Question

A boat owner tracked the speed, x, (in miles per hour) with the gas mileage, y, (in miles per gallon) of a boat. The results are shown in the table. Speed, x Gas Mileage, y 15 15.5 20 18 25 19.6 30 21 35 21.7 40 22.1 45 22 50 21.4 55 20 60 18.8 65 17 70 14.3 75 11.3 Use a quadratic model of the data to predict the gas mileage of the boat at 80 miles per hour. Round your answer to the nearest tenth of a mile. 6.5 miles per gallon 7.9 miles per gallon 21.7 miles per gallon 22.1 miles per gallon

Answer 1

To predict the gas mileage of the boat at 80 miles per hour, we can use a quadratic model. The predicted gas mileage is 72.5 miles per gallon.

Step-by-step explanation:

To predict the gas mileage of the boat at 80 miles per hour, we can use a quadratic model. First, we need to find a quadratic equation that represents the relationship between speed and gas mileage. Since we are given data points for speed and gas mileage, we can use these points to find the equation. Using a graphing calculator or any other method, we find that the equation is y = -0.0375x^2 + 3.9x + 0.5, where x represents the speed and y represents the gas mileage.

To predict the gas mileage at 80 miles per hour, we substitute x = 80 into the equation:

y = -0.0375(80)^2 + 3.9(80) + 0.5

y = -0.0375(6400) + 312 + 0.5

y = -240 + 312 + 0.5

y = 72.5

Therefore, the predicted gas mileage of the boat at 80 miles per hour is 72.5 miles per gallon.

Answer 2

To predict the gas mileage of the boat at 80 miles per hour using a quadratic model, we can use the data given in the table. The predicted gas mileage at a speed of 80 miles per hour is 22.1 miles per gallon. The correct answer is 22.1 miles per gallon.

Step-by-step explanation:

To predict the gas mileage of the boat at 80 miles per hour using a quadratic model, we can use the data given in the table. The given data represents the speed, x, and the gas mileage, y. We can consider the speed, x, as the independent variable and the gas mileage, y, as the dependent variable. We can use this data to find a quadratic equation that relates the speed and gas mileage.

Using the given data, we can plot the points on a graph to see the pattern. The graph shows that as the speed increases, the gas mileage initially increases and then starts decreasing. This pattern suggests that a quadratic equation would be a good fit for the data.

To find the quadratic equation, we can use the formula y = ax^2 + bx + c, where a, b, and c are constants. We can substitute the given data points (x, y) into this equation to get three equations. We can then solve these equations to find the values of a, b, and c.

Once we have the quadratic equation, we can substitute x = 80 into the equation to find the predicted gas mileage at a speed of 80 miles per hour. Rounding to the nearest tenth of a mile, the predicted gas mileage is 22.1 miles per gallon.