Answer:
We accept H₀ we don´t have enough evidence to support that the mean thickness is greater than 41 mm
Step-by-step explanation:
Sample Information:
Results:
41.8
40.9
42.1
41.2
40.5
41.1
42.6
40.6
From the table we get:
sample mean : x = 41.35
sample standard deviation s = 0.698
Hypothesis Test:
Null Hypothesis H₀ x = 41
Alternative Hypothesis Hₐ x > 41
The test is a one-tail test
If significance level is 0.01 and n = 8 we need to use t-student distribution
From t-table α = 0.01 and degree of freedom df = n - 1 df = 8 - 1
df = 7 t(c) = 2.998
To calculate t(s) = ( x - 41 ) / s/√n
t(s) = ( 41.35 - 41 ) / 0.698/√8
t(s) = 0.35 * 2.83/ 0.698
t(s) = 1.419
Comparing t(s) and t(c)
t(s) < t(c)
t(s) is in the acceptance region we accept H₀
Answer with Step-by-step explanation:
We are given that
and 
are linearly independent.
By definition of linear independent there exits three scalar 
and 
such that
Where 
We have to prove that 
and 
are linearly independent.
Let 
and 
such that
...(1)
..(2)
..(3)
Because and are linearly independent.
From equation (1) and (3)
...(4)
Adding equation (2) and (4)
From equation (1) and (2)
Hence, and area linearly independent.
Answer:
32centimeters
Step-by-step explanation:
4 sides are in a sqaure and all of them are equal so
8 times 4 is 32
Answer:
Step-by-step explanation:
Composition of functions occurs when we have two functions normally written similar or exactly like f(x) & g(x) - you can have any coefficients to the (x), but the most commonly seen are f(x) and g(x). They are written as either f(g(x)) or (f o g)(x). Because our composition is written as 
, we are replacing the x values in the g(x) function with 2 and simplifying the expression.
Now, because we are composing the functions, this value we have solved for now replaces the x-values in the f(x) function. So, f(x) becomes f(6), and we use the same manner as above to simplify.
Therefore, when we compose the functions, our final answer is 
.
Because we don't have any set numbers for x or y, I believe that the solution set for both equations are infinite.
