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I saw this question just a moment ago.

How many times to you need to ask the same question?

If you do not like an answer say so on the original thread and give a reason!

There are 4 that have 1 entry point from the C, and you can't use the middle C, because if you get there, there is nothing to go to: 4(1*1*3) makes 12 (you have to move diagonally away, then vertical, then you are at the middle and can go diagonally or horizontal, making 3 possibilities.)

Starting from the middle outside: 4(2 + 10 = 12) = 48.

Staring from the top and bottom center: 2(2 + 3 + 3 + 2 = 10) = 20.

So there are 48 + 20 = 68 ways.

The roots are

-0.500000000000000 - 1.038260698286168 i

-0.500000000000000 + 1.038260698286168 i

-0.500000000000000 - 0.398736694441202 i

-0.500000000000000 + 0.398736694441202 i

-0.500000000000000 - 0.114121737195075 i

-0.500000000000000 + 0.114121737195075 i

Why would you think that no explanation is needed? 

How many times does the digit 9 appear in the list of all integers from 1 - 500?

9 cannot be in the first postion.

2nd position but not third

5*1*9=45

3rd position but not second

5*9*1=45

2nd and third position

5*1*1=5   2 each so that is 10

45+45+10=100

Subbing the expression  for x  into the radical, we have that

x = √[  x^2 +  √[2020 - x ] ]      square both sides

x^2  = x^2 + √[2020 - x ]

0  =  √[ [2020 - x ]

x = 2020

Thanks CPhill!

We have these integers

4, 8,  9,  12, 16, 18, 20, 24, 25,  27, 28, 32, 36, 40, 44, 45, 48, 49, 50

(19  integers )

Assuming that the  venue can hold  14,000 people  ( not,  12,000 people)

(a)  Let x  be the number of incremental increases

So  the number of tickets sold  = (14000 - 20x)

(b)

We have that

Profit  =  Revenue  -    Cost of staging concert

Revenue   =  Number of people  *  Price 

Let x be the number of   incremental price increases......so....

Revenue  =  (14000 - 20x) ( 100 + x)      simplify

Revenue =  1400000 - 2000x + 14000x - 20x^2  =  -20x^2 + 12000x  + 1400000 

So.....the total profit is given by

Revenue - Expenses...so.....

y = -20x^2 + 12000x + 1400000 - 1000000

y= -20x^2 + 12000x  + 400000

(c)   See the graph, here : https://www.desmos.com/calculator/kqdbrpbuuz

The domain is  [0, ≈ 632 ]   

(d) The range of prices that  will guarantee a profit =

(100 + 0 , ≈ 100 + 632)  =    [100, ≈732 ]    (in dollars)

(e)  Looking at the graph again.......the max occurs at  (300, 2,200,000)

So  the price that will guarantee a max =  (100 + 300)  = $400

And the  number of tickets sold at this price =  14000 - 20(300)  = 8000 tickets

it's 19... but thanks for trying! I appreciate the help

You have: 1, 2, 3, 4, 5, 6, 7 =6 perfect square FACTORS. Their perfect squares are:1, 4, 9, 16, 25, 36, 49.

listforeach(x, a=(-1, 1, 2), listforeach(y, b=(-2, -1, 0, 1, 2), c=x^y

OUTPUT =(1, -1, 1, -1, 1, 1, 1, 1, 1, 1, 0.25, 0.5, 1, 2, 4) = 13  positive values.

But only 5 are DISTINCT =0.25, 0.5, 1, 2, 4

The sum works out to -2.38495 + 8.900753, which corresponds to an angle of theta = 105 degrees.

x^2 -3lxl  + 2   = 0        factor as

( l x l - 2 )  ( l x l  - 1 )   = 0

So either                           or             l x l - 1   = 0

lx l - 2  = 0                                         l x l    = 1

x = 2, -2                                             x = -1, 1         

The possible values of a are -1 and 2.

Use the on-site calculator to get:

Arctan(0.301) = ~ 16.75 degrees.

Looking at cases x = -1, x = 1, and x = 2, there are 9 values of x^y that are positive.

A positive integer has the same remainder of 2019 when divided by 2020 and 2021. What is the remainder when this number is divided by 235?

The number is: 2019

2019 mod 2020 = 2019

2019 mod 2021 = 2019

2019 mod 235   = 139 - The remainder. 

250 - 25 + 1 = 226 integers between 25 and 250.

27, 64, 125, 216 = 4 perfect cubes.

226 - 4 = 222 integers that are NOT perfect cubes.

By DeMoivre's Theorem, the smallest possible value of r is 3^6 = 729.

Hello again! I managed to solve the problem! I first figured out how many ways to line the boys and girls and multiplied them: 5!*4!=2880. 

Then, I found how many ways to line them all up. 9! = 362880. Once I found out how to line them all up, I subtracted that from the result of the boys and girls: 362880 - 2880 = 360000. And 360000's the answer!

Here is a link to a similar problem that should help you solve this: https://web2.0calc.com/questions/in-how-many-ways-can-you-spell-the-word-cool-in-the-grid-below-you-can-start-on-any-letter-then-on-each-step-you-can-step-one-letter-in-an