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!!!

the expected value of the random variable : 0, 1 and 2

step-by-step explanation:

the smallest possible measurement of the width is 14 feet

step-by-step explanation:

let's assume length of parallelogram is 'l'

width of parallelogram is 'w'

the perimeter of a parallelogram must be no less than 40 feet

so, we get

we are given

length of parallelogram is 6 feet

so,

l=6

we can plug it

now, we can solve for w

subtract both sides by 12

divide both sides by 2

and we get

so,

the smallest possible measurement of the width is 14 feet