Answer:
3 2/3 is greater
Step-by-step explanation:
3 2/3 is 3.6666 while √11 is 3.32
Jeff made $210 by selling 30 pumpkins.
Step-by-step explanation:
Given,
Selling price of each Pumpkin = $7
Number of pumpkins sold by Jeff = 30
We will multiply number of pumpkins sold by selling price per pumpkin.
Amount made by Jeff = Price per pumpkin * Number of pumpkins
Amount made by Jeff = 7 * 30 = $210
Therefore;
Jeff made $210 by selling 30 pumpkins.
Keywords: multiplication
Learn more about multiplication at:
#LearnwithBrainly
Answer:
Total area of figure = [3x² + 7x + 6] feet²
Step-by-step explanation:
By dividing both rectangle by vertical line;
Given:
Length of big rectangle = (x + 3) feet
Width of big rectangle = (x + 2) feet
Length of small rectangle = 2x feet
Width of small rectangle = (x + 1) feet
Find:
Total area of figure
Computation:
Area of rectangle = Length x width
Total area of figure = Area of big rectangle + Area of small rectangle
Total area of figure = [(x + 3)(x + 2)] + [(2x)(x + 1)]
Total area of figure = [x²+ 2x + 3x + 6] + [2x² + 2x]
Total area of figure = [3x² + 7x + 6] feet²
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.
