Answer:
0.0579 is the probability that mean systolic blood pressure is between 119 and 122 mm Hg for the sample.
Step-by-step explanation:
We are given the following information in the question:
Mean, μ = 114.8 mm Hg
Standard Deviation, σ = 13.1 mm Hg
Sample size = 23
We are given that the distribution of systolic blood pressures is a bell shaped distribution that is a normal distribution.
Formula:
Standard error due to sampling:
P(blood pressure is between 119 and 122 mm Hg)
0.0579 is the probability that mean systolic blood pressure is between 119 and 122 mm Hg for the sample.
Combining like terms is pretty simple. First, you would identify which terms are similar to what terms. For example, you can't combine two terms that aren't similar like 2x and 3y. It would have to be 2x and 3x to combine. Next, be sure to add/multiply/subtract/divide/etc. the terms. For example, if you had the problem 2x + 4x + 3y, you would combine the "x" terms and the resultant problem would be 6x + 3y. Hope this helped :)
3n = 1/81; divide both sides by 3 to isolate n:
3n/3 = 1/81 divided by 3. Remember that when you divide, you use the reciprocal and multiply instead!!
n = 1/81(1/3) = 1/243. Now plug 1/243 back in for n, and 3/243 is equivalent to 1/81
Answer:
Step-by-step explanation:
It is a result that a matrix 
is orthogonally diagonalizable if and only if is a symmetric matrix. According with the data you provided the matrix should be
We know that its eigenvalues are 
, where 
has multiplicity two.
So if we calculate the corresponding eigenspaces for each eigenvalue we have
,
.
With this in mind we can form the matrices 
that diagonalizes the matrix so.
and
Observe that the rows of 
are the eigenvectors corresponding to the eigen values.
Now you only need to normalize each row of dividing by its norm, as a row vector.
The matrix you have to obtain is the matrix shown below
Answer:
2nd option
Step-by-step explanation:
r + 1 = 23 ( subtract 1 from both sides )
r = 22 ( multiply both sides by 3 to clear the fraction )
r = 66 ( divide both sides by )
r = 
× 
( rationalising the denominator )
r = 
= 33
