Aregional soccer tournament has 64 participating teams. in the first round of the tournament, 32 games are played. in each successive round, the number of games played decreases by 1/2. find a rule for the number of games played in the nth round, then find the total number of games played in the regional soccer tournament.

A regional soccer tournament has 64 participating teams.

In the first round of the tournament, 32 games are played.

In each successive round, the number of games played decreases by 1/2.

Part A:

We know;

So, we get;

The rule for the number of games played in the nth round is given by:

where

Part B:

As in each successive round the rounds are decreasing by 1/2 we have.

round 1 = 32

round 2 = 16

round 3 = 8

round 4 = 4

round 5 = 2

round 6 = 1

So, the total number of games played in the regional soccer tournament are:

g = (2, 2)

step-by-step explanation:

given the ratio is 1 : 1 then f is the midpoint of eg

let the coordinates of g = (x, y)

using the midpoint formula

(0 + x) = 1 ( multiply both sides by 2 )

0 + x = 2 ⇒ x = 2

similarly

(4 + y) = 3 ( multiply both sides by 2 )

4 + y = 6 ( subtract 4 from both sides )

y = 2

coordinates of g = (2, 2)

d. $180

step-by-step explanation:

if the dimensions of the room is 9ft by 12 ft, we have the area of the floor as,

so the area of the floor is 108 square feet, converting that into square yards we get,

the cost of carpet is $15 per square yard, therefore the cost of carpet for 12 square yards is,

hence, the cost of carpet is $180.

assuming the dimensions of the room be,

15 ft by 12 ft

so, the area of the floor of that room is,

we can convert 180 square feet into square yards, we know that,

1 sq ft = 0.111 sq yard

so, 180 square feet is,

so the area of floor is 20 square yards.

now, the cost of carpet is 15 dollars per square yard, therefore the cost of carpet for 20 square yards is,

so, it will cost $300.