A family of four is trying to choose health insurance that will cost the least based on their typical care needs from the prior
1 answer:
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Answer with Step-by-step explanation:
1. We are given that an expression
We have to prove that this expression is always is even for every integer.
There are two cases
1.n is odd integer
2.n is even integer
1.n is an odd positive integer
n square is also odd integer and n is odd .The sum of two odd integers is always even.
When is negative odd integer then n square is positive odd integer and n is negative odd integer.We know that difference of two odd integers is always even integer.Therefore, given expression is always even .
2.When n is even positive integer
Then n square is always positive even integer and n is positive integer .The sum of two even integers is always even.Hence, given expression is always even when n is even positive integer.
When n is negative even integer
n square is always positive even integer and n is even negative integer .The difference of two even integers is always even integer.
Hence, the given expression is always even for every integer.
2.By mathematical induction
Suppose n=1 then n= substituting in the given expression
1+1=2 =Even integer
Hence, it is true for n=1
Suppose it is true for n=k
then is even integer
We shall prove that it is true for n=k+1
=
=
=Even +2(k+1)[/tex] because is even
=Sum is even because sum even numbers is also even
Hence, the given expression is always even for every integer n.
Answer:
1. CYNARG
Step-by-step explanation:
This a example of Caesar's Cipher, in which each letter in the original word leads to a ciphered letter according to the following equation:
In which C is the index of the Ciphered letter in the alphabet, P is the index of the original letter and o is the offset.
Finding the offset:
O is coded B
O is the 15th letter in the alphabet, so .
B is the 2nd letter in the alphabet, so
So
PLANET:
P
P is the 16th letter in the alphabet.
So P is coded C.
L
L is the 12th letter in the alphabet:
L is coded Y(25th letter in the alphabet)
A
A is the 1st letter in the alphabet
A is coded N
N
N is the 14th letter in the alphabet
N is coded A
E
E is the 5th letter in the alphabet
E is coded R
So the correct answer is:
1. CYNARG