I need help plz. Binary math

========================================================

Explanation:

Whenever you have a series of nothing but '1's like this, the base 10 equivalent is always going to be 1 less than a power of 2.

The number will be of the form where n is a nonnegative integer.

If you're familiar with the list of powers of 2, then you'll likely realize that 64 is a power of 2 since . One less than this is

This leads to choice A as the answer.

The other answer choices are not one less than a power of 2, so we can cross those off the list.

------------------------------

Further explanation:

Each slot in the binary number given represents a power of 2. We multiply those '1's by a power of 2 and add them up like so

1*(2^5) + 1*(2^4) + 1*(2^3) + 1*(2^2) + 1*(2^1) + 1*(2^0)

1*32 + 1*16 + 1*8 + 1*4 + 1*2 + 1*1

32 + 16 + 8 + 4 + 2 + 1

63

Summing the first n powers of 2 leads to the result

So, summing the first 6 powers of 2 leads to

so firstly, we need to isolate the y variables to be able to solve these inequalities. firstly, add 0.5x on both sides of the first inequality and subtract 1.5x on both sides of the second inequality:

now since the slope is positive for the first inequality, this means that the line going upwards belongs to the first inequality, and the line going downwards belongs to the second inequality.

next, since y ≥ in the first inequality, this means that the shaded region will be above the first inequality's line, thus shading regions a and b.

next, since y ≤ in the second inequality, this means that the shaded region is going to be below this line, thus shading regions a and c.

since both lines shade region a, this means that region a is the solution.

step-by-step explanation:

mark brainliest!