There a six bands competing in a competition. how many different ways can the 1st, 2nd, and 3rd place be awarded

120

Step-by-step explanation:

Given : There a six bands competing in a competition.

To find : The number of different ways can the 1st, 2nd, and 3rd place be awarded.

We use permutations here since order matters.

Number of permutation of n things taking r at a time is given by :-

For n= 6 and r= 3 , we have  the different ways can the 1st, 2nd, and 3rd place be awarded as:

Hence, the 1st, 2nd, and 3rd place can be awarded in 120 ways.

the 3rd option is right

step-by-step explanation:

answer: the price of one pound cabbage = $ 0.8

the point (10,8) represents that the cost of 10 pounds cabbage is $ 8

step-by-step explanation:

since, here is a proportional relation between the number of pounds of cabbage (x) and the price in dollars (y).

therefore, we can write,

⇒ y = k x

where k is the constant of proportionality.

now, point (5,4) is in the line.

thus, it will satisfies the above equation of line.

⇒ 4 = 5 k

⇒ k = 0.8

thus, the equation of the line is,

y = 0.8 x

a) for x = 1,

y = 0.8

therefore, the cost of one pound of cabbage is 0.8 dollars.

b) in the below graph (10,8) represents that the cost of 10 pounds of cabbage is 8 dollars.