Natalie and John are both saving coins in jars for a rainy day. Natalie currently has 1 1/8 jars of coins, and John has 9/14 of
1 answer:
Answer:
Natalie will have jars of coins all together after receiving John's coins.
Step-by-step explanation:
Given that:
Coins Natalie have = jars of coins
Coins John have = jars of coins
When John will give all his coins to Natalie.
Total coins Natalie have = Her coins + John's coins
Total coins Natalie have =
Total coins =
Total coins =
Total coins =
Hence,
Natalie will have jars of coins all together after receiving John's coins.
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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.