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\(1+\frac{1}{5^2}+\frac{1}{5^4}+ \mbox{ } ... \mbox{ } = \displaystyle\sum_{n=1}^{\infty} 5^{-2(-1+n)} = \frac{25}{24}\) .

(10901, 11011, 12221, 13431, 14641, 15851, 17171, 18381, 19591, 20702, 21912, 22022, 23232, 24442, 25652, 26862, 28182, 29392, 30503, 31713, 32923, 33033, 34243, 35453, 36663, 37873, 39193, 40304, 41514, 42724, 43934, 44044, 45254, 46464, 47674, 48884, 50105, 51315, 52525, 53735, 54945, 55055, 56265, 57475, 58685, 59895, 61116, 62326, 63536, 64746, 65956, 66066, 67276, 68486, 69696, 70807, 72127, 73337, 74547, 75757, 76967, 77077, 78287, 79497, 80608, 81818, 83138, 84348, 85558, 86768, 87978, 88088, 89298, 90409, 91619, 92829, 94149, 95359, 96569, 97779, 98989, 99099) >>Total = 82 palindromes that are divisible by 11

(5, 10, 15, 20, 25, 30, 35, 40, 45, 50)==275 - multiples of 5

(2, 4, 6, 8, 10, 12, 14, 16, 18, 20) ==110 - first 10 even numbers.

abs[275  -  110] ==165

When the distance is fixed and the speeds are known, the easiest solution is to take the "harmonic mean" of the 2 speeds:

[2 x 45 x 63] / [45 + 63] ==5,670 / 108 ==52.50 mph -the average speed to arrive on time.

Note: You can do it the long way by using: Average speed==Total distance / total time.

You should, however, get the same result.

four workers must be kept to complete 2/3 remaining job in remaining 24 days

The x-coordinates is 14/5.

There are 180 ways that Andrew and Mary could have chosen their numbers.

The smallest n is 54,832.

The minimum value is -161.

a = -18.

The answer is 8.

The radius of the circle is 16.

do you have some sort of explanation?

There are 56 5-digit palindromes that are divisible by 11.

yep! good job

can you please include an explanation? i am mainly interested in how to solve it.

The side length of the square is $\frac{21 + \sqrt{43}}{2}$, so $b = 43$.

Do you know how many "divisors" does 50! have??!!

It has: 4,464,046,080 divisors!!  It should ,however, have:  2 × 3 × 5 × 7 × 11 × 13 × 17 × 19 × 23 × 29 × 31 × 37 × 41 × 43 × 47 ==15 prime divisors.

HELP PLS... 

THIS IS THE LAST DAY TO DO THIS!!!!

The answer is 24 degrees.

Steve must keep at least 6 workers.

e = 35º

f = 55º

g = 55º 

h = 125º

The sum of 2 opposite angles in a cyclic quadrilateral is 180º.   g + h = 180

∠OVU + ∠h = 180º

f(f(1)) = f(4) = 3.  The only solution is x = 1, so the number of solutions is $\boxed{1}$.

Maybe it consists of the regions where the induced hemispheres overlap?

Solution 1: It's a ratio of 6 to 30 which simplifies to a ratio of 1 to 5, so if we multiply nine from one to get 9 keychains we also have to multiply 9 tot he 5 and get 45 mins to make those keychains.

Solution 2:  It can be solved intuitively by thinking if 6 keychains are finished in 30 mins, the time taken to do 9 is just that time plus half of that time taken so 15 + 30 = 45 mins