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MODELING REAL LIFE The table shows the temperatures x (in degrees Fahrenheit) and the numbers y of shoppers at a mall. Temperature, x 53 76 64 61 78 58 Number of 422 331 384 390 326 409 shoppers, y a. Approximate the number of shoppers when the temperature is 70°F. b. Predict the number of shoppers when the temperature is 85°F.​

User Zaira
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Final answer:

a. To approximate the number of shoppers when the temperature is 70°F, we can use the table to find the nearest temperature values and their corresponding shopper numbers. b. To predict the number of shoppers when the temperature is 85°F, we can use the regression equation to calculate the estimated shopper number.

Step-by-step explanation:

a. To approximate the number of shoppers when the temperature is 70°F, we can find the corresponding value of y from the given table. The nearest temperatures to 70°F in the table are 64°F and 78°F.

The corresponding number of shoppers for 64°F is 384, and for 78°F is 326. Since 70°F is closer to 64°F, we can estimate the number of shoppers to be approximately 384.

b. To predict the number of shoppers when the temperature is 85°F, we can use the regression equation.

From the given data, we can find the slope, m, to be -2.775 and the y-intercept, b, to be 657.55.

Substituting x = 85 into the equation y = mx + b, we get y = -2.775(85) + 657.55 ≈ 434.6.

Therefore, we can predict the number of shoppers to be approximately 435 when the temperature is 85°F.