Questions and Answers

Your Questions About X100

July 20, 2013

Carol asks…

How do you find the mass percentage of a composition?

can someone explain to me how to find the mass percentage?
the question is:

Calculate the mass percent composition of Nitrogen in each of the following nitrogen compounnds.
a) N2O3
b) NF3

explain the steps to get this i dont really understand.

Administrator answers:

%age of an element in a compound = mass of element / molar mass of compound x 100

so amount of N in grams in N2O3 = 2×14=28
molar mass of N2O3=2×14+3×16=76
%of N=28/76 x 100= 36.84%

% of nitrogen in NF3 = 14/71 x100= 19.718%

Mary asks…

I need to find what percentage is wasted?

I have a square that’s 1x1m in perimeter. Inside i have placed 10 circles with a circumference of 3.79cm . I need to find what percentage of the square is wasted.

Could you also explain how you got the answer and show the working.

Thank you in Advance.

Administrator answers:

Convert the measurements of the perimeter to cm and use that to solve for the area:

1m = 100cm
therefore, 100cm x 100cm = 10,000cm^2

Now for the area of the circles.

Circumference is equal to pi*diameter, so work backwards.

3.79cm = pi*diameter
3.79cm / pi = diameter
1.206cm = diameter

The area of a circle is pi*radius^2.

Radius = diameter / 2
radius = 1.206cm / 2
radius = 0.603 cm

A = pi*0.603^2
A = 1.142 cm^2

If you have 10 circles, then that’s 1.142cm^2 x 10 = 11.42 cm^2

Back to your square’s area of 10,000 cm^2.

10,000 cm^2 – 11.42 cm^2 = 9,988.58 cm^2 is wasted.

For the percentage…

(9988.58 / 10000) x100 = 99.8858% of your square is wasted.

Hope that helps.

Helen asks…

How big should I make my backyard?

I am build a 1,900 square foot house on 5 acres and I want a good sized backyard but don’t have any idea how to conceptualize the size. I want a large yard but manageable. I don’t need to take up the remaining five acres.

Administrator answers:

Depends on your lot configuration and on how you plan on using it now and in the future. Ever going to put in a pool? Have kids that like to play football, soccer, baseball? Need a fenced in area for a pet or pool?

If you have a natural high area on the property, it’s an ideal place to situate the house.

Personally, I’d try to have a large front yard and back yard. Many people put their house very close to the road, leaving them little room to landscape the front of the house. I love the look of a long, winding driveway through a well-landscaped yard.

Segment your property into garden rooms – some with paths and plants, some with hardscapes or structures, some with open green areas for play.

Sounds like you have plenty of room to work with. Draw a plot of your property, then sketch out various configurations to see what you like best.

Typical pools are 16′ x 32′, and any kid would love a 50′x100′ flat play area.

Maria asks…

What is the likeliest 5th divisor of a randomly chosen number with at least 5 divisors?

With the divisors sorted in ascending order, e.g., 1, 2, 3, 4, 6, 12.

And how do you generalize it beyond 2 (obviously 1 is the certain first divisor, 2 is the likeliest second divisor)

Administrator answers:

I agree that it’s 6, but I found the percentage different.
Numbers that are divisible by 6 is definitely divisible by 1,2, and 3. We only need one more factor to make 6 into 5th factor. It’s either 4 or 5. But not both since if it’s divisible by both 6 will be the 6th factor. So, the number that has 1, 2, 3, 4, 6,… Or 1, 2, 3, 5, 6,…. As factors are numbers that are divisible by smallest common multiplication of those numbers. That means, it has to be divisible by 12 or 30 but not 60. The percentage of numbers divisible by 12 but not 60 is 1/12 X 4/5 (as one in every 5 multiplication of 12 is divisible by 60) X 100% = 6.6666%
The percentage of numbers divisible by 30 but not 60 is 1/30 X 1/2 (because every two multiplication of 30 is divisible by 60) X 100% = 1,6666%
As they don’t intersect, we can just sum the percentage. The percentage of numbers with 6 as 5th factor is 8.33%

Finding the formula is hard, though. I think it’s better to try it out with brute force, but it’s troublesome for large numbers.
But first, to find the number with largest percentage as nth factor we need to find the number as small as possible. The reason is because the percentage of random number having m as nth factor is obviously smaller than 1/m X 100%. But it doesn’t mean that the smaller the number the better, as you will see. Having certain number as nth factor may force you to include too many primes as factors and that result in having to multiply them all, resulting in small percentage. Let’s try with the first few n
I think to find the number with largest percentage of random numbers having it as nth factor we can start with the number n itself. We can right away exclude numbers that are much larger than it. But this method is quite impractical

if n=1, it’s obviously 1 (100%)
for n=2, it’s obviously 2 (50%)
for n=3, is it 3? If it’s 3 the numbers we want need to be divisible by 6 as the factors are 1,2,3,… Resulting in percentage 16,66%
if it’s 4 with 1,2,4,… Then it needs to be divisible by 4, but not divisible by 3, resulting in percentage 1/4 X 2/3 X 100% =16.66%
we can already exclude the numbers with prime above 4, because such number will definitely need another prime to make it into 4th place factor in it’s own factor or as the factor before it. Even 5 multiplied with the smallest other prime, that is 2, will result in 10, causing the percentage to be less than 10%.
The remaining number is 9. But that won’t work as the percentage is less than 11,1%

For n=4, if it’s 4, we have 1,2,3,4,… Which means the number should be divisible by 12, and no other requirement, resulting in percentage 8.33%
If it’s 5, it’s either 1,2,3,5,… Or 1,2,4,5,… The number required needs to be divisible by 30, or 20, but not both. So it can’t be the number divisible by 60. The percentage becomes 1/30 X 1/2 X 100% + 1/20X 2/3X100% = 5%
If it’s 6, it can only be 1,2,3,6,… Which means the required number needs to be divisible by 6, but not by 4 or 5. That results in percentage 1/6X1/2X4/5 X100% = 6.666%
that’s all for now

Charles asks…

how can i tell wat my telescope can look for?

I have an ORion XT8 classic and with my eyepiece it should be x100,,,, so how do i measure if i can see something is it with the objects magnitude or light years,,,,for an example the andromeda galaxy is 2.9 million light years away,,,, will the telescope that i have even barely see that thing if it does walk me through how i can tell what i can see with the telecsope i have

Administrator answers:

This is a good scope. Enjoy.

After you have looked at the Moon, which is well-positioned for the next few evenings, get yourself some star charts.

For general observing information (which it sounds like you need), pick up a copy of Nightwatch. Then buy Pocket Sky Atlas for the most user-friendly star charts currently available. Buy and read the current issue of Sky & Telescope. Make contact with local astronomers.

Ruth asks…

I am going away and want to buy a really good digital small camera I have a SLR but looking for a small one to?

but need to take a small one which can give me good shots . Any suggestions ?

Administrator answers:

While Fuji’s DSLR cameras may have sucked, don’t discount them when it comes to cmpact cameras. The FinePix F550EXR is an excellent compact camera for under $300. If you want a top notch smaller camera and budget is not an issue, take a look at the X100.

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