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x = -3/4.

z - 26=25 what does the z stand for? 

The z stands for the quantity that makes the equality true. 

In this case z stands for 51, because 51 – 26 = 25  

Voldemort   

I couldn't understand what you were trying to say, until late last night – while I was brushing my teeth, if it matters – and then it dawned on me. 

You were trying to tell me that the 2 to 1 ratio of umbrellas to raincoats has to take into account the umbrellas and raincoats of the students who brought both.  What I did wrong was to dismiss the number of umbrellas and raincoats brought by students who brought both.  A clumsy mistake.  No wonder the darn thing seemed too easy.   

I looked this question up, and I found it answered by CPhill.  I don't know if you recognize that name, but he was a Moderator on this site for like forever.  He hasn't been around for a while.  I hope he's just taking a break, and not gone permanently. 

This is the URL of Chris' answer:  https://web2.0calc.com/questions/on-a-rainy-day-every-kid-at-margo-s-school-brings-a-raincoat  

It's the same problem, except that it has 8% of students bringing both an umbrella and a raincoat, rather than 10%. 

I would have copied Chris' calculations and pasted the entire thing in, except that thread had a dissenting opinion.  That other opinion is worth taking a look at, but I think Chris is correct.  A fellow can go broke in a hurry, betting against CPhill. 

_.

XY = 180/7.

what are the zeros to the quadric equation y=-x^2+6x-5   

Rewriting the equation   

because I almost missed   

the negative sign at x²                     y  =  –x² + 6x – 5   

To find the zeros, then

set y equal to zero                           –x² + 6x – 5  =  0 

I recognize this as a   

factorable quadratic  

Factor out the –1 so  

that it's easier to see                        (–1) * (x² – 6x + 5)  =  0 

You could've just multiplied 

both sides by –1, but you  

need to leave it there to show  

that the parabola opens down.           

Factor the quadratic                      (–1) * (x – 1) * (x – 5)  =  0    

So the zeros are at                          x = 1  and  x = 5    

_.

whats the solution? x^2-55=9  

                                           x² – 55  =  9  

Add 55 to both sides      x² – 55 + 55  =  9 + 55  

                                                   x²  =  64 

Take square root of both sides         x  =  + 8      

That's read as "x equals plus or minus eight"  

_.

Let's test 420 ... 56 * 420 * 360 = 8,467,200   

Now taking the 4^th root of 8,467,200 ...... 

The 4^th root is 53.94298 ... NOT AN INTEGER  

So 420 is wrong    

There are 12*4 = 48 favourable sets of 3 cards

52C3 = 22100 sets of 3 altogether 

So what do you think the answer is?

343 = 7^3, so log₇ 343  =  log₇ 7^3  = 3 log₇ 7 = 3

2. Theorem of rays

\(\overline {PR}:x=\overline {PQ}:(\overline {PQ}-x)\\ 10:x=10:(10-x)\\ 10x=10\cdot (10-x)\\ 10x=100-10x\\20x=100\\ \color{blue}x=5\)

The side length of the square is 5.

  !

Your comment:  "you are stating that 60% of people ONLY brought umbrellas"  

Correcamundo.  I am saying that, because the question asked it.  

Quoting the question:  "What percent of the students bring an umbrella only?"  

emphasis added   

_.

Yes, something doesn't add up because in your argument, you are stating that 60% of people ONLY brought umbrellas and 30% ONLY brought raincoats but the question is saying that the TOTAL number of umbrellas brought(which includes students who brought not ONLY umbrlelas, but also raincoats) is twice the amount of people who brought raincoats.  

Thank you so much for answering!!!! 

ooops, I made a typo  

36 = 2, 2, 2, and 7  should say  56 = 2, 2, 2, and 7  

_.

When it rains, every student in Margo's school brings a raincoat, an umbrella, or both.  And 10% of the students bring both.  The total number of umbrellas brought is equal to twice the number of raincoats.

What percent of the students bring an umbrella only?  Explain your solution in complete sentences. 

So 90% brought only one thing 

Twice as many are umbrellas,

so it looks like 60% brought an umbrella and 30% brought a raincoat.   

Have I done something wrong?  That seemed too easy.  

_.

What is the smallest positive integer n such that the fourth root of 56*n*360 is an integer?  

I don't know if it's the smallest integer, but I can help with an answer.  Here's what I did:  

I broke down 56 and 360 into their smallest factors 

36 = 2, 2, 2, and 7    and    360 = 2, 2, 2, 3, 3, and 5  

Combined those and so    56 * 360 = 2, 2, 2, 7, 2, 2, 2, 3, 3, and 5    

We want a perfect 4^th power, so I added enough of each factor to make 4 of them   

The ones I added are

highlighted in dark blue               2, 2, 2, 2, 7, 7, 7, 7, 2, 2, 2, 2, 3, 3, 3, 3, 5, 5, 5, and 5  

Multiply the added (blue) ones together    2 * 7 * 7 * 7 * 2 * 3 * 3 * 5 * 5 * 5  =  1,543,500  

So 1,543,500 is one integer that will work.  I just don't know if it's the smallest. 

Check answer:   56 * 360 * 1,543,500  =  31,116,960,000   the 4^th root of which is 420  

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uhh its wrong

Not correct :(