Catarina

For each number, there are ten choices. For each letter, there are \(26\) choices. 

To get the number of passwords for the old website, multiply the number of choices possible for each character: 

\(10 \cdot 10 \cdot 10 \cdot 26 = 26000\)

To get the number of passwords for the new website, you can do the same with the choices for each character of the new passwords. 

I am not going to give you the answer, because if I did that, you would not learn how to do the problem. You have to figure out how to do the problem from the steps I gave you. 

I hope this is helpful,

Catarina

Since rectangles have right angles, we can use the Pythagorean Theorem here. 

Let's call this rectangle \(CATS\), where \(CA = 40\), \(AT = 48, TS = 40, \)and \(CS = 48\) inches. 

The diagonals are \(CT\) and \(AS\). 

A right triangle is formed by \(CA, CT, \) and \(AT\), with legs of \(48 \) inches and \(40 \) inches. The length of the hypotenuse is what we want to find.

Let's call the length of \(CT\) "\(d\)".

Using the Pythagorean Theorem, \(48^2 + 40^2 = d^2\).

\(48^2 = 2304\)

\(40^2 = 1600\)

\(d^2 = 2304 + 1600\)

\(d^2 = 3904\)

\(d = \) the square root of \(3904\)

\(d\) inches, to the nearest inch, is \(62\) inches. 

ANSWER: \(62\) inches.

I hope this is helpful,

Catarina