Mikela claims that the sum of any two numbers is greater than the larger of the two numbers. jim claims that the sum of any two natural numbers is greater than the larger of the two numbers.

ANSWER:  

The statement of Jim is correct

SOLUTION:  

Given statements are  

Mikela claims that sum of any two numbers is greater than the larger of the two numbers.  

Jim claims that the sum of any two natural numbers is greater than the larger of the two numbers.

Let a,b be the two numbers and a is the greatest of a and b

According to the mikela statement = a + b > a

b > a – a

b > 0

Here, we got an condition that b > 0, but it may not be true always.  

Above condition fails when b is either 0 or negative number.  

Jim - sum of any two natural numbers is greater than the larger of the two numbers.

Let a,b be the two natural numbers. And a is the greatest of a and b

According to the jim statement  =  a + b > a

b > a – a

b > 0

Here, we got an condition that b > 0,

And this statement will always be true because b is an natural number, so it will be greater than 0.

Hence jim’s statement is true.  

b. 6

step-by-step explanation:

we are given the table representing an exponential function.

we can see from the table that, as x is increasing, the value of y is increasing in the power of 6.

i.e. the following relation is obtained,

x = 1, y = 6

x = 2, y = 36 =

x = 3, y = 216 =

x = 4, y = 1296 =

x = 5, y = 7776 =

so, the geometric series obtained is .

thus, the common ratio is given by = = 6.

hence, the common ratio is 6.