Answer:
The area of the shaded region is 30.5 cm^2.
Step-by-step explanation:
So, first you need to find the area of the circle and rectangle separately.
The diagram shows that the circle radius is 5 cm; use the formula pi*r^2 to solve for the area.
The area of this circle:
3.14*5^2
3.14*25
=78.5 cm
The area of this rectangle:
8 cm*6 cm = 48 cm
Now subtract the rectangle's area from the area of the circle.
78.5-48 = 30.5 cm
It is in standard form: y=mx+b
4√7
This is similar to collecting like terms in algebra
take out a common factor of √7 from each term
= √7( 5 + 1 - 2 ) = 4√7
Answer:
Design 3: An SRS of size 3000 from a population of size 300,000,000
Step-by-step explanation:
To check the SRS designs will give the most precision (smallest standard error) for estimating a population mean, we'll make use of the following formula:
V(y) = S²/n( 1 - n/N)
Where S² is a constant for the three SRS designs
Check the first design
n = 400
N = 4000
So, V(y) = S²/400 (1 - 400/4000)
V(y) = S²/400(1 - 0.1)
V(y) = 0.0025S²(0.9)
V(y) = 0.00225S²
V(y) = 2.25S²E-3
The second design
n = 30
N = 300
So, V(y) = S²/30 (1 - 30/300)
V(y) = S²/30(1 - 0.1)
V(y) = S²/30(0.9)
V(y) = 0.03S²
V(y) = 3S²E-2
The third design
n = 3,000
N = 300,000,000
So, V(y) = S²/3,000 (1 - 3,000/300,000,000)
V(y) = S²/3,000(1 - 0.00001)
V(y) = S²/3,000(0.99999)
V(y) = 0.00033333
V(y) = 3.33S²E-4
It's the third one because as Kendall spent more time training or running, their distance increased