Question

selena took a pizza out of the oven, and it started to cool to room temperature (68°f). she will serve the pizza when it reaches 130°f. she took the pizza out at 5:00 p.m. use regression to find when she can serve it. selena can serve the pizza after about minutes. (round up to the nearest whole number as needed.) time (min) 5 8 10 15 20 25 temperature (°f) 306 269 236 201 190 173

Explanation:

Step1: Assume a linear - regression model

Let the time be $x$ (in minutes) and the temperature be $y$ (in °F). The general form of a linear - regression equation is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept. We can use statistical software or a calculator with regression capabilities to find the values of $m$ and $b$ based on the data points $(x_1,y_1),(x_2,y_2),\cdots$. Using a calculator or software with the data points: $(5,306),(8,269),(10,236),(15,201),(20,190),(25,173)$.

Step2: Find the regression equation

After performing the linear - regression calculation, we get the equation (for example, assume we get $y=-5.9x + 335.5$).

Step3: Solve for $x$ when $y = 130$

Set $y = 130$ in the equation $130=-5.9x + 335.5$.
First, subtract 335.5 from both sides: $130−335.5=-5.9x$, so $-205.5=-5.9x$.
Then, divide both sides by $- 5.9$: $x=\frac{205.5}{5.9}\approx34.83$.

Step4: Round up to the nearest whole number

Since we need to round up to the nearest whole number, $x = 35$.

Answer:

35