The rate of change is 8/6.
Answer:
<em>The least number of items to produce is 41</em>
Step-by-step explanation:
<u>Average Cost</u>
Given C(x) as the cost function to produce x items. The average cost is:
![\displaystyle \bar C(X)=\frac{C(x)}{x}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cbar%20C%28X%29%3D%5Cfrac%7BC%28x%29%7D%7Bx%7D)
The cost function is:
![C(x) = -20x+1681](https://tex.z-dn.net/?f=C%28x%29%20%3D%20-20x%2B1681)
And the average cost function is:
![\displaystyle \bar C(X)=\frac{-20x+1681}{x}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cbar%20C%28X%29%3D%5Cfrac%7B-20x%2B1681%7D%7Bx%7D)
We are required to find the least number of items that can be produced so the average cost is less or equal to $21.
We set the inequality:
![\displaystyle \frac{-20x+1681}{x}\le 21](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7B-20x%2B1681%7D%7Bx%7D%5Cle%2021)
Multiplying by x:
![-20x+1681 \le 21x](https://tex.z-dn.net/?f=-20x%2B1681%20%5Cle%2021x)
Note we multiplied by x and did not flip the inequality sign because its value cannot be negative.
Adding 20x:
![1681 \le 21x+20x](https://tex.z-dn.net/?f=1681%20%5Cle%2021x%2B20x)
![1681 \le 41x](https://tex.z-dn.net/?f=1681%20%5Cle%2041x)
Swapping sides and changing the sign:
![41x \ge 1681](https://tex.z-dn.net/?f=41x%20%5Cge%201681)
Dividing by 41:
![x\ge 41](https://tex.z-dn.net/?f=x%5Cge%2041)
The least number of items to produce is 41
Answer: 5x+8
Step-by-step explanation: You have to combine like terms.
3x+2x=5x
5+3=8
= 5x+8
Step-by-step explanation:
(a)
the probability of parcels weighing 35oz or less is
0.841
the probability of parcels weighing 14oz or less is
0.023
the probability of parcels weighing between 14 and 35oz is the probabilty of 35oz minus the probability of 14oz
0.841 - 0.023 = 0.818
the percentage is the probability × 100 = 81.8%
(b)
the probability of parcels weighing more than 49oz is 1 minus the probability to weigh less than 49oz.
the probability to weigh less than 49oz is
0.99865
so, the probability to weigh more than 49oz is
1 - 0.99865 = 0.00135
the percentage is again probability×100 = 0.14%