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The Honeybee Waggle Dance When honeybee scouts find a food source or a nice site for a new home, they communicate the location to the rest of the swarm by doing a waggle dance.They point in the direction of the site and dance longer for sites farther away. The rest of the bees use the duration of the dance to predict distance to the site. Table 1 shows the distance, in meters, and the duration of the dance, in seconds, for seven honeybee scouts. Duration 0.40 0.45 0.95 1.30 2.00 3.10 4.10 Distance 200 250 500 950 1950 3500 4300 Table 1 Duration of a honeybee waggle dance to indicate distance to the source Check out a honeybee waggle dance on youtube! 2Seeley. T, Honeybee Democracy, Princeton University Press, Princeton, NJ, 2010, p. 128. (a) Which is the response variable O Distance Duration(b) Figure 1 shows a scatterplot of the data. 4000 3000 2000 0 Duratlon Figure 1 Using dance duration to predict distance to source Does there appear to be a linear trend in the data? If so, is it positive or negative? No, there appears to be no linear trend in the data. O Yes, there appears to be a positive linear trend in the data. O Yes, there appears to be a negative linear trend in the data. (c) Use technology to find the correlation between the two variables Round your answer to three decimal places.(d) Use technology to find the regression line to predict distance from duration. Round your answers to the nearest integer. Distance = (Duration) (e) Interpret the slope of the line in context. O The slope tells the expected distance if the duration is 1 second more. O The slope tells the expected duration if the distance is 1 meter more. The slope tells the expected change in distance if the duration is 1 second more. O The slope tells the expected change in duration if the distance is 1 meter more. (f) Round your answers to the nearest integer. Predict the distance to the site if a honeybee does a waggle dance lasting 1 second. distance after 1 second meters Predict the distance to the site if a honeybee does a waggle dance lasting 3 seconds. distance after 3 seconds meters

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a Pistance res pance varioie es There cappe ars to be positi ve inear trend in the dat a d) Dista399. 0 S3 + 1174.268 Duration 2The slope teils the expected chane in f) - distance-after-1 seconde- -775-245-nefen, if the cigtagee is 1 metey more Seconc dista nce after3 seconos 31 2-3.721 meter.

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