CPhill

a suit is on sale for $214.60, which is 71% less than the regular price. What is the regular price?

Well....if it's 71% less....it must only be worth 29% (.29) of what it used to be.

So....call "x" the regular price.

And 29% of x = what's it worth now (the sale price)    ......   "of" means "multiply," so we have

.29 * x = 214.60   now divide by .29 on each side

x = 214.60 / .29  = $740

And that's the regular price......

bioschip is correct...we can't simplify it further.

If, however, you mean "simplify" by expressing it as a decimal, we have 3/4 = .75

Re: 2000+48x2+3-248.5/43

First....let's write this in a more understandable fashion !!!  We have

2000+(48x2)+3-(248.5/43)

2000+ 96 + 3 - 5.779

See how much easier things become by the proper use of parentheses??

Now...it's just addition and subtraction, and you should be able to handle that................... 

what happens to the surface area of an object when enlarged

Think about it this way....area is just a function of some "width" times some "length"

Now suppose that I have 1 "square foot" of area. That would be a square with one side = 1 foot

Now suppose that I doubled the length of each side ( a scaling factor of 2)....I would have 2ft X 2ft = 4 square feet of "area"......4 times as much.

Now suppose that, instead of doubling each side, I tripled it ( a scaling factor of 3)....I would have 3ft X 3ft = 9 square feet of "area"......9 times as much

Again, suppose that, instead of doubling each side, I quadrupled it (a scaling factor of 4)....I would have 4ft X 4ft = 16 square feet of "area"......16 times as much

This leads us to believe that each suare foot of the surface of an object would behave the very same way.

Thus, the surface area increases by (n²) times when we enlarge it by some scaling factor  "n" ...(Note that n needn't be an integer....it could be anything > 1.)

I hope that helps......

what makes a number rational or irrational?

If it can be expressed as a fraction (a ratio) it is rational

Thus (2/3), (5/1), (6/239) are rational....."Repeating" decimals are rational, as well - ex., .3333333333= (1/3)

Also, any "mixed" number is also rational.....5+(1/3) = 16/5

As you might have guessed by now, anything that we can't express as a fraction is "irrational"

Non-repeating decimals are irrational. Thus, things like "pi" or "e"  are irrational. Anything that remains under a "root" is also irrational....√(2), √(pi), 4√(13), for example....

Hope that helps....

What is the diameter of a circle with an area of 254.34mm²?

The area of a circle is A = (pi) * r²

So we need to "solve" for r  and then double our answer, since the diameter is twice the radius

So we have

254.34 mm² = r²    Take the sqare root of both sides

15.948 mm = r

and twice 15,948 = 31.886 mm

And there you are !!.....

Well....let's suppose you had a square with a side length of 2.

The area of a square is given by

A = (s)², where A is the area and s is the side length

So,

A = (2)² = 4

See if you can do it now.......

Sydney's grades were being averaged. Her grades were 83,63, and 100. What is her final grade that her teacher should put on her report card?  

Add the grades and divide by 3......that will give you your answer   

On a stock exchange,3 times as many shares of PDQ Electronics were traded today as yesterday.If another 300 shares of the stock had been traded,the total number of shares traded for the two days would have been 600.How many shares were traded today?

Let x be the number traded yesterday. Then 3x were the number traded today.

So we have

x + 3x + 300 = 600

4x + 300 = 600

Subtract 300 from each side

4x = 300

Divide by 4 on each side.

x = 75......This is the number traded yesterday

And 3(75) =The number traded today = 225.

Re: PEMDAS:What does it stand for?

It's an "acronym" that is supposed to remind us of  the "correct" "order of operations".......it stands for

Parenthesis

Exponents

Multiplication

Division

Addition

Subtraction

However,  this "order" isn't exactly "correct." Many students think they're supposed to always perform "Multiplication" before "Division" and "Addition" before "Subtraction."

A more "correct" order of things would be

Parenthesis (or Brackets)

Exponents

(Multiplication    Division)   or  (Division  Multiplication)

(Addition    Subtraction)    or  (Subtraction  Addition)

The first two liness should be self-explanatory....work inside any parenthesis first and then apply any exponents!!

The last two lines require some explanation. Multiplication and Division are performed at what is known as the same level of "precedence." This means that we perform these operations as we encounter them from "left to right." The same thing applies to Addition and Subtraction.

Let me demonstrate what I'm talking about - first with Multiplication and Division, and then with Addition and Subtraction.

Let's supppose we have this :

36 / 9 X 4

Many students assume that they're supposed to perform the "multiplication" first and then the "division.'

So we get (wrongly).....  36 / 36   ..and then, "dividing," we have the "answer'....."1"

This is incorrect...we perform any multiplication or division as we encounter them from "left to right."

Correctly...we would have .....36 /9 = 4 and multiplying this by 4  we obtain 16. Note that that's a lot different than "1.'

Addition and Subtraction behave the same way. Suppose we have:

14 - 3 + 10

Uising the "incorrect" way, we would add the 3 + 10 to get 13, and then subtract this from 14 to get '1.'

The correct way is to evaluate (14 -3) first - (11) - and then add this to (10) getting 21. Note that that's a different answer from  "1.' 

Oddly enough, the beginning maths seem to make this more difficult by their reluctance to use any parentheses (or brackets). I don't find this to be true of the higher maths - In these, it's usually explicitly spelled out what's to be done. Take, for example, the addition and subtraction problem we just did.

The "lower maths" tend to write it just as we did, i.e.,  14 - 3 + 10. In the upper maths, it would be written as (14 -3) + 10. Note that there is no confusion about what to do here.......the operation inside the parenthesis is done first, and then the "10" is added to the result !!!!

Also.....note the confusing nature of something like the following:

3 x 6 / 10 + 8 - 4 / 2

....Ouch!!....that makes my head hurt just looking at it !!!

This is far easier to understand:

[(3 x 6) / (10) ] + 8 - (4/2).........don't you agree ???

Yep....I'm long-winded !!!  ....but, I hope this helps !!!