Question

number of guests
80
70
60
50
40
30
20
10
10 20 30 40 50 60 70 80 90 100 110 x
temperature (°f)

26 guests
33 guests
41 guests
44 guests

Explanation:

Identify the data points from the scatter plot

The scatter plot shows the relationship between Temperature (\(x\)) and Number of Guests (\(y\)). The visible data points are:

$$ (75, 18), (78, 20), (80, 26), (91, 30), (94, 29), (96, 33), (100, 40), (102, 37) $$

Estimate the line of best fit

Using two representative points to find a linear trend, such as \((75, 18)\) and \((100, 40)\):

$$ m = \frac{40 - 18}{100 - 75} = \frac{22}{25} = 0.88 $$

$$ y - 18 = 0.88(x - 75) \implies y = 0.88x - 48 $$

Predict the number of guests at 100°F

Using the linear model at \(x = 100\):

$$ y = 0.88(100) - 48 = 88 - 48 = 40 $$

Comparing this prediction to the given multiple-choice options (26, 33, 41, 44), the closest value is 41.

Answer:

• 26 guests
• 33 guests
• 41 guests (Correct answer)
• 44 guests