5. How many different
codes can a combination
lock have if there are three
numbers on the lock and
each number can be from
0-9?

A three digit combination with a selection of 1 - 9 (Nine numbers) would have 729 combinations,

Correct  Vr = 10³ = 1,000  or  V = 720

Step-by-step explanation:

Given:

Input set of numbers S = {0, 1, 2, 9} ⇒ x = 10

A string that changes n = 3

I guess the numbers can be repeated as 1,1,1 or 2,3,2

then these are variations with repetition and the formula is:

Vr (x  n) = xⁿ

Vr (10  3) = 10³ = 1,000

if the numbers cannot be repeated then these are variations without repeating and the formula is :

V = (x  n) = x (x -1) (x -2) (x - n +1)

(10 - 3 + 1) = 8

V = (10  3) = 10 ·9 · 8 = 720

God is with you!!!

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4

think about the doctor who treated the major and the speaker in the short story "in another country." put yourself in the shoes of the doctor, and based on what you read in the story, write what you think his thoughts about the major and the speaker would be. use the following vocabulary in your response and change the form of these words as needed: detached resign withered