Eagletrons are all electric cars produced by mogul motors. one of the concernsof mogul is that the eagletrons be capable of achieving appropriate maximumspeeds. to monitor this, mogul executives take samples of 8 eagletrons at atime. for each sample, they determine the average maximum speed and the rangeof the maximum speeds within the sample. they repeat this with 35 samples toobtain 35 sample means and 35 ranges. they find that the average sample mean is88.50 mph and the average range is 3.25 mph. using these results, theexecutives decide to establish an r chart. they would like this chart to beestablished so that when it shows that the range of a sample is not within thecontrol limits, there is only approximately a .0027 probability that this is dueto natural variation. what will the upper control limit (ucl) and the lowercontrol limit (lcl) in this chart?

trying to confirm that what i came up with is correct.

what is the question? i am guessing you are looking for the area.

to find an area, you have to do length x width.

in this case, it would be 12 ft x 4 ft = 48 sq. ft

30,40,50 is correct answer

a) 40 more; b) old factory:   10%, new factory:   16%; c) week 4

explanation:

a) at week 0, we see in the graph that the new factory produces 190 specialty items.  

using the function, substituting 0 in for w,

this is a difference of 230-190 = 40.

b) the function for the old factory is written in the form f(x) = a(1+r)ˣ, where a is the original amount, x is the amount of time and r is the growth rate.   the equation for the old factory is ; 230 is in place of a and is the original amount; w is the amount of time; which means 1+r = 1.1.   this means that r must be 0.1 or 10%.

for the new factory, we find the percent of increase to find the growth rate; the formula for this is

between the first two points, the amount of change is 220-190 = 30; this gives us

30/190 = 0.158 ≈ 0.16 = 16%

c) at week 0, the old factory has 230 while the new factory has 190.

at week 1, the old factory has 230(1.1) = 253 while the new factory has 220.

at week 2, the old factory has 230(1.1²) = 278.3 while the new factory has 252.

at week 3, the old factory has 230(1.1³) = 306.13 while the new factory has 290.

at week 4, the old factory has 230(1.1⁴) = 336.743 while the new factory has 337.   this is the first week that the new factory surpasses the old.