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Sheesh, why am I so clumsy?  The first term is 7 of course.  

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The 67th term should be: C, E, A, B, D

Find the 8th term of the geometric sequence 7, -21, 63,    

The factor seems to be –3 so your sequence would be 

Term Number           Term Value  

       1                                   3  

       2                               –21  

       3                                 63  

       4                             –189  

       5                               567  

       6                          –1,701  

       7                            5.103  

       8                        –15,309  

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Oh, sorry, five feet.

What is the width of the cut of Kirk's mower?

The probability is 13/52*4/52 = 1/52.

listfor(n,1, 25, (1 /(5*n - 2)))==(1 / 3, 1 / 8, 1 / 13, 1 / 18, 1 / 23, 1 / 28, 1 / 33, 1 / 38, 1 / 43, 1 / 48, 1 / 53, 1 / 58, 1 / 63, 1 / 68, 1 / 73, 1 / 78, 1 / 83, 1 / 88, 1 / 93, 1 / 98, 1 / 103, 1 / 108, 1 / 113, 1 / 118, 1 / 123).              1/123 would be the 25th term.

Good job, Phill!!!

1 - The expected number of times that number 1 will come up should be: 30 * (1/6) = 5 times.

2 - The probability that number 1 will come its expected number of times should be: (30 C 5) * (1/6)^5 * (5/6)^25 ==19.21%

Forget the above !!!! I didn't read "How many possible Aopslandian license plates are there which contain at least four 's?"

This may help you to solve those problems: 

https://www.mathplanet.com/education/geometry/circles/advanced-information-about-circles

You want miles/hour    (miles per hour)  

    just put the numbers you have in that order  5/8 mile / 1/4 hr =  5/8*4/1 m/hr = 20/8 m/hr     simplify if needed ......

5/        6² = 4 (4 + x)                     6/      12² = 8 ( 8 + x)

          36 = 16 + 4x                                144 = 64 + 8x

           x = 5                                            x = 10

For how long did he invest his money? I will assume 1 year.

Let the amount he invested @ 10% =T

Then, the amount he invested @ 6% =2T

0.10T + 0.06*2T ==286

0.22T == 286

T =286 / 0.22

T==1,300 dollars @ 10%

1,300 x 2 =2,600 dollars @ 6%

A triangle has vertices at A(6,8), B(0,0), and C(16,0).  A square is inscribed in triangle ABC so that one side of the square aligns with side AB.  Find the side length of the square.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

BC = 16

AB = sqrt(8² + 6²) = 10

AC = sqrt(8² + 10²) = √164

Use the law of cosine to calculate  ∠ABC and ∠BAC

Use this formula to find "a"               (a / tan∠BAC) + a + (a / tan∠ABC) = AB

For cylinder, V = pi*r^2*h

A = 2*pi*r*h + 2*pi*r^2

dV/dt = pi*r*dr/dt*h + pi*r^2*dh/dt

dA/dt = 2*pi*dr/dt*h + 2*pi*dr/dt*2

Plug in V = 500 and A = 100 to get r = 5 and h = 10, so A = 150*pi  ==> 5 gallons of paint

  a       b

180     1
90     2
60     3
45     4
36     5
30     6
20     9
18     10
15     12
12     15
10     18
9     20
6     30
5     36
4     45
3     60
2     90
1     180

Just count them and sum them up, if that is what they want!

The 4 positive integers are:

[1  x  3  x  5  x  7] mod 8 == 1

 ○ ○  = 5△ + 6