CPhill

Difference between combinations and permutations

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Combinations count sets of things

Permutations count arrangements within sets

For instance, in combinations, the set {1,2} is the same as set {2,1}. The set is counted once.

However, permutations view the two sets as completely different things. Thus, in permutations, {1,2} ≠ {2,1}.  

what is the radius of circle that has a circumference of 56 ft?

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Mmmmm...... let's reject that last answer...it isn't correct......

We have that

C = 2*pi*r    where C is the circumference and r is the radius....for convenience, I'll use 3.14 for pi

So we have

56 = 2 * 3.14 * r

Divide both sides by  2 * 3.14  and we have

(56)/ (2 * 3.14) = r

8.91 = r       

Just go to the on-site calculator and evaluate it....we're not "solving" anything........

In a survey of 700 voters, the ratio of men to women taking part was 17:18. How many women took part in the survey?

Think about it this way....we have 35 equal parts of 700 voters..........17/35 are men.........18/35 are women......do you see how to get the answer???    

logarithm of number 9 to base 3

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We're just asking ourselves, what exponent (power) do we put on 3 to raise it to 9??

In other words

log₃9

In exponential form, we have

3^x = 9

Do you see what the answer is ????  (I hope) 

5 3/4 X 2 3/5=

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OK...let's convert both things to fractions

5 3/4 = 23/4          2 3/5 = 13/5

Now, we have

(23/4) * (13/5)

If we can "reduce," we should, but unfortunately, nothing "cancels."

So we have (23 * 13) / (4 * 5) = 299/20

Writing this back as a "mixed number," we have

14 + 19/20    

how do I figure logrhthms on calculator other than power 0f 10

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Let me show you how to do this ...... 

Suppose we have log_a(b)   where "a" is the base and "b" is what we're trying to take  the log of.... (that's some bad English, isn't it??)

Exponentially, what this says is

a^x = b

Now take the "log" of both sides .....  we have

loga^x = logb

And, by a property of logs, we can bring the "x" out front

(x)loga  = logb

Solving for x gives

x = log(b)/log(a)

And "x" is just the exponent (power) that we need to "raise" "a" to in order to obtain "b"

But, that is the definition of a logarithm.

So, to find the log in any other base than 10 or "e," just divide the log of the number you're trying to find the log of by the log of the base you're using......  

a car consumed in its first ride 25% of her fuel. on the second ride she consumed 20% fuel of the remaining fuel in the car ( after using 25%) after the 2 rides the remaining fuel amount of was bigger by 8 than the amount of fuel used for both rides together.

what L of fuel the car had at the begining ? (before the rides)

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OK........let's call the amount of fuel in the tank before the rides = x

After the first trip, we used .25x, so we have [x - .25x] = .75x left

On the second trip, we used 20% of what remains = .20[.75x]

So, what we had left after the first trip less what we consumed after the second trip is "8 more" than what we used on both trips. Mathematically, this sets up as:

[.75x] - .20[.75x] - 8  = [.25x] + .20[.75x]

Notice that, if the left side is "8 more" than the right, then we have to subtract 8 to "equalize" both sides.

So we have

[.75x] - [.15x] - 8 = [.25x] + .20[.75x]

Simplifying, we have

[.60x] - 8 = [.25x] + [.15x]

[.60x] - 8 = [.40x]

Subtract [.40x] from both sides

[.20x] - 8 = 0

Add 8 to both sides

[.20x] = 8

Divide by .20 on both sides

x = 40L

Make sure that you check this answer in the original equation......I think it "works"  

225/4 simplified

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Factoring 225, we have 5² * 3²

Factoring 4, we have 2²

So 225/4 =  [ 5² * 3² ] / [2² ]

Thus, this IS simplified........(nothing on "top"  and "bottom"  "cancels")

All we can do to "simpify" this is to express it as a mixed number..........56 + (1/4)