The partial products are: 42 x 28 = (40 + 2) x (20 + 8) = 40 x 20 + 40 x 8 + 2 x 20 + 2 x 8
<span>= 800 + 320 + 40 + 16
</span>
I used substitution method! hope this helps! feel free to clarify
Answer:
Proved
Step-by-step explanation:
Given
![B =(-2,-1)](https://tex.z-dn.net/?f=B%20%3D%28-2%2C-1%29)
![U = (0,3)](https://tex.z-dn.net/?f=U%20%3D%20%280%2C3%29)
![G = (3,2)](https://tex.z-dn.net/?f=G%20%3D%20%283%2C2%29)
![S = (4,-3)](https://tex.z-dn.net/?f=S%20%3D%20%284%2C-3%29)
Required
Prove BUGS is a trapezoid
Given the coordinates, to prove a trapezoid; all we need to do is to check if one pair of sides is parallel.
<u></u>
<u>Taking BU and GS as a pair</u>
First, we calculate the slope using:
![m = \frac{y_2 - y_1}{x_2 - x_1}](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7By_2%20-%20y_1%7D%7Bx_2%20-%20x_1%7D)
For BU
--- ![(x_1,y_1)](https://tex.z-dn.net/?f=%28x_1%2Cy_1%29)
--- ![(x_2,y_2)](https://tex.z-dn.net/?f=%28x_2%2Cy_2%29)
So, we have:
![m = \frac{3 - -1}{0- -2}](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7B3%20-%20-1%7D%7B0-%20-2%7D)
![m = \frac{4}{2}](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7B4%7D%7B2%7D)
![m = 2](https://tex.z-dn.net/?f=m%20%3D%202)
For GS
--- ![(x_1,y_1)](https://tex.z-dn.net/?f=%28x_1%2Cy_1%29)
--- ![(x_2,y_2)](https://tex.z-dn.net/?f=%28x_2%2Cy_2%29)
So, we have:
![m = \frac{-3-2}{4-3}](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7B-3-2%7D%7B4-3%7D)
![m = \frac{-5}{1}](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7B-5%7D%7B1%7D)
![m = -5](https://tex.z-dn.net/?f=m%20%3D%20-5)
<em>The slope of BU and GS are not the same; hence, they are not parallel.</em>
<u>Taking BS and GU as a pair</u>
Calculate the slope
For BS
--- ![(x_1,y_1)](https://tex.z-dn.net/?f=%28x_1%2Cy_1%29)
--- ![(x_2,y_2)](https://tex.z-dn.net/?f=%28x_2%2Cy_2%29)
So, we have:
![m = \frac{-3 - -1}{4- -2}](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7B-3%20-%20-1%7D%7B4-%20-2%7D)
![m = \frac{-2}{6}](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7B-2%7D%7B6%7D)
![m = -\frac{1}{3}](https://tex.z-dn.net/?f=m%20%3D%20-%5Cfrac%7B1%7D%7B3%7D)
For GU
--- ![(x_1,y_1)](https://tex.z-dn.net/?f=%28x_1%2Cy_1%29)
--- ![(x_2,y_2)](https://tex.z-dn.net/?f=%28x_2%2Cy_2%29)
So, we have:
![m = \frac{3-2}{0-3}](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7B3-2%7D%7B0-3%7D)
![m = \frac{1}{-3}](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7B1%7D%7B-3%7D)
![m = -\frac{1}{3}](https://tex.z-dn.net/?f=m%20%3D%20-%5Cfrac%7B1%7D%7B3%7D)
The slope of BS and GU are the same; hence, they are parallel.
<em>BUGS is a trapezoid because BS and GU have the same slope</em>
Answer: c. 10
Step-by-step explanation:
Given : An independent-measures research study compares three treatment conditions using a sample of n = 5 in each treatment.
For this study, the three sample means are, M1 = 1, M2 = 2, and M3 = 3.
Grand mean =
[All sample have equal elements]
![=\dfrac{1+2+3}{3}=2](https://tex.z-dn.net/?f=%3D%5Cdfrac%7B1%2B2%2B3%7D%7B3%7D%3D2)
For ANOVA,
, where i= 1, 2 , 3
![SS_{between}=5((1-2)^2+(2-2)^2+((3-2)^2)](https://tex.z-dn.net/?f=SS_%7Bbetween%7D%3D5%28%281-2%29%5E2%2B%282-2%29%5E2%2B%28%283-2%29%5E2%29)
![SS_{between}=5((-1)^2+(0)^2+((1)^2)= 5(1+1)=10](https://tex.z-dn.net/?f=SS_%7Bbetween%7D%3D5%28%28-1%29%5E2%2B%280%29%5E2%2B%28%281%29%5E2%29%3D%205%281%2B1%29%3D10)
Hence,the value would be obtained for
.
hence, the correct answer = c. 10
By solving a quotient, we conclude that 495 crates can be loaded on the container.
<h3>
How many 40-kg crates can be loaded on the shipping container?</h3>
We know that the capacity of the container is 27,500 kilograms, and we also know that there is 7,700 kg already on the container.
So the capacity left is:
27,500 kg - 7,700 kg = 19,800 kg
The number of 40kg crates that enter in the container is given by the quotient between the capacity left and the weight of each crate, so we will get:
N = (19,800 kg)/40kg = 495
This means that 495 crates can be loaded on the container.
If you want to learn more about quotients:
brainly.com/question/8952483
#SPJ1