18. Determine the greatest three-digit number in each of the following bases.
a. Base two
b. Base twelve

If you're asking about the largest number that can be written with 3 digits in the given base:

• In base 2, the largest number with 3 digits is

111₂ = 1•2² + 1•2¹ + 1•2⁰ = 7

• In base 12, the largest number with 3 digits is

bbb₁₂ = 11•12² + 11•12¹ + 11•12⁰ = 1727

(in base 12, a₁₂ = 10 and b₁₂ = 11)

option 2 is correct.

step-by-step explanation:

we are given two inequality equation

x+y> 5 and -3x+2y< -2

first we draw the graph of both function using t-table method

equation: x+y> 5

for x=0, y=5

for x=-5, y=0

table:

x   :   0     5

y   :   5     0

test point (0,0) , 0> 5

false

equation: -3x+2y< -2

for x=0, y=-1

for x=2, y=4

table:

x   :   0     2

y   : -1       4

test point (0,0) , 0< -2

true

now we draw the graph. see the attachment for graph.

common region would be solution set.

option 2 is correct.