The population of a local species of dragonfly can be found using an infinite geometric series where a1 = 48 and the common ratio is one fourth. write the sum in sigma notation and calculate the sum that will be the upper limit of this population.

The sum of the given geometric series and its sigma notation is given below :

Step-by-step explanation:

First term, a = 48

The series is given to be geometric series and the sum of geometric series is given by :

And for sigma notation,

the answer is c

hope this !

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.