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51-22 = 29.

n = 29.

The probability is 2/11.

The length of the path is 6 - pi.

WJ/WK = 35.

Let the cost of 1 box of truffles == T

Let the cost of 1 box of peanut brittles == P

77T  +  82P ==641.......................(1)

77T  +  54P ==501.......................(2), solve for T, P

Use substitution to get:

T ==$3 - cost of 1 box of truffles, which is what the Band earns.

P ==$5 - cost of 1 box of peanut brittle, which is what the Band earns

\(z^{2}+z= w,\\ |z^{2}+z|=|w| =1.\)

z is to be purely imaginary, so let z = iy, where y is a real number.

Then,

\(|-y^{2}+iy|=1,\\ \sqrt{y^{4}+y^{2}}=1,\\ y^{4}+y^{2}-1=0,\\ \displaystyle y^{2}=\frac{-1 \pm\sqrt{5}}{2}\)

y is to be a real number, so the negative sign is rejected, and then 

\(\displaystyle y = \pm\sqrt{\frac{\sqrt{5}-1}{2}}\)

so,

\(\displaystyle |z|=\sqrt{\frac{\sqrt{5}-1}{2}}.\)

I get the following:

How about 1800 ?

For 1. see https://web2.0calc.com/questions/help-is-needed_7#r5

First consider the red dashed line.  The y-intercept is -1.  The slope is 2/1 = 2.

Therefore the equation of the line can be written as y = 2x - 1

The yellow region is below y, so the yellow region ca be expressed as  y < 2x - 1  

However, you are asked to exress it in the form ax + by + c >0, so subtract y from both sides of the previous equation to get 0 < 2x - y - 1

This is the same as  2x - y - 1 > 0

I've used > rather than >=, but if the yellow region is meant to include the red line then replace > by >=.

Answered here: https://web2.0calc.com/questions/expected-value_28#r1

The band earns 17 dollars from each box of truffes and 8 dollars from each box of peanut brittle.