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
What do we know about these angles? Immediately, you might notice that (4y-8)° and (16x-4)° share a line. The same is true of (16x-4)° and (14x+4)°. Any straight line forms what's called a <em>straight angle</em>, which measures 180°, so we know that, since they add up to form a straight angle, (14x+4)° and (16x-4)° must add up to 180°. We can use that fact to set up an equation to solve for x:
(14x+4)+(16x-4)=180
After you solve for x, you should look to solve for y. How can we figure out what y is? If you're familiar with the vertical angle theorem, you'll know that all vertical angles (angles that are directly across from each other diagonally) are equal. So we know that 14x+4=4y-8. You can use the value of x you solved for before to solve this one fairly easily, and then you'll have both values.
3x + 5 = 23
5 more than(addition) 3 times(multiplication) a variable(x) is(equals) 23
(you add 5 to 3x)
If you need to solve for "x", you need to isolate/get the variable "x" by itself in the equation:
3x + 5 = 23 Subtract 5 on both sides
3x + 5 - 5 = 23 - 5
3x = 18 Divide 3 on both sides to get "x" by itself
x = 6
Answer:
n=27 degrees
m=36 degrees
Step-by-step explanation:
So the inside triangle has two equal sides. To find these angles you would do the degrees of a triangle (180) minus the known value and then divided by two.
so it is: 180-126/2 which gives you 27 degrees.
this means the n value is 27.
to find m, you have to take away 90 degrees and the n value from 180.
so it is: 180-90-27 which gives you 63 degrees.
now you must take the smaller angle from 63 degrees to find m.
so it is: 63-27 which gives you 36
therefore...
n=27 degrees
m=36 degrees