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Thanks, Melody....I missed that other corner point.....curses on you !!!! (LOL !!!)

I think I just had a.......

Thanks Geno, 

I had to think about that one!   

It stands for Standard Deviation.

It is a statistical term.    

OR

you can have a sD memory card.  I don't know what that stands for.    

CPhill's solution is 24 chairs and 14 tables

This gives a profit of

$${\mathtt{24}}{\mathtt{\,\times\,}}{\mathtt{450}}{\mathtt{\,\small\textbf+\,}}{\mathtt{14}}{\mathtt{\,\times\,}}{\mathtt{80}} = {\mathtt{11\,920}}$$   dollars

I will also check that this fits the limitations.

mahogony = 24*5+14*20=400 good

hours = 24*10+14*15=450  good

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My solution is  45 chairs and no tables

This gives a profit of  

$${\mathtt{45}}{\mathtt{\,\times\,}}{\mathtt{450}} = {\mathtt{20\,250}}$$   dollars 

I will also check that this fits the limitations.

mahogony = 45*5=225 good

hours = 45*10=450  good

Here if my graph.   The movable line represents profit.  Basically I just added this to CPhill's graph.

If he needed 7 more pens, he would have 147.

And...dividling that by 3, we have that there must be 49 students......

Thanks CPhill, you're awesome!

We have

(1200(1-1.0216^n))/(1-1.0216)=10000   divide both sides by 1200

(1-1.0216^n))/(1-1.0216) =25/3    multiply both sides by (1-1.0216)

(1-1.0216^n)) = (25/3) (1-1.0216)     and 1-1.0216 = -.0216    .. so we have

(1-1.0216^n)) = -(25/3)(.0216)    rearrange

1.0216^n  = 1 + (25/3)(.0216)     and  1 + (25/3)(.0216) = 1.18    so we have

1.0216^n = 1.18    take the log of both sides

log 1.0216^n = log 1.18      and we can write

n log 1.0216  = log 1.18      divide both sides by log 1.0216

n = log(1.18) / log(1.0216)  = about 7.745

Thanks Chris :)

We tried rebooting the computer but it only fixed CPhill's machine.

Mine is still malfunctioning.  I am doing my best to fix the subprocessor but it is a work in progress.  Sorry.

Nice, Melody....I like the way you presented that....!!!

Sorry, Anonymous....but it's WAY more than that....!!!!

2^99 =  633825300114114700748351602688....

And that's chickenfeed compared to 2^21914....!!!

The slope of the perpendicular line to the given one is the negative reciprocal of 4 = -1/4

So we have

y - 1  = (-1/4)(x - 8)  simplify

y - 1 = (-1/4)x + 2     add 1 to both sides

y = (-1/4)x + 3

x^2= 16x - 28         rearrange as

x^2 - 16x + 28 = 0      factor  as

(x - 2) (x - 14) = 0       and setting each factor to 0, we have that x = 2 and x = 14

We are trying to maximize

P = 450x + 80y

Subject to these  constraint equations:

x ≥ 0,  y ≥ 0,  5x + 20y ≤ 400   and  10x + 15y ≤ 450 ..... where x is the number of chairs produced and y is the number of tables produced

Well...I'm not a "professional"....or even a "sub-professional".......more like a "recreational mathematician"......but.....I'll do my best.....!!!

I assume you want to find the number of each type of stamp.

Let x be the number of US stamps and y be the number of foreign stamps

So we have

x + y = 12

And the statement....The number of U.S stamps is 3 less than twice the number of foreign stamps.....can be written as

x + 3 = 2y

So using the first equation, we can let  y = 12 - x....so...in the second equation, we have

x + 3  = 2(12 -x)   simplify

x + 3 = 24 - 2x     add 2x to both sides and subtract 3 from both sides

3x = 21     divide by 3 on both sides

x = 7    which implies that y = 5

So, he has 7 US stamps and 5 foreign stamps....

(1 + 1)  is just 2 in any of these bases.....!!!!

I assume you want to start with .02, double every successive day, and calculate the sum at the end of the year.....(Warning..it's  huge  number..!!)

WolframAlpha gives the final sum as

To write it without scienific notation, just move the decimal point to the right 108 times....!!!!

This is an "alternating" series ... we have

4 = 7/ [1 - (- r)]  = 7/(1 + r)   and solving for r, we have

4 = 7 / (1 + r) → (1 + r) = 7/4 → r = 3/4

And the form of this series is ..  ∑ 7 *(-3/4)^(n-1)   from 1 to infinity

And the result of dividing the third term by the second term is just (-3/4)  .... as we would expect....!!!!

This word question could be answered with a word answer:

"What number can you add 4 to and divide by 7 to get the number 1?"

You can work your way backwards to the answer. To reverse the last part, "what can you divide by 7 to get the number 1", remember that any number divided by itself equals 1. Therefore you would divide 7 by itself (7) to get 1. So now you have an intermediate question:

"What number can you add 4 to to get the number 7."

For this, you reverse again: 7-4=3.

Nice one, saseflower...!!!

thank you so much Heureka!

(x + 4)/7 = 1

Multiply by 7 on both sides

x + 4 = 7

Subtract 4 on both sides

x = 3

And there's your answer :)

If Justin has 9 apples and 10 more apples came, he would have 19 apples.