${\mathrm{End}}_{\mathrm{ℝ}\left[x\right]}\left(M\right)$ where ${\displaystyle M=\frac{\mathbb{R}\left[x\right]}{(x^2+1)}}$ is a module over the ring ${\displaystyle \mathbb{R}\left[x\right]}$

Proving that the set of units of a ring is a cyclic group of order 4
The set of units of ${\displaystyle \frac{\mathbb{Z}}{10}\mathbb{Z}}$ is ${\displaystyle \{\bar{1},\bar{3},\bar{7},\bar{9}\}}$, how can I show that this group is cyclic?
My guess is that we need to show that the group can be generated by some element in the set, do I need to show that powers of some element can generate all elements in the other congruence classes?
For example $7^2=49\equiv 9\pm \mathrm{mod}10$, i.e. using 7 we can generate an element in the congruence class of 9, but can not generate 29 for example from any power of 7, so is it sufficent to say that an element is a generator if it generates at least one element in all other congruence classes?

Let K be the number of heads in 200 flips of a coin. The null hypothesis H is that the coin is fair. Devise significance tests with the folowng properties.
Note: Your answers below must be integers
a) The signficance level is ${\displaystyle \alpha }$ =0.08 and the rejection set R has the form $\{|K-E\left[K\right]|>c\}.$
Use the Central Limit theorem to find the accsptane ce set A.
$A=\{\dots ,\dots ,\dots \}$
b) Now tho significance level is ${\displaystyle \alpha }$ = 0.016 and the rejection set R has the form $\{K>c^1\}$
Again, use tho Central Limit Theorem to find tho accaptance set A.
$A=\{\dots ,\dots ,\dots \}$

to 4x^2y"+17y=0, y(1)=-1, y'(1)= -1/2

$f ( x ) = 7 x^{2 }+ 2$ and $g ( x ) = 5 x^{3 }+ 7 x^{2 }+ 6 x$, find the derivative of the quotient $\frac{f ( x ) }{g ( x ) }$.

use squeeze theorem find the following lim x,y-0,0 y^2(1-cos2x) /x^4 +y^2

A Harris Interactive survey for InterContinental Hotels & Resorts asked respondents, “When traveling internationally, do you generally venture out on your own to experience culture, or stick with your tour group and itineraries?” The survey found that 23% of the respondents stick with their tour group (USA Today, January 21, 2004).

a. In a sample of six international travelers, what is the probability that two will stick with their tour group?

b. In a sample of six international travelers, what is the probability that at least two will stick with their tour group?

c. In a sample of 10 international travelers, what is the probability that none will stick with the tour group?