3.4 hours. The efficiency of a worker is the amount of work divided by time needed. The efficiency of Sanjay alone is 500/6, and the efficiency of Felipe alone is 500/8. When they work together, their combined efficiency is 500/6+500/8=3500/24. Therefore, they need 500/(3500/24)=24/7=3.4 hours.
140/100 * 65 = 91 people
Divide 140 by 100 to find 1 percent then multiply by 65 to find 65 percent.
If you have to compare two shapes you basically count the number of shapes there are of each type then you say for example 6:4. If they ask you to give the number of shapes to the number of shapes there are you count all the shapes and then you count the shape they asked you to find and then you will get something like 4:15
Answer:
Constructive Proof
Step-by-step explanation:
Let x be a positive integer
x must be equal to sum of all positive integers exceeding it
i.e.
x = x + (x - 1) + ( x - 2) + ......... + 2 + 1
Equivalently,
x = ∑i (where i = 1 to x)
The property finite sum;
∑i (i = 1 to x) = x(x + 1)/2
So,
x = x(x + 1)/2 ------- Multiply both sides by 2
2 * x = 2 * x(x + 1)/2
2x = x(x + 1)
2x = x² + x ------- subtract 2x from both sides
2x - 2x = x² + x - 2x
0 = x² + x - 2x ----- Rearrange
x² + x - 2x = 0
x² - x = 0 ------ Factorise
x(x - 1) = 0
So,
x = 0 or x - 1 = 0
x = 0 or x = 1 + 0
x = 0 or x = 1
But x ≠ 0
So, x = 1
The statement is only true for x = 1
This makes sense because 1 is the only positive integer not exceeding 1
1 = 1
It is a Constructive Proof
A proof is constructive when we find an element for which the statement is true.
