The new Elk Grove radio station KFIN, features the top 60 songs for that week. The #1 song is played 60 times, the #2 song is played 59 times, the #3 song is played 58 times, and so on until the #60 song is played once. Each song takes 3 minutes to play.
The station also has 24 ten-minute news breaks each day, and the rest of the time is sold for advertising. If the station charges $100 for every 30 seconds of advertising, how much money do they take in each week?

Step-by-step explanation:

The number of times that each song is played is reducing in arithmetic progression. We would determine the total number of time for plating all the songs in a week by applying the formula for determining the sum of the n terms in an arithmetic sequence. It is expressed as

Sn = n/2(2a + (n - 1)d

Where

d represents the common difference

n represents the number of terms

a represents the first term of the sequence

Sn represents the sum of n terms if the sequence.

From the information given,

a = 60

n = 60

d = - 1

Sn = 60/2(2 × 60 + (60 - 1)-1)

Sn = 30(120 - 59)

Sn = 1830 times

The 60 songs are played for 1830 times in a week. If each song takes 3 minutes to play, then the total time taken to play the songs for 1830 times in a week is

3 × 1830 = 5490 minutes

7 days = 1 week

24 hours = 1 day

60 minutes = 1 hour

The number of minutes in a week is

7 × 24 × 60 = 10080 minutes

The station also has 24 ten-minute news breaks each day. The number of minutes of break for each day is

24 × 10 = 240 minutes

The amount of break time in a week is

240 × 7 = 1680 minutes

If the remaining minutes is meant for advertising, then the number if minutes available for advertising is

10080 - (5490 + 1680) = 2910 minutes

1 minute = 60 seconds

2910 minutes = 2910 × 60 = 174600 seconds

If the station charges $100 for every 30 seconds of advertising, then the amount that they take in each week(for 174600 seconds) is

(174600 × 100)/30 = $5820000

there are lots of ways.   pick's theorem tells us if the vertices are lattice points the area a is

a = b/2 + i - 1

where b is the number of boundary lattice points and i is the number of interior lattice points.

in the figure i count b=16, i=50 so

a = 8 + 50 - 1 = 57

let's try the shoelace formula.   the area is half the sum of the cross products of the sides.  

a(-2,6)   -2(2)-6(-5) = 26

b(-5,2)   -5(-3) - 2(-2) = 19

c(-2,-3) -2(-3) - (-3)(4) = 18

d(4,-3)   4(3) - (-3)(5) = 27

e(5,3)   5(3) - 3(1) = 12

f(1,3)     1(6) - 3(-2) = 12

a(-2,6)

each of the cross products is twice the area of the triangle with the associated side and one vertex the origin. so the area of abo=26/2=13.

area = (1/2) (26 + 19 +   18 + 27 + 12 + 12) = 57

that checks!

$450

step-by-step explanation:

first, you have to multiply 150x2=300

next, you have to add 150+300= 450