Question

1. the number of calories and the fat content in grams are shown in the scatterplot for major hot dog brands. $y = 1.78 + 0.11x$ models the data.

(a) what is the predicted grams of fat for a hot dog that has 155 calories?
(b) describe the correlation.

1. a scatterplot of the mean precipitation (in centimeters) and the mean temperature (in $^circ$c) is shown. $y = 0.05x + 10.3$ models the data.

(a) what is the predicted temperature for a precipitation of 425 cm?
(b) describe the correlation.

1. the scatterplot shows the vehicle weight and highway fuel economy for different trucks. $y = 42.2 - 0.004x$ models the data

(a) what is the predicted fuel economy (mpg) for a truck that weighs 4900 pounds?
(b) describe the correlation.

Explanation:

Problem 10 (a)

Step1: Identify the formula

The model is \( y = 1.78 + 0.11x \), where \( x \) is calories and \( y \) is fat in grams.

Step2: Substitute \( x = 155 \)

Substitute \( x = 155 \) into the formula: \( y = 1.78 + 0.11 \times 155 \)

Step3: Calculate the value

First, calculate \( 0.11 \times 155 = 17.05 \). Then, \( y = 1.78 + 17.05 = 18.83 \)

Step1: Identify the formula

The model is \( y = 0.05x + 10.3 \), where \( x \) is precipitation (cm) and \( y \) is temperature (\(^\circ\)C).

Step2: Substitute \( x = 425 \)

Substitute \( x = 425 \) into the formula: \( y = 0.05 \times 425 + 10.3 \)

Step3: Calculate the value

First, calculate \( 0.05 \times 425 = 21.25 \). Then, \( y = 21.25 + 10.3 = 31.55 \)

Step1: Identify the formula

The model is \( y = 42.2 - 0.004x \), where \( x \) is weight (pounds) and \( y \) is fuel economy (mpg).

Step2: Substitute \( x = 4900 \)

Substitute \( x = 4900 \) into the formula: \( y = 42.2 - 0.004 \times 4900 \)

Step3: Calculate the value

First, calculate \( 0.004 \times 4900 = 19.6 \). Then, \( y = 42.2 - 19.6 = 22.6 \)

Answer:

18.83 grams

Problem 11 (a)