we have been asked to find the sum of the series
As we know that a geometric series has a constant ratio "r" and it is defined as
The first term of the series is 
Geometric series sum formula is
Plugin the values we get
On simplification we get
Hence the sum of the given series is 
Answer:
The probability of that at least one marble is drawn is 2/7
Step-by-step explanation:
1/7+ 1/7=2/7
Answer:
a. 5177 cm³
b. 3,451 cm³
c. 67%
Step-by-step explanation:
Given:
Diameter of each ball (d) = 13 cm
Radius of the ball (r) = radius of the cylinder = ½(13) = 6.5 cm
Height of the cylinder (h) = the sum of the diameters of the 3 balls = 3(13) = 39 cm
a. Volume of cylinder = πr²h
Plug in the values
Volume of cylinder = π*6.5²*39 = 5176.56 ≈ 5177 cm³
b. Total volume of the three balls = 3(volume of 1 ball) = 3(volume of sphere) = 3(⁴/3πr³)
Plug in the value
Total volume of the 3 balls = 3(⁴/3*π*6.5³) = 3(1150.35) = 3,451.05 ≈ 3,451 cm³
c. % of volume of the container occupied by the 3 balls = total volume of the three balls / volume of cylinder × 100
Plug in the values
= 3,451/5177 × 100
= 66.6602279
≈ 67%
The domain and the range is [-6 to +inf)
Answer:
1/2.25 or 4/9
Step-by-step explanation:
