When growing giant pumpkins for competitions, growers need to keep track of the weights of the pumpkins while they are growing. It is difficult to weigh a large pumpkin before it is harvested, so a method has been developed for estimating the weight. The grower measures around the pumpkin both horizontally and vertically, then adds the results. This is called the OTT (over the top) measurement and is used to predict the weight of the pumpkin. Following are the OTT measurements and actual weights of the largest pumpkins entered into official competitions in a recent year.

Question

When growing giant pumpkins for competitions, growers need to keep track of the weights of the pumpkins while they are growing. It is difficult to weigh a large pumpkin before it is harvested, so a method has been developed for estimating the weight. The grower measures around the pumpkin both horizontally and vertically, then adds the results. This is called the OTT (over the top) measurement and is used to predict the weight of the pumpkin. Following are the OTT measurements and actual weights of the  largest pumpkins entered into official competitions in a recent year.
OTT (inches)	Weight (pounds)
490	2528
451	2114
456	2077
454	2138.9
490	2433.9
450	2017.5
473	2166
454	2020.5
477	2157.5
469	2469

The equation is y= -2426.6043+9.946x.

(c) If two pumpkins differ in OTT by 10 inches, by how much would you predict their weights to differ? Round the answer to two decimal places as needed.

GPT-4o mini · Answer

To determine how much the weights of two pumpkins would differ based on a 10 inch difference in their OTT measurements, you can use the slope of the equation provided.

The equation is given as:

\[ y = -2426.6043 + 9.946x \]

Here, \( y \) is the predicted weight and \( x \) is the OTT measurement. The coefficient of \( x \), which is 9.946, tells us how much the predicted weight changes for each 1 inch change in OTT.

So, if two pumpkins differ in OTT by 10 inches, the difference in their predicted weights can be calculated as:

\[ \text{Difference in weight} = \text{slope} \times \text{difference in OTT} \] \[ \text{Difference in weight} = 9.946 \times 10 \]

Calculating this gives:

\[ \text{Difference in weight} = 99.46 \]

Thus, if two pumpkins differ in OTT by 10 inches, you would predict their weights to differ by 99.46 pounds.

Answer

(d) Predict the weight of a pumpkin whose OTT is 490 inches. Round the answer to two decimal places as needed.

GPT-4o mini · Answer

To predict the weight of a pumpkin with an OTT measurement of 490 inches using the given equation:

\[ y = -2426.6043 + 9.946x \]

we will substitute \( x = 490 \) into the equation.

Calculating the weight:

\[ y = -2426.6043 + 9.946 \times 490 \]

First, calculate \( 9.946 \times 490 \):

\[ 9.946 \times 490 = 4874.54 \]

Now substitute this value back into the equation:

\[ y = -2426.6043 + 4874.54 \]

Perform the subtraction:

\[ y = 2447.9357 \]

Rounding this to two decimal places gives:

\[ y \approx 2447.94 \]

Thus, the predicted weight of a pumpkin whose OTT is 490 inches is 2447.94 pounds.