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Darn, it took me at least 5 min to find out how to solve this... :)

P: Pepperoni

M: Mushroom

U: one or the other or both

∩: Both at the same time

P U M = 12       P = 5      M = 8

A formula (that I got from probability theory) says that:

A ∩ B = A + B - A U B 

In our case:

P ∩ M = P + M - P U M = 5 + 8 - 12 = 1 

So the pizza consists of 4 slices w/ only pepperoni, 7 slices w/ only mushroom, and 1 slice w/ both. 

The first natural number greater than 150 that is divisible by is 153

And the natural number that is closest to - and less than - 300 that is divisible by 9 is 297

So, the answer you're seeking is given by ..... [(297 - 153) / 9]  +  1` =  17

Any three can be in the first position...any three in the second and any three in the last

So

3 x 3 x 3   = 27

This also implies that for any number of n different letters...nⁿ "words" can be formed in this manner...

298 K is just 25 ^oC, or "room temperature".

[H⁺] = 5.35 * 10^-3 M 

We know that:

[H⁺][OH^-] = 10^-14 M²

[OH^-] = 10^-14 M²/[H⁺] ≈ 1.87 * 10^-12 M

There are 6 odd numbers in each row x 11 rows = 66

Hit the "2nd" key.....you will see the inverse functions.....asin, acos, etc.

10^(log (20)/240)=

(log (20)/240)= 0.0054209583152666

So  ...   10^{0.0054209583152666} = about 1.013

The measure in degrees can be found by using the inverse tangent

We have

tan^-1(-5/2)  =  about - 68.198°.....but this is - 68.198° in the 4th quadrant = about 291.8°

Here's a pic......

The arcsec u just means an angle, Θ, whose secant = u.... or just .... u /1

Thus, since the secant ratio is r / x....this means that r = u   and x = 1

And y = √[r^2 - x^2]  = √[u^2 - 1^2] = √[u^2 - 1]

And the cotangent of such an angle is just x / y  =  1 / √[u^2 - 1]    and "rationalizing" the denominator, we have

cot (arcsec u) = cot Θ  = √[u^2 - 1] / [u^2 - 1]

Here's a Venn diagram showing the numbers in each "cat"egory.....Mmmmm....maybe it should be each "dog"etory, huh??

I may actually have a quite hard time describing the way to solve it but, I hope this website may be helpful.

I actually have not a clue how to do this because not enough information is supplied. Though with a guess you may have to divide or multiply as in an example with how to get 24 from 1/6. You would flip 1/6 to 6/1 and then multiply. So you would multiply 24 by 6 and get your answer. If there is any more information if you would be able to provide it I may have a clue.

There is a simple way that you can figure this out. You see 45 ants walking in a line. Though you find 2 ants and bring them to the line. Add all of the ants and find how many ants there are. Which would be 47 ants.

From 40, we can subtract the 12 that liked neither.

This gives us 28.

So, to find the ones that like both, add the 18 that like apple pie and the 15 that like chocolate cake and subtract 28 from this.

So 18 + 15 - 28 = 5 liked both.

Pi is actually something that will help you a lot in life depending on your job. Say if you work at a construction area and you need to find the area of a circle so you can build a fountain that size. If you use pi then you would be able to find the caculations easier. It is one of those things that you just have to go with.

The answer is 19. For example if you want an easier way to figure it out then here is an example. You have 10 fingers. Though you friend comes along and holds 9 fingers up next to them. Count how many fingers are held up and you will get 19 fingers.

We have 20 ways to pick the president.

And, after he/she is chosen, 19 ways to pick the vice-president.

And then, 18 ways to pick a treasurer.

So  20 x 19 x 18 = 6840 different ways

We could also find this answer by using a permutaion  .... P(20,3)  = 6840  .... OR ....by counting sets

C(20,3) = 1140 possible sets of 3 different people.....but.....each set can be arranged in 3! = 6 ways.

So  ...  1140 x 6  =  6840

I always like this last one best......we have two tasks .... 1) pick all of the possible different sets, 2) arrange each of these in all possible ways.....

You seem to have gone slightly astray here.

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Let's first start off by applying the distributive property: 2*4x=8x, 2*(-3)=-6

We get 8x-6-8=4+2x.

Use subtraction to simplify it to 8x-14=4+2x

Add 14 to both sides: 8x=18+2x

Subtract 2x from both sides: 6x=18

Divide both sides by 6, and you get x=3, which is the answer.

Check: 2[(4*3)-3]-8=4+(2*3)

(2*9)-8=4+6

18-8=4+6

10=10

In each row there is one more dot than there are horizontal toothpicks, and in each column there is one more dot than there are vertical toothpicks, so:

a) Number of horizontal toothpicks = 10*(20 + 1) = 210

    Number of vertical toothpicks     = 20*(10 + 1)  = 220

    Total number of toothpicks = 430

   Number of dots = (10 + 1)*(20 + 1) = 11*21 = 231

b) Number of horizontal toothpicks = h*(v + 1)

    Number of vertical toothpicks = v*(h + 1)

   ... I'll leave you to finish off.

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The first odd number can be found from:  2*1 - 1  = 1

The 2nd odd number can be found from:  2*2 - 1  = 3

The 3rd odd number can be found from:   2*3 - 1  = 5

The 4th odd number can be found from:   2*4 - 1  = 7

...

so the 2004th odd number can be found from:   ..........  ?

Please explain thoroughly in this question. I am so sorry! I forgot to include this in the quesiton!! Thanks, this website is very helpful.