Prove or give a counterexample: Every positive integer can be expressed as the sum of three or fewer perfect squares. (A perfect square is an integer n for which there is an integer k with the property: n

Statement is incorrect

Step-by-step explanation:

Every positive integer cannot be expressed as the sum of three or fewer perfect squares.

Supposing the number 7 only squares less than are 0, 1  and   4

Clearly 7 can not be written using three or fewer of these numbers

It is proved

By taking Cube root of 7

= 1.912931183

Now By taking  

= 2.64575131

So both values 1.912931183 and 2.64575131 are not positive integers.

Hence the statement is incorrect.

b. 1.25 hr

step-by-step explanation:

if you have a constant speed of 60 mph, then you have a ratio between 60 mi. to 1 hr. dividing both sides by 60 we get the ratio

1 mi. to

then mult. both sides by 75 we get the ratio

75 mi. to

simplifying we get

75 mi. to

or 1.25 hr.

the answer is ! ?