Answer:
$ 78.78
Step-by-step explanation:
Calculate 15% of 68.50. then add it to the total bill.
Let us check series : -10 /-2 = 5 -50/-10 = 5
so it is a geometric series with a= -2 and r= 5
sum formula for n terms of geometric series = a ( r^n -1 ) /( r-1)
here we find S5 that is n= 5 = -2 ( 5^ 5 - 1) /( 5-1)
= -2 ( 3125 -1) / 4 = -1562
second series is : 1.5/1 = 1.5 2.25/1.5 = 1.5
this is also geometric series but n = 12 a= 1 and r= 1.5
we use same formula
S12 = 1 ( (1.5) ^12 -1) /( 1.5-1) =
128.74 / 0.5 = 257.49
Last is 2/1= 2 4/2 = 2 8/4 = 2 so r = 2 a = 1 and n = 12
we use same formula 1 ( 2^12 - 1) / (2-1)
= 4095
Answers : -1562 , 257.49 , 4095
There are 26 letters in the alphabet, 5 are vowels, therefore, the probability of choosing a vowel the first time is:
![\frac{5}{26},](https://tex.z-dn.net/?f=%5Cfrac%7B5%7D%7B26%7D%2C)
and the second time is:
![\frac{4}{25}\text{.}](https://tex.z-dn.net/?f=%5Cfrac%7B4%7D%7B25%7D%5Ctext%7B.%7D)
Continuing with this reasoning, we get that the probabilities each time are:
![\frac{5}{26},\frac{4}{25},\frac{3}{24},\frac{2}{23}\text{.}](https://tex.z-dn.net/?f=%5Cfrac%7B5%7D%7B26%7D%2C%5Cfrac%7B4%7D%7B25%7D%2C%5Cfrac%7B3%7D%7B24%7D%2C%5Cfrac%7B2%7D%7B23%7D%5Ctext%7B.%7D)
Finally, the probability that you get all vowels is the product of the probabilities:
![\frac{1}{2990}\text{.}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2990%7D%5Ctext%7B.%7D)
Writing the above result as a percentage we get:
![0.033\%.](https://tex.z-dn.net/?f=0.033%5C%25.)
Answer: