Determine if numbers are odd or even, find three consecutive ages that sum to 45, and identify prime numbers and their sum.

Let the three consecutive ages be $x$, $x+1$, and $x+2$.
Their sum is 45.

Subtract 3 from both sides:

Divide by 3:

The three consecutive ages are:
First age: $x = 14$
Second age: $x+1 = 14+1 = 15$
Third age: $x+2 = 14+2 = 16$
The ages are 14, 15, and 16.

Based on the student's work, the numbers to consider are 13 and 43.
A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself.

• For 13: The only divisors are 1 and 13. So, 13 is a prime number.
• For 43: The only divisors are 1 and 43. So, 43 is a prime number.

The sum of the prime numbers is:

The sum of the prime numbers is $\boxed{56}$.

Let the shorter sides of the right-angled triangle be $a = 4$ cm and $b = 7$ cm.
Let the hypotenuse be $c$.
Using the Pythagorean theorem, $a^2 + b^2 = c^2$:

To determine if $\sqrt{65}$ is rational or irrational, we check if 65 is a perfect square.
$8^2 = 64$ and $9^2 = 81$. Since 65 is not a perfect square, $\sqrt{65}$ cannot be expressed as a simple fraction of two integers.
Therefore, $\sqrt{65}$ is an irrational number.

The reciprocal of a number $x$ is $\frac{1}{x}$.