ANSWER
EXPLANATION
We want to determine the value of f(3) that will lead to an average rate of change of 19 over the interval [3, 5].
The average rate of change of f(x) over the interval [a,b]:
If the average rate of change over the interval [3, 5] is 19, then;
From the to table f(5)=13
Answer:
Keith must remove 90-75 = 15 bags in order to meet the weight requirements
Step-by-step explanation:
This problem can be solved by consecutive rules of three problem.
Rule of three problem:
In a rule of three problem, the first step is identifying the measures and how they are related, if their relationship is direct of inverse.
When the relationship between the measures is direct, as the value of one measure increases, the value of the other measure is going to increase too. In this case, the rule of three is a cross multiplication
When the relationship between the measures is inverse, as the value of one measure increases, the value of the other measure will decrease. In this case, the rule of three is a line multiplication.
In this problem, the measures are:
- The number of bags
- The total weight
As the number of bags increases, so do the total weight. So, the relationship between the measures is direct.
To know how many bags does Keith need to remove in order to meet the weight requirements, we first need to know how many bags are in the truck currently.
The problem states that each bag weighs 40 pounds and the weight of the truck is 3600 pounds, so:
1 bag - 40 pounds
x bags - 3600 pounds
40x = 3600
x = 90.
Keith currently has 90 bags in the truck.
Now, we have to know how much bags he can have in the truck, that is, 3000 pounds worth of bags. So:
1 bag - 40 pounds
x bags - 3000 pounds
40x = 3000
x = 75.
The truck's capacity is at most 75 bags.
So, Keith must remove 90-75 = 15 bags in order to meet the weight requirements