Tutoring services: the community college survey of student engagement reports that 46% of the students surveyed rarely or never use peer or other tutoring resources. suppose that in reality 40% of community college students never use tutoring services available at their college. in a simulation we select random samples from a population in which 40% do not use tutoring. for each sample we calculate the proportion who do not use tutoring. if we randomly sample 100 students from this population, the standard error is approximately 5%. would it be unusual to see 46% who do not use tutoring in a random sample of 100 students?

No, this would not be unusual because 46% is only 1.2 standard errors from 40%

Step-by-step explanation:

Consider the provided information.

The standard error is approximately 5%

Standard error(SE)=0.05

As we know

Here x=46%=0.46 and μ=40%=0.40

Now use the formula:

Substitute the respective values in the above formula.

Hence, this would not be unusual because 46% is only 1.2 standard errors from 40%

A] the relationship between angles  ∠7 and  ∠8 are defined as vertically opposite angles, they are those angles that opposite to each other when two line cross.  they are vertical in the sense that they share the same vertex (the same corner angles) as opposed to the usual up-down meaning of vertical. 

b] the angles created by this intersection between c and d are special because they are equal to each other, to solve for y we shall have:
(5y-29)=(3y+19)
this is because they are vertical angles, hence solving the above we get:
5y-3y=19+29
2y=48
y=48/2
y=24°

c] to solve for  ∠7 and  ∠8 we proceed as follows;
angles in a straight line add up to 180:
therefore:
(5y-29)+∠7=180
substituting the value of y in the above and solving for  ∠7 we get:
(5×24-29)+∠7=180
91+∠7=180
∠7=180-91
∠7=89

but remember that  vertical angles are equal to each other, therefore:
∠7=∠8=89°