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Only one way to have to take 3 times to select a red ball. You  have to  select the two blue balls on the  first two draws;

Number of  all  possible arrangements of  draws =  5! / [2! * 3!] = 10

Probability = 1 / 10

The six faces of a three-inch wooden cube are each painted red. The cube is then cut into one-inch cubes along the lines shown in the diagram. How many of the one-inch cubes have red paint on at least one face?     

I count 26 of them.  The cube has been cut into 27 small cubes.     

Only the one-inch cube in the very center will have no paint on it.     

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On what data is the parallelogram ABCD based?

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A toilet paper company sells rolls of toilet paper where the cardboard portion in the middle has a diameter of 1.8 inches and a height of 3.75 inches. How many square inches of cardboard would there be in a package of 24 rolls of toilet paper? Round your answer to the nearest roll.     

Area of one tube  =  circumference times length  =  1.8 • π • 3.75     

                                                                              =  1.8 • 3.1416 • 3.75     

                                                                              =  21.2058     

Area of 24 tubes  =  24 times Area of one tube    =  24 • 21.2058     

                                                                              =  508.9392  —>  rounds to 509     

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Tony invests $3,000 dollars in an account earning 12% interest per year.     

How long will it take him to make $3,960 dollars in simple interest?     

3000 • 1.12ⁿ  =  3960     

3000 • 1.12^2.45  =  3960.09     

so it will take 2.45 years, aka 2 years, 5 months, & 12 days     

_.     

Find the measures of the exterior angles on following polygons.     

The sum of the exterior angles of any polygon is 360^o     

so, since the number of angles will be the same as the     

number of sides, then all you have to do is divide 360     

by the number of sides.     

• triangle                360 / 3    120     

• quadrilateral        360 / 4      90     

• pentagon             360 / 5      72     

• octagon               360 / 8      45     

• decagon              360 / 10    36     

• triacontagon        360 / 30    12     

• pentacontagon    360 / 50      7.2     

• hectogon             360 / 100    3.6     

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Let X stand for the number of $2 books     

Let Z stand for the number of $3 books     

    X + Z  =  65      multiply both sides by 3  —>     3X + 3Z  =  195     

2X + 3Z  =  155                                           —>     2X + 3Z  =  155     

                                subtract                                    X          =    40     books @ $2     

    X + Z  =  65                                             —>        40 + Z  =  65     

                                                                                          Z  =  65 – 40     

                                                                                          Z  =  25     books @ $3     

check answer     

does   2•40 + 3•25  =  155  ?     

                  80 + 75  =  155  ?     

                        155  =  155  true     

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Find all integers n such that when the clock strikes n o'clock, the acute angle between the hour and minute hands is 90 degrees.     

On a 12-hour clockface, at the top of the hour, the angle is 90^o at 3:00 and 9:00.  BTW, 90^o is not an acute angle.     

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Write the phrase as an expression:     

The quotient of a number x and the sum of 3 and 7.     

I don't know if the phraseology implies a particular construction.     

If not, then there are two of them, namely:     

             x                             x     

         ––––––    which is    –––      is one of them.     

          3 + 7                         10     

          3 + 7                        10     

         ––––––    which is    –––      is the other one.     

             x                             x     

_.     

 Is it possible that two people in different tax brackets will have the same effective tax rate? Why or why not?     

Yes.  One could have more deductions, such as for dependenys, or business expenses, or medical expenses.     

_.     

what are two alternatives expressions of (7 x)+(n-1)     

                                     7x + n – 1  and  7x – (1 – n)     

_.     

Find the coefficient of z in the product  (-3z^2 - 7z + 4)(6z^2 + 6z - 1).      

                                                              (–-3z² – 7z + 4)(6z² + 6z – 1)   —>   +  7z     

                                                              (–-3z² – 7z + 4)(6z² + 6z – 1)   —>   +24z     

                                                                                                               total   +31z     

_.     

show your work and no image

Q: 

let w = e^(4i*pi/7). Evaluate (2+w)(2+w^2)(2+w^3)(2+w^4)(2+w^5)(2+w^6)

Feel free to type your answer in the comments box. Does this look familliar to you?

A: We encounter the product of binomials in the seventh roots of unity. 

\(z^7-1 = (z-1)(z-r_1)(z-r_2)(z-r_3)(z-r_4)(z-r_5)(z-r_6), \) where all of the \(r_i\) are the 7th roots of unity besides 1. We recognize that \(w\) is a 7th root of unity because w^7 = 1. 

so  \(z^7-1 = (z-1)(z-w)(z-w^2)(z-w^3)(z-w^4)(z-w^5)(z-w^6).\) We can let z = 2 into the equation and get

-129 =  -3 (-1)^6 (2+w)(2+w^2)(2+w^3)(2+w^4)(2+w^5)(2+w^6) the answer is 43

w = e^(4i*pi/7)

(2+w)(2+w^2)(2+w^3)(2+w^4)(2+w^5)(2+w^6)

=(2+(e^(4i*pi/7)))(2+(e^(4i*pi/7))^2)(2+(e^(4i*pi/7))^3)(2+(e^(4i*pi/7))^4)(2+(e^(4i*pi/7))^5)(2+(e^(4i*pi/7))^6)

= 43     WolframAlpha

  !

The answer is 20/7.