Answer:
The proof assumes that n=m=2k, which is false in general.
Step-by-step explanation:
If n is an even number, then n=2k for some integer k. In the same way, if m is an even number, then m=2j for some integer j. It is important to write two different letters, k and j, because these integers are not necessarily equal.
For example, take n=10 and m=30. Then k=5 and j=15, so they are different. The fallacy of this proof is that it assumes k=j.
A correct proof would continue like this: by the usual laws of algebra we have that n+m=2k+2j=2(k+j). Since k+j is an integer, n+m=2p for some integer p=k+j, hence n+m is even.
Answer:
1, 7
Step-by-step explanation:
Because the product is 0, either (x-1) or (x-7) is equal to 0. That means that x = 1, or 7
Answer:
The Probability of strictly increasing or decreasing order is 20/216
Step-by-step explanation:
First Die 1 2 3 4 5 6
Second Die 1 2 3 4 5 6
Third Die 1 2 3 4 5 6
Total number of outcomes= 6*6*6= 216
Possible outcomes of increasing order
1,2,3-----1,2,6 (4)
1,3,4------1,3,6 (3)
1,4,5------1,4,6 (2)
1,5,6 (1)
2,3,4—-2,4,6 (3)
2,4,5—-2,4,6 (2)
2,5,6 (1)
3,4,5—-3,4,6 (2)
3,5,6 (1)
4,5,6 (1)
Total number of possible moves of increasing order= 4+3+2+1+3+2+1+2+1+1= 20
Probability of strictly increasing order is 20/216
Similarly Probability of strictly decreasing order is calculated which is also equal to 20/216
Answer: 
Step-by-step explanation:
The exponential function h, represented in the table, can be written as 
From table, at x=0, h(x) =10
Put theses values in equation,, we get
Also, for x= 1 , h(x) = 4, so put these values and a=10 in the equation , we get
Put value of a and b in the equation ,
→ Required equation.
