N = population size
n = sample size
sigma = population standard deviation
xbar = sample mean
SE = standard error
fpc = finite population correction
In this case,
N = 200
n = 49
sigma = 14
xbar = 56
Since n/N = 49/200 = 0.245 is larger than 0.05, this means we must use a finite population correction factor. I'll use fpc in place of 'finite population correction'.
If we ignore the fpc, then the SE would be simply sigma/sqrt(n) = 14/sqrt(49) = 2.
However we cannot ignore the fpc. We must use it due to the fact that n/N > 0.05.
--------------------------
Let's compute the fpc factor
fpc = sqrt((N-n)/(N-1))
fpc = sqrt((200-49)/(200-1))
fpc = 0.87108780834612
--------------------------
With the fpc factor, we'll have the true SE to be SE = fpc*sigma/sqrt(n) = 0.87108780834612*14/sqrt(49) = 1.74217561669224
The final answer, accurate to 6 decimal places, is therefore 1.742176
The only difference between the two following expressions is
their exponent though it’s equal. If you would analyze carefully, the two
expressions are equal since 2/4 is just equal to ½. The two expressions are
equal in value so the presentation of the exponent is their only difference.
If <span>point M is the midpoint of segment QR then QM = MR</span>
16 + x = 2(x+2)
16 + x = 2x + 4
16 - 4 = 2x - x
12 = x
If x = 12 then
QR = 2*QM = 2(16+x) = 2*(16+12) = 2 * 28 = 56
Hi! We’re going to use the pythagorean theorem to answer this.
3 + x^2 = 8
subtract 3 from 8
x^2=5
take the square root of both sides
x=sqrt5
