Acomputer system uses passwords that contain exactly 7 characters, and each character is 1 of the 26 lowercase letters (a–z) or 26 uppercase letters (a–z) or 10 integers (0–9). let ω denote the set of all possible passwords, and let a and b denote the events that consist of passwords with only letters or only integers, respectively. determine the probability that a password contains all lowercase letters given that it contains only letters. report the answer to 3 decimal places.

0,008 or 0,8%

Step-by-step explanation:

To calculate the probability the selected password is made out only of lower-case letters, if it's only letters, we have first to find out how many passwords could be formed with only letters and with only lower-case letters.

For lowercase letters, we can make this many passwords, since for each of the 7  characters, we can pick among 26 lowercase letters:

NLL = 26 * 26 * 26 * 26 * 26 * 26 * 26

In the same fashion, for the number of passwords consisting only of letters, we can pick among 52 letters for each each character (26 lower-case, 26 upper-case):

NOL = 52 * 52 * 52 * 52 * 52 * 52 * 52

We can rewrite NOL differently to ease our calculations:

NOL = (2 * 26) * (2 * 26) * (2 * 26) * (2 * 26) * (2 * 26) * (2 * 26) * (2 * 26)

or

NOL = 26 * 26 * 26 * 26 * 26 * 26 * 26 * 2 * 2 * 2 * 2 * 2 * 2 * 2

Now we have to find out the probability a password containing only letters (NOL) is a password containing only lowercase letters (NLL).  So, we divide NLL by NOL:

The probability is thus 1/2^7 or 1/128 or 0,0078125

Which we are asked to round to 3 decimals... so 0,008 or 0,8%

step-by-step explanation:

when the line is solid:

when the line is dashed:

this > inequality sign means:

this < inequality sign means:

this > inequality sign means:

this < inequality sign means:

about the problem:

srry i'm not done ! i'll

a.   we have two

lines:   y = 4-x   and  

y = 8-x^-1

given two simultaneous equations that are both to be

true, then the solution is the points where the lines cross. the intersection is

where the two equations are equal. therefore the solution that works for both

equations is when

4-x = 8-x^-1

this is where the two lines will cross and that is the

common point that satisfies both equations.

b.   4-x = 8-x^-1

  x           4-x       8-x^-1

-3           7        

8.33

-2           6         8.5

-1           5         9

  0           4        

-

  1           3        

7

  2           2        

7.5

  3           1         7.67

the table shows that none of the x values from -3 to 3 is

the solution because in no case does

4-x = 8-x^-1

to find the solution we need to rearrange the equation to

find for x:

4-x = 8-x^-1

multiply both sides with x:

4x-x^2 = 8x-1

x^2+4x-1=0

x= -4.236, 0.236

therefore there are two points that satisfies the

equation.

find y:  

x=-4.236

y = 4-x   = 4 – (-4.236)

= 8.236

y = 8-x^-1 =   .236)^-1

= 8.236

x=0.236

  y = 4-x   = 4 – (0.236) = 3.764

y = 8-x^-1 =   8-(0.236)^-1

= 3.764

thus the two lines cross at 2 points:

(-4.236, 8.236) & (0.236, 3.764)

c.   to solve

graphically the equation 4-x = 8-x^-1

we would graph both lines: y = 4-x   and   y

= 8-x^-1

the point on the graph where the lines cross is the

solution to the system of equations.

just graph the points on part b on a cartesian coordinate

system and extend the two lines.   the

solution is, as stated, the point where the two lines cross on the graph.

step-by-step explanation:

mark brainliest!