Gauss' method for addition relies on the fact that you can 'pair' certain numbers together. Look at the example:
1+2+3+4+5+6+7+8+9+10
We could manually add all these together from left to right but a clever way to think about this is if we add together the ends of the sum (10+1) we get 11. If we then move one in from the ends and add these (2+9) we also get 11. This means that 1+2+...+9+10 is the same as 11+11+...+11+11.
Because each 2 numbers adds to 11 we know the total number of 11's we have to add together is the length of the sum divided by 2. In our case 5 (10 ÷ 2). We need to add 5 lots of 11 to get our answer. This is the same as 11 × 5 which is easily seen to be 55.
(If you add the 10 numbers together on a calculator you'll see 1+2+3+4+5+6+7+8+9+10 = 55) so this method really makes it a lot quicker.
Looking at your sequence, if we pair the ends together we get 401 (400+1) and we multiply this by the length of the sequence divided by 2. In your case, 200 (400 ÷ 2).
So the sum of all the numbers from 1 to 400 must be 401 × 200 = 80,200.
Remember the steps:
1. Pair the ends together and add them
2. Times this number by the length of the sequence halved
Hope this helps.
Answer:
The frequency of oranges is the classroom is 47.37%.
Step-by-step explanation:
The relative frequency of oranges is the number of oranges divided by the total number of fruits.
We have that:
8 students brought 2 apples each. So there are 8*2 = 16 apples
4 students brought an apple and an orange each. So there are 16 + 4*1 = 20 apples and 4*1 = 4 oranges.
7 students brough 2 oranges each. So there are 4 + 2*7 = 18 oranges.
There are 18 oranges, and 20+18 = 38 fruits in total.
So the frequency of oranges in the classrom is
Maybe let's just do the prime factorization.
40=2x2x2x5
answer:2^3x5
Answer:
735 mm³
Step-by-step explanation:
49 x 15 = 735
