Question

Is it A) , B) , C), D) , E)

Answer 1

Part A) The statement is True

Part B) The statement is False

Part C) The statement is True

Part D) The statement is True

part E) The statement is False

Explanation:

Part A) we have

`1.66..=1 (6)/(9)`

The statement Is True

Convert the repeating decimal 1.66.. to an equivalent fraction

Let

`x=1.66..\\ 10x=16.66..\\ 10x-x=16.66..-1.66..\\ 9x=15\\ x=15/9`

Convert to mixed number

`15/9=9/9+6/9=1 (6)/(9)`

therefore

`1.66..=1 (6)/(9)`

Part B) we have

`0.6 < 6\%`

The statement is false

Because

`6\%=6/100=0.06`

so

substitute

`0.6 < 0.06` -----> is not true

Part C) we have

`45\% \leq4.5`

The statement is True

Because

`45\%=45/100=0.45`

substitute

`0.45 \leq4.5` ----> is true

Part D) we have

`5^(2) \geq 16`

The statement is True

Because

`5^(2)=25`

substitute

`25 \geq 16` ----> is true

Part E) we have

`9.25 > 9(3)/(4)`

The statement is false

Because

Convert mixed number to an improper fraction

`9(3)/(4)=(9*4+3)/(4)=(39)/(4)`

Convert decimal number to an improper fraction

`9.25=9(1)/(4)=(9*4+1)/(4)=(37)/(4)`

substitute

`(37)/(4) > (39)/(4)` -----> is not true