A common computer programming rule is that names of variables must be between one and eight characters long. The first character can be any of the 26 letters, while successive characters can be any of the 26 letters or any of the 10 digits. For example, allowable variable names include A, BB, and M3477K. How many different variable names are possible? (Ignore the difference between uppercase and lowercase letters.)

Total number of possibilities 2,095,681,645,538.

Step-by-step explanation:

The variables can be 1 to 8 characters long.

The first space can be filled by any of the 26 letters.

The remaining n places can be filled by any of the 26 letters or any of the 10 digits.

For a single character variable the number of ways to select a variable name is,

n (1 character) = 26

For two character variable the number of ways to select a variable name is,

n (2 character) = 26 × 36 = 936

For three character variable the number of ways to select a variable name is,

n (3 character) = 26 × 36 × 36 = 26 × 36² = 33,696

For four character variable the number of ways to select a variable name is,

n (4 character) = 26 × 36 × 36 × 36 = 26 × 36³ = 1,213,056

And so on.

Similarly for the eight character variable the number of ways to select a variable name is,

n (8 character) = 26 × 36 × 36... × 36 = 26 × 36⁷ = 2,037,468,266,496

Total number of possibilities 2,095,681,645,538.

the system of inequity is

step-by-step explanation:

from the given graph it is noticed that we have two related lines. one is solid and another is dashed.

if a line passing through two points, then the equation of line is

the solid line passing through the points (0,4) and (4,0).

the related equation of solid line is .

similarly, find the related equation of dashed line. the dashed liune passing through the points (0,0) and (3,1).

the related equation of dashed line is

from the given graph it is noticed that the point (0,1) lies on the shaded region, therefore the point (0,1) must be satisfied by the related equations.

check the related equations by the point (0,1).

this statement is true if the sign of inequality is < instead of equality. since it is an solid line therefore the sign of inequality will be . the required inequality is

similarly, check the second related equation.

it is a dashed line, so this statement is true if the sign of inequality is > . the required inequality is