CPhill

20 / 100  =  .20  = 20%  discount

One way of doing this is to first convert feet to meters

1 ft  ≈ .3048 m

So.....

12 ft  =  12 * .3048m ≈  3.66m

38 ft =  38 * .3048 m ≈ 11.58

So the total cost =

Area [ in m^2] *  price [per m^2]  =

( 3.66 * 11.58) * 9.99   ≈ 423.4 pounds

The common ratio  is given by :

243 / 27  =  r^2

9  =  r^2    →   3  = r

And the first term  is

27 / 3^2  =   27/9 = 3

And the sum ofr the first 10  terms  is given by :

first term  [ 1 - common ratio^10] / [1 - common ratio ]  =

3 [ 1 - 3^10] / [ 1 - 3 ]  = 88572

By "doubling the sales." I'm assuming that you mean the previous day's sales......

We can find the total number of tickets sold with this sum

10

∑  2ⁿ  =  2046 

n = 1

On the 10th day he would have sold  2^10 =  1024 tickets

His total sales   =  2046 * .50  =  $1023

Since he makes a commission of 5%, he receives  $1023 * .05  =  $51.15

Look here :  https://www.mathsisfun.com/whole-numbers.html

Thanks, Melody and Tiggsy......I'm never good at these probability things and your explanations were easy to see......

Thanks for that correction.....I don't think that I'm fully awake yet....!!!!!

Let's convert liters to cubic centimeters

1 L =   1000 cubic centimeters  = 1000cc

The vo,ume of the 1 marble  = .04 L  X      1000cc / 1 L  =   40 cc

So the volume of tank =  the volume of the  50 marbles plus the 33L of water =

[50 x 40cc] +  33 [ 1000cc]  =  35000cc

If he has 20L of water, then he has 20000cc of water

So.....the number of marbles required to fill the remainder of the tank =

Remaining volume to be filled / volume of each marble  =

[ 35000 - 20000] cc / 40cc   =

15000 / 40  =

375 marbles  .......just as the guest found !!!

0 = 2x(3/x - 3/2) - 7     distribute the 2x over the terms in the parentheses

0 = 6 - 3x - 7                combine like terms

0 = 13 - 3x                  add 3x to both sides

3x  = 13                       divide both sides by 3

x =  13 / 3