Part A:
Given
defined by
but
Since, f(xy) ≠ f(x)f(y)
Therefore, the function is not a homomorphism.
Part B:
Given
defined by
Note that in
, -1 = 1 and f(0) = 0 and f(1) = -1 = 1, so we can also use the formular
and
Therefore, the function is a homomorphism.
Part C:
Given
, defined by
Since, f(x+y) ≠ f(x) + f(y), therefore, the function is not a homomorphism.
Part D:
Given
, defined by
but
Since, h(ab) ≠ h(a)h(b), therefore, the funtion is not a homomorphism.
Part E:
Given
, defined by
, where
denotes the lass of the integer
in
.
Then, for any
, we have
and
Therefore, the function is a homomorphism.
Answer:
We can conclude that there is significant evidence that Northwood residents owned their homes for a longer period of time compare to residents in the Southlake area
Step-by-step explanation:
H0 : μ1 = μ2
H1 : μ1 < μ2
Given :
n1 = 14 ; n2 = 28
x1 = 7.4 ; x2 = 9.1
s1 = 2.3 ; s2 = 2.9
α = 0.05
Test statistic :
(x1-x2) ÷ sqrt[(((n1-1)*s1² + (n2-1)*s2²) ÷ df) * (1/n1+1/n2)]
(7.4 - 9.1) ÷ sqrt[(((13*2.3^2) + (27*2.9^2)) ÷ 40) * (1/14 + 1/28)]
t = -1.7 ÷ sqrt[((68.77 + 227.07) / 40) * 0.1071428]
t = -1.7 ÷ sqrt(0.7924281488)
t = - 1.7 ÷ 0.8901843
t = - 1.909
t = - 1.91
The Pvalue :
P(t < - 1.91) = 0.028067
At α = 0.05 ;
Pvalue < α ; We reject the Null
We can conclude that there is significant evidence that Northwood residents owned their homes for a longer period of time compare to residents in the Southlake area
Answer:
140 degrees
Step-by-step explanation:
because they're congruent
4 Answer:
Since 4*4*4 is 64
Step-by-step explanation: