A manufacturing machine has two processes. One of them is repeated 4 times and the second only once. The entire cycle can take no longer than 3 minutes. Which graph represents the overall equation represented by this scenario (all
points may not apply to the scenano)?

The last graph in the option represents the overall equation of this scenario (it is option D if the last graph shown is the fourth option).

Explanation:

A manufacturing machine has two processes.

First let's represent the time of the two processes with variables:

The time of 1st process = a

The time of 2nd process = b

Since 1st process is repeated 4 times = 4×a = 4a

Also 2nd process is repeated only once = 1×b = b

Then we would represent the equation of the entire process

The entire cycle is said not to take longer than 3 minutes, meaning it less than or equal to 3 = ≤3

The equation of the entire process gives an inequality:

4a+b ≤ 3

Next, we would derive values for a to get b and vice versa in order to plot the graph using the equation: 4a+b = 3

For a = 0

4(0) +b= 3

b = 3

(a,b) = (0,3)

For b = 0

4a + 0 = 3

a= 3/4 = 0.75

(a,b) = (0.75, 0)

Let (a,b) represent (x,y) on the graph

Plotting the graph with coordinates (a,b) = (x,y) : (0,3), (0.75, 0); we get a line going downward passing, through 3 on y axis and 0.75 on x axis. The shaded portion represent the inequality: 4a+b ≤ 3

The last graph in the option represents the overall equation of this scenario (it is option D if the last graph shown is the fourth option).

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a surging, seething, murmuring crowd of beings that are human only in name, for to the eye and ear they seem naught but savage creatures, animated by vile passions and by the lust of vengeance and of hate.

during the greater part of the day the guillotine had been kept busy at its ghastly work: all that france had boasted of in the past centuries, of ancient names, and blue blood, had paid toll to her desire for liberty and for fraternity.

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