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CONTINUED  HERE

The sum of the first "N" positive odd  integers = N^2

There are 13 odd imtegers between 1 and 26, inclusive.....and there are 4 odd integers between 1 and 8, inclusive

So....the sum of the odd integers between  8 and 26  equals the difference in the above, and we have....

13^2  - 4^2  =   169  - 16  =  153

From 9 to 25 : sum of odd Integers us 53

N.T

Thiere is a mistake in this one so you had best ignore it ://

$$\\y=18.5+6sin((9(\pi/12)) - (10(\pi/12)))\\\\
y=18.5+6sin(3\pi/4) - (5\pi/6)\\\\
y=18.5+6sin(3\pi/4) - (5\pi/6)\\\\
$second quad so the sine is positive$\\\\
y=18.5+6sin(\pi-\3pi/4) - (5\pi/6)\\\\
y=18.5+6sin(\pi/4) - (5\pi/6)\\\\
y=18.5+6*\frac{1}{\sqrt2} - (5\pi/6)\\\\
y=18.5+6*\frac{1*\sqrt2}{\sqrt2*\sqrt2} - (5\pi/6)\\\\
y=18.5+6*\frac{\sqrt2}{2} - (5\pi/6)\\\\
y=18.5+3\sqrt2 - \frac{5\pi}{6}\\\\$$

Sorry i was wrong in the previous abswer as 76 is not prime. Melody you are genious... In all cases they cannot be three numbers because the sum of units must end up with entire tens (220) and the prime numbers end with 3, 7, 9 and 1... The numbers 3+7 =10 and 9+1=10 .. they can never be three numbers. 

N.T

Let's divide 220 by 3 we will get 73.3333

So one of the prime no's is 73 and it should be the middle one

previous one is 71

Next one is 76

Check: 71+73+76 = 220

N.T

2nd.    asin  angle

Or

asIn(angle)

asin stands for arc sine which is the same as inverse sine :)

Diagonal^2 = 5^2 + 12^2

=25+144

=169

Cable length = 169 ^ (1/2)=13

Sum = 13*3= 39 feet

N.T

To get the answer of 5, change the first '5' into a '2':

2^{x + 1} + 5·2^{x - 2} = 104   

If you graph the function  y  =  2^{x + 1} + 5·2^{x - 2} - 104, you will get the solution  x = 5. 

Exponential Equations, I only know that result is x=5

This would be everything below 1.282 standard deviations below the mean.

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Just enter tan(20) in the calculator on the Home page.

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Each cable is 13 ft (because √(5^2 + 12^2) = 13) so total length = 3*13 ft = 39 ft

.

Here's a numerical approach:

x ≈ 1.858042273

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This would be a difficult one to solve, algebraically.....here's a graph of the solution......

Let x be the number of match boxes that Fred started with....then, Joe had 432 - x

And we know that :

x  - (2/5)x + (1/4)[(432 -x) +(2/5)x] = [ (432 -x) + (2/5)x - (1/4)[(432 - x) +(2/5)x]   simplify

x - (2/5)x + 108 - (1/4)x + (1/10)x = 432 -x + (2/5)x - 108 +(1/4) x - (1/10)x

108 + (9/20)x = 324 - (9/20)x

(18/20)x = 216

(9/10)x = 216       multiply both sides by (10/9)

x = 240    →     this is what Fred started with

@@ End of Day Wrap    Sat 15/8/15     Sydney, Australia Time   1:30am      ♪ ♫   

 Yes it is Sunday     

Hello everyone 

Our diligent answerers have been Alan, Geno3141, CPhill, jdh3010, Heureka, Knk98, Rubenhh and Dragonlance.  Thank you for all your great answers  

Q: Is it to be or not to be Melody?-Shakespeare

A: It is not to be Melody.

You see here, I am not Melody, but one of the many family birds from Melody's family parrot nest.  And that's how I am like Melody (except for the fact that she does everything perfectly). 

I'm sure Melody is pleased to see her sister-in-law for the 1st time since she flew out of her nest, and went searching for her own. :)

Happy " I"  Day, rosala.......are there going to be a lot of festivals???

cassie purchases 3000 shares at $6.75 each and sold them for $8.98 each 9 months later. Brokerage is 2%, GST (10%) applies and the investor's marginal tax rate is 40%. what is the capital gain?

This is what I think

Total cost = $${\mathtt{3\,000}}{\mathtt{\,\times\,}}{\mathtt{6.75}} = {\mathtt{20\,250}}$$

brokerage on this is  $${\mathtt{0.02}}{\mathtt{\,\times\,}}{\mathtt{20\,250}} = {\mathtt{405}}$$       (My goodness that is expensive)

Total revenue = $${\mathtt{3\,000}}{\mathtt{\,\times\,}}{\mathtt{8.98}} = {\mathtt{26\,940}}$$

brockerage on this is  $${\mathtt{0.02}}{\mathtt{\,\times\,}}{\mathtt{26\,940}} = {\frac{{\mathtt{2\,694}}}{{\mathtt{5}}}} = {\mathtt{538.8}}$$

Total brockerage = $${\mathtt{405}}{\mathtt{\,\small\textbf+\,}}{\mathtt{538.8}} = {\frac{{\mathtt{4\,719}}}{{\mathtt{5}}}} = {\mathtt{943.8}}$$

Capital Gain = $${\mathtt{26\,940}}{\mathtt{\,-\,}}{\mathtt{20\,250}}{\mathtt{\,-\,}}{\mathtt{943.8}} = {\mathtt{5\,746.2}}$$

In Australia the Goods and Services tax is already included in the quoted brockerage cost and I don't think there is any GST on anythihng else but I could be wrong :/  [plus of course I do not know what country you are in]

The investor's marginal tax rate is irrelevant.

These graphs are always a nice addition to the answers.........thanks, Melody

Let a, b, c, d and e be the digits in that order...so,we have the following system:  

c + e = 14  

d - b  = 1

2b - a = 1 

b + c = 10

a + b + c + d + e  = 30    (5)

Notice that 

c + e = 14

c + b = 10      subtracting the second equation from the first, we have

e - b = 4    → e = b + 4

And c = 10 - b

And d = 1 + b

And a = 2b - 1

And substituting all these into equation (5), we have

(2b - 1) + b + (10 - b) + (1 + b) + (b + 4) = 30    simplify

4b + 14 = 30     subtract 14 from each side

4b = 16  → b = 4

Then

c = 10 - 4 = 6

d = 1 + 4 = 5

e = 4 + 4  = 8

a = 2(4) - 1 = 7

And the code is:

abcde = 74658

Just as Anonymous found!!!!!

$$\\\left(\frac{-125}{27}\right)^{-1/3}\\\\
=\left(\frac{27}{-125}\right)^{+1/3}\\\\
=\frac{27}{-5}\\\\
=-5\frac{2}{5}\\\\$$