The average number of customers per day at a home improvement store is given in the following table.  The sine regression equation was found to be y = 33.690sin(0.887x + 1.337) + 81.684, where x represents the day where 1 = Sun of the first week, 7 = Sat of the first week, 8 = Sun of the second week, and 14 = Sat of the second week.  Use this model to predict the average number of customers on Thursday.  Round to the nearest customer.

Day
Sun
Mon
Tue
Wed
Thu
Fri
Sat
Number of Customers
114
75
60
51
 	
86
118

a.
72
b.
65
c.
70
d.
64

To solve this problem, we need to use the given sine regression equation:

\[
y = 33.690\sin(0.887x + 1.337) + 81.684
\]

where \( y \) represents the number of customers, and \( x \) represents the day of the week.

Since Thursday is the 5th day of the week (based on the mapping given in the problem), we substitute \( x = 5 \) into the equation to predict the number of customers for that day.

Let's compute this.Using the sine regression equation, the predicted number of customers on Thursday is approximately **65**.

The correct answer is **b. 65**.

Would you like further details or have any questions? Here are some related questions to consider:

1. How do changes in the amplitude or frequency affect the sine regression model?
2. What does each parameter (A, B, C, D) represent in the sine regression equation?
3. How can we interpret the phase shift in the sine equation for this context?
4. How would the predicted number of customers change for other days of the week?
5. How could we test the accuracy of this sine regression model?

**Tip:** When interpreting a sine regression equation, remember that the amplitude represents the maximum variation from the mean, and the period controls how quickly the sine wave oscillates over the domain.

The average number of customers per day at a home improvement store is given in the following table. The sine regression equation was found to be y = 33.690sin(0.887x + 1.337) + 81.684, where x represents the day where 1 = Sun of the first week, 7 = Sat of the first week, 8 = Sun of the second week, and 14 = Sat of the second week. Use this model to predict the average number of customers on Thursday. Round to the nearest customer.

Learn how to predict customer traffic at a home improvement store using a sine regression equation. This problem explores key trigonometric concepts and functions. The sine model is used to predict customer numbers for Thursday based on the equation y = 33.690sin(0.887x + 1.337) + 81.684. Suitable for high school students in Grades 10-12.

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