The trapezoidal approximation will be the average of the left- and right-endpoint approximations.
Let's consider a simple example of estimating the value of a general definite integral,

Split up the interval
![[a,b]](https://tex.z-dn.net/?f=%5Ba%2Cb%5D)
into

equal subintervals,
![[x_0,x_1]\cup[x_1,x_2]\cup\cdots\cup[x_{n-2},x_{n-1}]\cup[x_{n-1},x_n]](https://tex.z-dn.net/?f=%5Bx_0%2Cx_1%5D%5Ccup%5Bx_1%2Cx_2%5D%5Ccup%5Ccdots%5Ccup%5Bx_%7Bn-2%7D%2Cx_%7Bn-1%7D%5D%5Ccup%5Bx_%7Bn-1%7D%2Cx_n%5D)
where

and

. Each subinterval has measure (width)

.
Now denote the left- and right-endpoint approximations by

and

, respectively. The left-endpoint approximation consists of rectangles whose heights are determined by the left-endpoints of each subinterval. These are

. Meanwhile, the right-endpoint approximation involves rectangles with heights determined by the right endpoints,

.
So, you have


Now let

denote the trapezoidal approximation. The area of each trapezoidal subdivision is given by the product of each subinterval's width and the average of the heights given by the endpoints of each subinterval. That is,

Factoring out

and regrouping the terms, you have

which is equivalent to

and is the average of

and

.
So the trapezoidal approximation for your problem should be
Answer:
47.4%
Step-by-step explanation:
It has to be below 50% because those weights fall at or below the average.
75.
Explanation: from 3 to 12, you add 9, and then double the 12 to get to 24, and then add 9 again to get to 33, and double it to get 66, so the pattern is to add 9 and then double.
Answer:
there are 7 outcomes.
the chances of one is one in 7 and the chances of two is 1 in 14. the third is somewhere around 43%
Hope this helps!!! Brainliest?!
Step-by-step explanation:
Answer:
90 arrangements
Step-by-step explanation:
Since there are no repititions of letters, there are unique 10 letters in total.
THe number of arrangements would be 2 permutation 10. We need the formula for permutation. That is:

Now, n = 10 [total] and r is 2, so we have:

So, there can be 90 arrangements