Step-by-step explanation:
We will prove by mathematical induction that, for every natural ,
We will prove our base case, when n=4, to be true.
Base case:
Inductive hypothesis:
Given a natural ,
Now, we will assume the induction hypothesis and then use this assumption, involving n, to prove the statement for n + 1.
Inductive step:
With this we have proved our statement to be true for n+1.
In conlusion, for every natural .
Answer:
-
Step-by-step explanation:
I hope this helps
As angle 6y° and angle( 13y - 10 )° are interior angles on the same side of transversal their sum will be equal to 180° .
Then :-
Which means :-
= 13y - 10
= 13 × 10 - 10
= 130 - 10
= 120°
Then angle 6y :-
= 6 × 10
= 60°
As angle 60° and angle 9x + 12° are a linear their sum will also add up to form 180° .
Which can be written as :-
Then :-
= Angle 9x + 12
= 9 × 12 + 12
= 108 + 12
= 120°
Therefore , the value of y = 10 and the value of x = 12 .
Answer:
-8 and 6
Step-by-step explanation:
Coordinate of point M = -1
Distance between M and a point N = MN = 7
Therefore, the possible coordinates of N can either be:
To the left => -1 - 7 = -8
Or
To the right => -1 + 7 = 6
Check:
If M = -1, and N = -8, MN = |-1 -(-8)| = |-1 + 8| = 7
Or
If M = -1, and N = 6, MN = |-1 - 6| = |-7| = 7
So, our answer is right.
Possible coordinates of point N are -8 and 6
Answer:
As sample sizes increase, the sampling distributions approach a normal distribution. With "infinite" numbers of successive random samples, the mean of the sampling distribution is equal to the population mean (µ).
Step-by-step explanation:
population variance =σ
sample variance=}[/tex]
where n is sample size
so as n increases ,}[/tex] decreases, so sample variance decreases