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367^367^367 mod 11==9 - the remainder.

4553.00==4179 x [1 +  0.0486/4]^N, solve for N

4553.00/4179.00 ==1.01215^N

1.0894950945 ==1.01215^N

Take the log of both sides

N==log(1.0894950945) / log(1.01215)

N ==7.09745 - Number of quarters on deposit

N ==7.09745 /4 ==1.7744 years - or about 1 year and 9+ months. 

        F    +        C = 280 ------ (1)

\(1 {3 \over 20}\) F    +    \(1 {1 \over 5}\) C = 328 ------ (2)

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 \( {3 \over 20}\)F + \( {1\over 5}\)C = 48

3F + 4C = 960

4F + 4C = 1120

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

  F = 160
  C = 280 - 160 = 120

sum_(k=1)^n k (k + 1) (k + 2) = 1/4 n (n + 1) (n + 2) (n + 3) - this is the closed form.

1 - There are NO perfect cube divisors except 1 itself.

2 - 12! + 231 == 3 * 7 * 11 * 2073601 ==479,001,831

3 - There are NO perfect square divisors except 1 itself.

N mod 10 ==5

N mod 13 ==6

LCM(10,13) ==130

N==130m + 45, where m=0, 1, 2, 3.......etc.

When m=1, N ==130 + 45 ==175

175 mod 130 ==45

There are 266,666 numbers that are relatively prime to 1,200,000 between 1 and 1,000,000.

20 C 3 ==1,140 combinations

My computer says there are 1,020 combinations whose products are EVEN.

Then, the probability is ==1,020 / 1,140 == 17 / 19

The other factor is \(x^4 + x^3 y + x^2 y^2 + x y^3 + y^4\)

The value of the product abc is 12.

The area of the region is 55/6.

You should have:

4 choices for the first digit x 10 choices for the 2nd x 10 choices for the 3rd x 10 choices for the 4th x 5 choices for the last digit ==20,000 such numbers.

n/2 will be ODD for the following values of n:

1 = 2
2 = 6
3 = 10
4 = 14
5 = 18
6 = 22
7 = 26
8 = 30
9 = 34
10 = 38
11 = 42
12 = 46
13 = 50
14 = 54
15 = 58
16 = 62
17 = 66
18 = 70
19 = 74
20 = 78
21 = 82
22 = 86
23 = 90
24 = 94
25 = 98
 

1 - gcd((98!+99!), 6^50)==9978781 2032686921 0670542716 6130077696

2 - 98! + 99! ==942689 0448883247 7456261857 4305724247 3809693764 0789516634 9423877729 4707070023 2237988829 7615920772 9119823605 8505886084 6042941264 7567360000 0000000000 0000000000 [24 trailing zeros]

When the distance covered going back and forth is the same, then the:

Average speed ==Harmonic mean

[2 * 40 * 60] / [40 + 60] ==4800 / 100 ==48 mph - the average speed.

How do I create a Thread?

The side length of the large square is sqrt(3) + 2.

The solutions are (-42,1), (-2,9), (0,7), and (28,3).

How am i suppose to know where my teacher got this? Do you think i'm some sort of magician?

The sum of all integers x is 15.

ab = 280.

c = -2/7.