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[3.1  x  10^5] / 40 words per minute =7,750 minutes

1 hour = 60 minutes.

7,750 /60 = 129 1/6 - hours to type 3.1 x 10^5 words.

OR:

40 words per minute x 60 minutes =2,400 words - that he can type in 1 hour

[3.1   x  10^5] / 2,400 words per/h =129 1/6 hours to type 3.1  x  10^5 words.

Great job, Alan!

[512 - 100 +1000 - 50] =1362 dollars

1362  -(4/5 * 1362) =272.40 dollars -what he has now.

in a village the number of houses and the number of flats are in the ratio 7:4 the number of flats and the number of bungalows are in the ratio 8:5 . there are 50 bungalows in the village . how many houses are in the village    

H stands for Houses 

F stands for Flats  

B stands for Bungalows  

F:B is 8:5 

B is 50

F:B is F:50  so   F = 80  

H:F is 7:4  

F is 80

H:F is H:80  so   H = 140  

_.

You need to supply distances between A and B and B and C in km for this to make sense.

You want

(x + c)² = k

Expand the left-hand side

x² + 2cx +  c² = k

Compare each term with

x² + 3x = -3

Clearly we need 2c = 3,  so c = 3/2.  That means we must add c² = 9/4 to each side (so k = -3 + 9/4 = -3/4)

(x + 3/2)² = -3/4

Hi Wolf,

I have not checked your final answer but your logic sounds really good. 

Stop, unwind, the revolution is all around you.

[1107 - 15] / 6 + 1 =183 numbers

What is the maximum value of \(4(x + 7)(2 - x)\), over all real numbers x?

Hello Guest!

\(f(x)=4(x + 7)(2 - x)\\ f(x)=4(2x-x^2+14-7x)\\ f(x)=-4x^2-20x+56\\ \frac{df(x)}{dx}=-8x-20=0\\ x_{min}=-2.5\\\color{blue} f(x)_{max}=81\),

The maximum value of \(4(x + 7)(2 - x)\) is 81.

  !

The interior angles of a quadrilateral form an arithmetic sequence. If the measure of the largest angle is 128 degrees, what is the measure of the second largest angle, in degrees?

52º + 77.333337º + 102.666667º + 128º = 360º

Test theories with smaller numbers

eg  

How many multiples of 6 are between 10 and 50?  I have chosen numbers that are not multiples of 6 (like your question)

My guess is  (50-10)/6 = 6 and a bit.  So I am guessing 6 or  7

12,18, 24, 30, 36,42,48    It is 7 I had to round up.

Another example

How many multiples of 6 are between 10 and 40?  I have chosen numbers that are not multiples of 6 (like your question)

about (40-10)/6 = 5    That is spot on.

Now you tell me what your one will be.

9x+5y then

I think you're right! I misunderstood the question.

I'll give you a plus, and to my self a minus.

(102, 108, 114, 120, 126, 132, 138, 144, 150, 156, 162, 168, 174, 180, 186, 192, 198, 204, 210, 216, 222, 228, 234, 240, 246, 252, 258, 264, 270, 276, 282, 288, 294, 300, 306, 312, 318, 324, 330, 336, 342, 348, 354, 360, 366, 372, 378, 384, 390, 396, 402, 408, 414, 420, 426, 432, 438, 444, 450, 456, 462, 468, 474, 480, 486, 492, 498, 504, 510, 516, 522, 528, 534, 540, 546, 552, 558, 564, 570, 576, 582, 588, 594, 600, 606, 612, 618, 624, 630, 636, 642, 648, 654, 660, 666, 672, 678, 684, 690, 696, 702, 708, 714, 720, 726, 732, 738, 744, 750, 756, 762, 768, 774, 780, 786, 792, 798, 804, 810, 816, 822, 828, 834, 840, 846, 852, 858, 864, 870, 876, 882, 888, 894, 900, 906, 912, 918, 924, 930, 936, 942, 948, 954, 960, 966, 972, 978, 984, 990, 996) Total = 150 such numbers

All of the streets in Tom's city are on a regular rectangular grid and run east-west or north-south. Tom starts at the intersection of Poyntz Avenue and Eleventh I FORGOT THE REST   

I found it on the internet.  It goes like this:  

All of the streets in Tom’s city are on a regular rectangular grid and run east-west or north-south. Tom starts at the intersection of Poyntz Avenue and Eleventh Street and walks 2 blocks east, then 3 blocks north, then 4 blocks east, then 5 blocks north. Tom then returns to his starting location by walking 6 blocks west, then 8 blocks south. What is the area, in square blocks, enclosed by Tom’s path?

F = 2/3 - First term
4/9 =F + 8D
D = - 1 / 36 - Common difference

5th term = 2/3 + (- 1/36 * 4)
               = 5/9

Sorry I meant 9x + 81y mod 19

160 (tan 22 - tan 18)  meters = .......... m

This might help: 

https://web2.0calc.com/questions/help_33617

HI! Wolf here. 

Ok so, I will give you hints and also my solution.

So there are multiply ways that you can do it, most commly the algebraic way. 

However I am not well versed in that method SO I will help u with a way that I learned how to to these questions!

1. Draw two rows with 4 dots in each

2. Every dot on the left is a politician and every dot on the right is a lawyer

3. Now draw a line one person in the lawyer collom to the other 4

4. Because the other people (politician) doesnt shake hands with the others, there is no overlap (I think)

So count those up! But the wording of the question is confusing me a bit. I am gonna assume that both of the handshake rules are in place at the same time. So that the politicians are still only shaking the hands once and that the lawyers also only shake there hand once too. 

This means that, the only thing we have to figure out is the politicians.

The way we do this is by counting how many hands the first person shakes then how man the second one shakes. 

HOWEVER!!! 

Because the first person already shook the second person hand, the second person can NOT shake person 1 agian, making 1 shaking 3 hands!! (also beliving that they dont shake there own hand)

Same with 3, the cant sake 1&2. and 4 cant shake anyone. 

Add the both numbers together and you will get your answer!

I cant figure out a way to hide my answer to here it is please look over the actuall way to solve it...

16+6= 22

I hope this helps!!!

~Wolf

Thanks guest! You were right! Thanks for the help!

For n = 16  and  19,  n^2-35n+306=2 - the smallest prime

Their product =16  x  19 =304

Cal, as a guest, I resemble that remark.  It's not only guests who post only the answer with no explanation. 

_.

There's the same kind of problem at https://web2.0calc.com/questions/algebra_15788