an automobile safety engineer states that one in every 8 automobile accidents is due to driver fatigue which is the standard deviation of the expected value if the last 12 automobile accidents are analyzed

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.

its c

the answer is $4.45. i started by figuring out the cost of the plates and napkins. the easiest way to figure this cost out is through the tax. we know the way they found the tax is by multiplying the cost of non-food items by the tax rate (5% or 0.5). so, all we have to do to find the cost before tax is set up an equation and work this formula backwards. the equation is 0.19=0.05x where x is the cost of the plates and napkins. now all you do is divide both sides by 0.05 to come up with 3.8=x. now that we know the cost of the plates and napkins is $3.80, all we have to do is subtract this cost from the total cost of $8.25 giving us the cost of the watermelon which is $4.45.