Question

An orchard uses a histogram each year to track the number of apples produced per apple tree. The number of apples harvested from the trees this year are 41, 43, 45, 46, 48, 49, 50, 51, 53, 54, 55, and 56.

For this situation, which is the appropriate way to label the number of apple intervals on the x-axis?

A) 41 − 46; 46 − 49; 49 − 52; 53 − 56
B) 41 − 45; 46 − 50; 51 − 55; 56 − 60
C) 40 − 44; 45 − 49; 50 − 55
D) 40 − 50; 50 − 55

Answer 1

Answer:

First you must come up with an equation of the yield

 

Yield = Bushels per tree * number of trees

 

Bushels per tree = 30 when the number of trees is 20 and decreases by 1 for each additional tree

 

x = number of trees

 

Bushels per tree = 30 when x = 20 so bushels per tree = (50 - x)    (50-20) = 30

 

Yield = (50 - x) * x

 

Yield = 50x - x2

 

take the derivative  and you get 50 - 2x

 

set this to zero to find the maximum  50 - 2x = 0    and 2x = 50 and x =25

 

Maximum yield will be given with 25 trees

 

you can test 24 and 26 to see that the yield is less

 

yield = (50-24)24 = 624

 

yield = (50-25)25 = 625

 

yield = (50-26)26 = 624

Answer 2

Answer:

D

Step-by-step explanation: