Hello :
all n in N ; n(n+1)(n+2) = 3a a in N or : <span>≡ 0 (mod 3)
1 ) n </span><span>≡ 0 ( mod 3)...(1)
n+1 </span>≡ 1 ( mod 3)...(2)
n+2 ≡ 2 ( mod 3)...(3)
by (1), (2), (3) : n(n+1)(n+2) ≡ 0×1×2 ( mod 3) : ≡ 0 (mod 3)
2) n ≡ 1 ( mod 3)...(1)
n+1 ≡ 2 ( mod 3)...(2)
n+2 ≡ 3 ( mod 3)...(3)
by (1), (2), (3) : n(n+1)(n+2) ≡ 1×2 × 3 ( mod 3) : ≡ 0 (mod 3) , 6≡ 0 (mod)
3) n ≡ 2 ( mod 3)...(1)
n+1 ≡ 3 ( mod 3)...(2)
n+2 ≡ 4 ( mod 3)...(3)
by (1), (2), (3) : n(n+1)(n+2) ≡ 2×3 × 4 ( mod 3) : ≡ 0 (mod 3) , 24≡ 0 (mod3)
Answer:
2nd choice B.
Step-by-step explanation:
You can use the options A-D to help you eliminate pretty quickly without actually graphing
So first chose says you have the graph on the left when x<1 But you should see our visual actually says we want to include what happens at 1 (the filled dot) so this isn't the answer
Second choice Possible
Third choice... I'm just going to look at one of the parts... x^2+4 for x<=1 says we should have part of a parabola to the left of x=1 (inclusive) but there is not parabola in our visual
Fourth choice: same reason as third choice
Answer is the 2nd
For the levels of qualitative, the variable called dummy variables is used in the multiple regression method.
According to the statement
we have given that the by which method we use the different levels of a qualitative independent variable and we have to explain about it.
So, For his purpose, we know that the
A dummy variable is a variable that takes values of 0 and 1, where the values indicate the presence or absence of something.
And in the multiple regression method there are a lot of different variables which are used for a qualitative and for this a variable is used which is called the dummy variables.
By this variables we show the analysis between the given data. it gives the output in the 0 and 1 numbers.
So, For the levels of qualitative, the variable called dummy variables is used in the multiple regression method.
Learn more about the Dummy variables here
brainly.com/question/17177646
#SPJ4
It's equivalent to 4.25 or 4 1/4
Answer:
82 cm
Step-by-step explanation:
In rectangles diagonals are equal and bisect each other
AO = BO
5x + 1 = 4x + 9
Subtract 1 from both sides
5x = 4x + 9 -1
5x = 4x + 8
Subtract 4x from both the sides
5x - 4x = 8
x = 8
AO = 5x + 1
= 5*8 +1
= 40 + 1
AO= 41 cm
Diagonal = 2*41 = 82 cm
