# The number of widgets that a manufacturing plant can produce varies jointly as the number of workers and the time that they have worked. Find the constant of proportionality k to 2 decimal places if 545 workers work 7 hours and can produce 43948.8 widgets.

The constant of proportionality for the scenerio given will be 11.53

What is the general equation of a Straight line?

The general equation of a straight line is -

[y] = [m]x + [c]

where -

[m] is slope of line which tells the unit rate of change of [y] with respect to [x].

[c] is the y - intercept i.e. the point where the graph cuts the [y] axis.

The equation of a straight line can be also written as -

Ax + By + C = 0

By = - Ax - C

y = (- A/B)x - (C/A)

We have 545 workers who worked 7 hours and  produced 43948.8 widgets and the number of widgets that a manufacturing plant can produce varies jointly as the number of workers and the time that they have worked.

The equation can be represnted using the equation of a straight line. We can write -

y = kx

Now, x = 545 x 7 = 3815

So -

43948.8 = (3815)k

k = 43948.8/3815

k = 11.52

Therefore, the constant of proportionality for the scenerio given will be 11.53

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k=545/43948.8

Step-by-step explanation:

widgets per second

## Related Questions

(16x)^1/2 x (25^3/2)

Solve for x:
31250 x^(3/2) = 0
Divide both sides by 31250:
x^(3/2) = 0
Raise both sides to the power of 2/3:

7.29 as a mixed number

7.29
= 7+ 0.29
= 7+ 29/100
= 7 29/100

The final answer is 7 29/100~

A manufacturing company prepays its insurance coverage for a three-year period. The premium for the three years is \$3,360 and is paid at the beginning of the first year. Seventy percent of the premium applies to manufacturing operations and thirty percent applies to selling and administrative activities. What amounts should be considered product and period costs respectively for the first year of coverage? Product Period
A) \$3,360 \$0
B) \$2,352 \$1,008
C) \$1,568 \$672
D) \$784 \$336

Amount considered for product = \$784

Amount considered for period cost = \$336

Step-by-step explanation:

Given:

The total premium for 3 years = \$3,360

Percentage of premium applied to manufacturing operations = 70%

thus,

the premium per year =  = \$1,120

Now,

Amount considered for product = premium applied to manufacturing operations

or

Amount considered for product = 70% of the premium for the first year

or

Amount considered for product = 0.70 × \$1,120 = \$784

and,

or

Amount considered for period cost = 30% of the premium for the first year

or

Amount considered for period cost = 0.30 × \$1,120 = \$336

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