point(s) they are. which ordered pair would best fit the trend of the scatter plot? (60, 34) (5, 2) (90, 10) based on the trend, if 20 ice cream cones were sold, would you expect the temperature to be above or below 80? why? using a trend line, predict how many ice cream cones would be sold if it was 55°

Explanation:

Step1: Determine the relationship type

Since as temperature increases, the number of ice - cream cones sold is likely to increase, the relationship between temperature and cones sold is positive. Also, a linear relationship is reasonable as we expect a somewhat proportional increase in sales with an increase in temperature, so it is linear. And if the data points follow the trend closely, we can assume it is strong. So the relationship is positive, linear, and strong.

Step2: Identify outliers

Outliers are points that deviate significantly from the overall pattern. Given the ordered pairs (5, 2), (60, 34), (90, 10), the point (90, 10) seems to be an outlier as when the temperature is 90 (high), we would expect a much higher number of ice - cream cones sold compared to 10, while the other points (5, 2) and (60, 34) follow the general increasing trend more closely.

Step3: Predict using trend - line

First, we would need to find the equation of the trend - line (using methods like least - squares regression if we had more data points). But assuming a simple linear relationship and using the general idea of the trend. Let's assume a linear equation of the form \(y=mx + b\). We can estimate based on the trend from the non - outlier points. If we consider the non - outlier points, as temperature increases, the number of cones sold increases. If the temperature is 55, based on the upward trend, we would expect a number of cones sold between the values corresponding to 5 and 60. Let's say we estimate a value around 25 (a rough estimate based on the trend).

Step4: Predict temperature for 20 cones sold

Again, using the trend. If 20 ice - cream cones were sold, looking at the upward trend of the non - outlier points, we would expect the temperature to be between 5 and 60. A rough estimate could be around 30 - 40. Since the relationship is positive, as the number of cones sold is more than 2 (at 5 degrees) and less than 34 (at 60 degrees), the temperature should be above 5 and below 60.

Answer:

1. Positive, linear, strong
2. (90, 10)
3. Approximately 25
4. Between 5 and 60, around 30 - 40