Random Puzzles 

Workings

Hint
You don't need to use a calculator.

Answer
Cube root of 2.

Reasoning
We could use a calculator to see that the tenth root of 10 = 1.2589 and the cube root of 2 = 1.2599.

But, if you've not got your calculator handy...

We have:

   10^1/10 vs 2^1/3

Raise each to the power of 30 (since 10 x 3 = 30) to give:

   (10^1/10)³⁰ vs (2^1/3)³⁰

   10^{1/10 x 30} vs 2^{1/3 x 30}

   10³ vs 2¹⁰

   1000 vs 1024

Therefore, the cube root of 2 is larger.

Workings

Hint
One of the words is Warm.

Answer
Insufficiently heated = cold
Insulated electrical wire = cord
The middle of an apple = core
Additional items = more
A female equine = mare
Pottery = ware
A bump on a toad? = wart
Insufficiently cooled = warm

Workings

Hint
The word MAY appears 39 times.

Answer
The word MAY appears 39 times.

Workings

Hint
Something's wrong with the letter O.

Answer
15.

Reasoning
The sentences should read:

As you can see, my printer replaces every third letter with the letter 'o'.

How many different letters have been replaced?