CPhill

To get the discount we use   [Old Price - New Price[ / Old Price....so we have

[19.50 - 8 ] / 19.50 = about .59  =  about 59%

$${\mathtt{\pi}}{\mathtt{\,\times\,}}{\mathtt{524\,952}} = {\mathtt{1\,649\,185.346\: \!687\: \!269\: \!140\: \!117\: \!4}}$$ 

6(2m - 1) = 138   simplify

12m - 6 = 138    add 6 to both sides

12m = 144    divide by 12 on both sides

m = 12

I interpreted the question as

4 (tan 3 + sin√5)

If we are dealing with rads, the answer becomes .....  2.576810353892

{Who knows ???}

We can evaluate   999log(9)  = 953.288

This equals about

 (10⁹⁵³)*10^.288 =

10⁹⁵³ * 1.942 =

1.942 x 10⁹⁵³

All in all......a really big number.....1942 followed by 950 zeros.......!!! {more or less}

Let the fraction be represented by a/b

And we are told that if we add 8 to the "top" the fraction becomes 1.

This implies that a + 8 = b

We are also told that if we add 9 to the "bottom,' we get 1/2

This implies that b+ 9  = 2a

So, rearranging the first equation, we have that a = b - 8    ....and substituting this into the second equation, we get .....

b + 9  = 2 (b - 8)   simplify

b + 9 = 2b - 16     simplify

b = 25  ..... and a = b - 8  ...so.... a =  25 - 8 = 17

So.....the fraction is 17/25

7 is prime and doesn't divide 108, so this is in lowest terms.....

6w^9 + 4w^2= 10w^11    ..... rearrange as

10x^11 - 6w^9 - 4w^2 = 0    .....factor

w^2 (10w^9 - 6w^7 - 4) = 0

w = 0 is one solution

w = 1 is also a solution

Note that, replacing w with x and graphing y = 10x^2 - 6x^7 - 4 ......there are no more solutions as shown here......

If the height is tripled and the radius is unchanged, the volume will triple.

To see this.....note that a cross-section of the cone will form a triangle. And triangles on the same bases are to each other as their heights. So, the triangle cross-section of the cone with its height tripled will have 3 times the area of the cone without its height tripled. And the sum of all these cross sections will form a volume three times of that of the sum of all the cross-sections of the cone with the "normal" height.

We have 28 ways to choose the first speaker, 27 ways to choose the second speaker, etc.

So...the total number of ways to choose 4 speakers is 28 x 27 x 26 x 25 = 491,400

For the second, we have 4! ways of arranging any 4 speakers = 24

Considering that John and Sam can be arranged two ways, either John first and Sam second, or vice-versa, and they can fill any of three positions.... (1,2) (2,3)(3,4)...then 2 x 3 = 6 arramgements. And for each of these the other two people can be arranged in two ways. So, 6 x 2  = 12 arrangements

So the probability that they speak next to each other is 12 arrangements/24 possible arrangements = 1/2 = 50%.