The dot plot below shows the amount of time two random groups of students took to solve a math problem:

based on visual inspection of the dot plots, which of the following groups, if any, shows a greater average time required to solve the problem?

a. group x
b. group y
c. both groups show about the same average time.
d. no conclusion about average time can be made from the data.

correct answers below:

step-by-step explanation:

bob the banana

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.

to find the unit price of an object, you divide the price by object. you are trying to find out how much an object cost per unit.

for instance, lets say you have 50lb of ice cream(object) that cost 8.00 dollars(price). to find the unit cost, we take the 8.00 and divide it by 50, which will give us .16 cents per pound. we can check this by multiplying .16 by 50 = 8.00

so

object = e2

price = d2

unit price = c2

formula for c2:

=d2 / e2

so in my example about ice cream, we would have the following.

e2 = 50

d2 = 8.00

c2 formula:

=d2 / e2