What is the sum of the described series? Use . A radio station is holding a trivia contest. The prize money starts at $20 for the first question. Each question is tougher than the one before it, and the station doubles the prize money from the previous amount. If the radio station has 8 trivia questions, how much total money will it hand out in prizes?

$5100

Step-by-step explanation:

Given, The prize money starts at $20 for the first question.

Let a= 20,

Also, Each question is tougher than the one before it, and the station doubles the prize money from the previous amount.

i.e. the sequence prize willbe : $20 , 2 x ($20) , 2² x ($20)x ....

That is its is an geometric progression with the common ratio r= 2,

Since the sum of n terms in GP is given by :-

So the total money will it hand out in prizes after 8 questions would be :

Hence, the total money it will hand out in prizes = $5100

geometry: triangles

solvers

lessons

answers archive

call the larger triangle abc

then the smaller triangle cde is similar to abc (all angles are equal, aaa).  

ab is the side that is 36, and we wish to find de, the side corresponding to ab

area_cde = area_abc - area_cde --> area_abc / area_cde = 2

let x=length of de

ratio of areas = (ratio of sides)^2

+2+=+%2836%2fx%29%5e2+

+2+=+1296%2fx%5e2+

++x%5e2+=+1296%2f2+=+648+

25.45584

b. 1.25 hr

step-by-step explanation:

if you have a constant speed of 60 mph, then you have a ratio between 60 mi. to 1 hr. dividing both sides by 60 we get the ratio

1 mi. to

then mult. both sides by 75 we get the ratio

75 mi. to

simplifying we get

75 mi. to

or 1.25 hr.