Answer:
1 Expert Answer
X + Y + Z = 264. Since Y is 1 bigger than X, Y = X + 1. Since Z is 1 bigger than Y, Z = Y + 1. But Y = X + 1, so Z = (X + 1) + 1 = X + 2.
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
Rancho middle school has an average of 23 3/8 students per teacher.write this mixed number as a decimal.
Answer:

Step-by-step explanation:
Given:
The given mixed number is 
We need to write the given mixed number as a decimal.
So, we find the decimal number by separating the parts.

The value of 


Therefore, the decimal number of given mixed number is 
Answer:
70.8
Step-by-step explanation:
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Answer:
The width of the walkway is 4 feet.
Step-by-step explanation:
The garden and a walkway around its perimeter have an area of 460 square feet.
The length of the garden = 15 feet
The width of the garden = 12 feet
Assuming that walkway is of uniform width, we can solve the following equation.

Expanding this we get;


We will solve this using quadratic equation formula:

Here a = 4 , b = 54 , c = -280
We get the roots as x = 4 and x = 
Neglecting the negative value, we will take x = 4 feet.
Hence, the width of the walkway is 4 feet.