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 A little more than what I thought they might be looking for (obviously).....and outside my realm !    Hopefully that is what they needed...

Thanx  Chris....

~jc

I double checked the work of Guest #1 and I concur 100% .      

~jc  (but I could be wrong...ha)

I think we need a logisitc growth model here......this is given by:

P = [ P₀K ] /  [ P₀ + (K  - P₀)e^(-rm) ]    

Where  P₀   = 29  = the initial no. of people       K  = 87  = the max no. of people     r = 10%  = .1     and m is the number of months   .....so we have

P  = [29 * 87] / [ 29 + ( 87  - 29)e^(-.1m) ]   = [2523] / [58e^(-.1m) + 29 ]

Here's the graph......notice that 87 is the "carrying capacity"   ........https://www.desmos.com/calculator/bs1mlbrbrc

[ Also....the graph is only valid for m >= 0 ]

Did you know that flies do a backfip to land on ceilings!

Well the MODEL would be

Pf = P (1.10)^m        Where P is the number of peole who attend NOW (29)    Pf = the number of people you would like to see attend (the problem stated 87)

When you plug in those numbers and solve for 'm' , you will find out how many months it will take if you anticipate 10% growth per month (which is what the problem stated)

Say if you want to see 130 people attending that would be Pf     130 = 29(1.1)^m    solving for 'm' shows it will take 15.7 months        See?

~jc

That would be like the third example I gave you....

13 is what percent of 73?      13/73 x 100 = 17.8%

   After a while it will make sense and seem obvious to you, but for now you just have to MEMORIZE (learn) how to do it this way !  Keep at it!!   G'Luck

how is that the model?? Ik im supposed 2 plug it into the calc...BUT idk what to plug in...

There isn't any arrow

As you know, water changes to ice at a constant temperature....that is, you must remove 'heat' from the water to make if form ice, but the temperature will not change.

At STP (Standard Temperature and Pressure) this occurs at 0 degrees C (or 32 Degrees F)......the amount of heat to be removed for this to happen is the 'Latent heat' of the substance....each substance has its own latent heat value  ......   molten lead will form a solid at a significantly higher temperature and with a different latent heat value.

For WATER the latent heat of FUSION (going from a solid crystal to liquid or vica versa) is 334 kj/kg  (I had to look that one up...it has been many years since I learned that)

so for .45kg of water to FREEZE      It starts at 0 degrees and when it turns to ice it is still at 0 degrees

.45kg  (334 kj/kg) = 150.3 kj    or 150300 joules of energy must be removed to make the ice.

If you want to make it back into wate you will have to ADD 150300 j of heat energy to it !         Cool?

~jc

THANKS 

🙂🙂🙂🙂🙂🙂🙂🙂🙂🙂😋🙂🙂🙂🙂🙂🙂🙂🙂🙂

this website has a scientific calculator, you could try to use that

Here is an example...I do not know what you need tough

What is 25%  of 48?     =  48 (.25) =  12      See how that works?

Sales tax is 5%    what is the tax on a $ 95.43  purchase?     95.43 (.05) = $ 4.77 tax  (which would be added to the total purchase price)

Is that what you need?

13 is what percent of   73?     73 (x) = 13    then  13/73 = x = .178  (this is percent expressed as a DECIMAL equivalent......to find the % number you must multiply this by 100 to get 17.8%      

Confused?   Need more help?  Can YOU be more specific???

~jc

19 (or 21 if you still find that meme funny)

For the second part, I think we have this

1800  = 5040 / [ 71 e^(-.182t)+1]   rearrange as

71 e^(-.182t)+1  =  5040/ 1800        subtract 1 from both sides

71e^(-.182t)  = [5040 - 1800] / 1800   simplify

71e^(-.182t)   = 1.8       divide both sides by 71

e^(-.182t)   = 1.8/ 71   take the ln of both sides

ln e^(-.182t)  = ln[ 1.8 / 71  ]      and we can write

-.182t ln e   =  ln [ 1.8/ 71]      and ln e = 1    so we can ignore this....and we have

-.182t   = ln [ 1.8 / 71]          divide both sides by -.182

t=  ln [ 1.8 / 71] /   [-.182 ]   = about   20.19 years

By / it by 100 than multiplying it by the percentage if that makes sense.

This is much like a lot of the financial problems posted on this forum

m =number of months to reach 87

P= number of attendees now 

We need to find the equation that defines how long it will take to get to 87  (The future value  or Pf)

Pf = P ( 1 + i)^m = 87     i was given as 10 percent or 0.010   so  Pf = P(1.010)^m = 87         and  P was given as starting at 29

  87 = 29 (1.010)^m  

Guest #2 is right...it is wrong, because I said 10 percent was .01....it is .1   D'oh!

should be   P = 87 =29(1.1)^m          Sorry !     It will take 11,5 months to reach 87 people using this model !

~ jc  (almost nearly close to the possible answer about 75 % of the time!     ha)

Nice try jc!!!!. Unfortunately for you, it is wrong!. Look at the numbers that Melody has calculated. That is the right answer to the penny!

Here's the proof........good luck!!!!  [ It's way above my pay grade......!!!! ]

http://www.artofproblemsolving.com/wiki/index.php/Fermat's_Two_Squares_Theorem

Ask for help from someone here.....

thats wrong ^ 

Very nice, Melody.....but....you stole my thunder on this one.....curses on you.....!!!!    [LOL!!!]

I had forgotten  - until  I thought about it awhile ago -  that  we could have had   7p - 24 =  5p  or  that 7p - 24  = -5p    and  it's obviously the second one that's correct

I might give myself points for just the thought......plus....you didn't even share any of your BBQ with me.....!!!!!

I still gave you 5 pts.....

4.) Mel is an enterprising woman. She sews quilled bags and sells them at $220 or $150 depending on the size. Today, of the 15 bags she brought, 3 were unsold and this gave her $2290. How many of each kind was she able to sell?

Let the number of bags of $220=t

Let the number of bags of $150=h

h + t=12, and,

220t + 150h=2290

Solve the following system:
{h+t = 12 |     (equation 1)
150 h+220 t = 2290 |     (equation 2)
Swap equation 1 with equation 2:
{150 h+220 t = 2290 |     (equation 1)
h+t = 12 |     (equation 2)
Subtract 1/150 × (equation 1) from equation 2:
{150 h+220 t = 2290 |     (equation 1)
0 h-(7 t)/15 = (-49)/15 |     (equation 2)
Divide equation 1 by 10:
{15 h+22 t = 229 |     (equation 1)
0 h-(7 t)/15 = -49/15 |     (equation 2)
Multiply equation 2 by -15/7:
{15 h+22 t = 229 |     (equation 1)
0 h+t = 7 |     (equation 2)
Subtract 22 × (equation 2) from equation 1:
{15 h+0 t = 75 |     (equation 1)
0 h+t = 7 |     (equation 2)
Divide equation 1 by 15:
{h+0 t = 5 |     (equation 1)
0 h+t = 7 |     (equation 2)
Collect results:
Answer: |  h=5      and     t=7
 

|x|   means the ABSOLUTE VALUE of 'x'      so   + x     or  - x    the ABSOLUTE VALUE is 'x'

2|x|-8 = -4   add '8' to both side to get

2|x| = 4       Divide both sides by '2' to get

|x| = 2         SO the absolute value of 'x' is '2'     so x can be either 2 or  -2       Does this make sense to you??

~jc

What is it that you need?

10a  x  3f  =  30 af        Is that it?

~jc