Question

the number of widgets that a manufacturing plant can produce varies jointly as the number of workers and the time that they have worked.

1. find the constant of proportionality, ( k ), to 2 decimal places if 80 workers work 9 hours and can produce 8892 widgets.

( k = square )

1. how many widgets (to the nearest tenth) can be produced by 130 workers in 40 hours?

widgets = square

Explanation:

Step1: Define Joint Variation Formula

Let \( W \) = widgets, \( n \) = workers, \( t \) = time. Joint variation: \( W = knt \).

Step2: Solve for \( k \)

Substitute \( W = 8892 \), \( n = 80 \), \( t = 9 \):
\( 8892 = k(80)(9) \)
Calculate \( 80 \times 9 = 720 \).
Then \( k = \frac{8892}{720} \approx 12.35 \).

Step3: Use \( k \) for Widgets Calculation

For \( n = 130 \), \( t = 40 \), \( k = 12.35 \):
\( W = 12.35 \times 130 \times 40 \)
First, \( 130 \times 40 = 5200 \).
Then \( W = 12.35 \times 5200 = 64220.0 \).

Answer:

s:

1. \( k = \boxed{12.35} \)
2. Widgets = \boxed{64220.0}