Proof by induction
Base case:
n=1: 1*2*3=6 is obviously divisible by six.
Assumption: For every n>1 n(n+1)(n+2) is divisible by 6.
For n+1:
(n+1)(n+2)(n+3)=
(n(n+1)(n+2)+3(n+1)(n+2))
We have assumed that n(n+1)(n+2) is divisble by 6.
We now only need to prove that 3(n+1)(n+2) is divisible by 6.
If 3(n+1)(n+2) is divisible by 6, then (n+1)(n+2) must be divisible by 2.
The "cool" part about this proof.
Since n is a natural number greater than 1 we can say the following:
If n is an odd number, then n+1 is even, then n+1 is divisible by 2 thus (n+1)(n+2) is divisible by 2,so we have proved what we wanted.
If n is an even number" then n+2 is even, then n+1 is divisible by 2 thus (n+1)(n+2) is divisible by 2,so we have proved what we wanted.
Therefore by using the method of mathematical induction we proved that for every natural number n, n(n+1)(n+2) is divisible by 6. QED.
That woul be pie chart graph, as it is suited to describe thevdifferent parts of something. In this context, it refers to the total studentsvatva sport camp, whereas they are taking part in activities.
Answer: 59.91%.
Step-by-step explanation:
- We know that the fraction of the variability in data values accounted by a model is given by
, where r is the coefficient of correlation.
We are given , that the correlation between a car’s engine size and its fuel economy (in mpg) is r = - 0.774.
Then, the fraction of the variability in fuel economy is accounted for by the engine size would be 
[Multiply 100 to convert a decimal into percent]
Hence, the fraction of the variability in fuel economy is accounted for by the engine size is 59.91%.
None of the options are correct.
Answer:
1 plane
Step-by-step explanation:
Let's suppose the number of planes waiting or on the runway " P "
the number of planes taking off per hour '
'
the time for waiting and the runway
so:
P =
x 
= 18 airplanes per hour
we know that 1 min = 60s
36s = 36/60 = 0.6 min
Also, 3 min and 30 s = 3 + 30/60 = 3.5 min
Next to find the time for waiting and the runway
∴
= 0.6 + 3.5 = 4.1 min/60 (converting into hour)
= 0.068 hour
P = 18x0.068 = 1.23
therefore, there is 1 plane either on the runway or waiting to take off
So, there is 1 plane either on the runway or waiting to take off
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The volume V of a cone with radius r is one-third the area of the base B times the height h.
so,
The answer is 57.3248408