Answer:
When we have a function like:

This function will have a discontinuity only if it diverges, and a divergence can happen when the denominator is equal to zero and the numerator is different than zero.
In this case, we have the equation:

Here the denominator is:
h(x) = x + 2
This is equal to zero when:
x + 2 = 0
x = -2
Now we need to see what happens with the numerator when x = -2
g(-2) = (-2)^2 + 2*(-2) = 0
Is equal to zero.
Then we need to see the limit when x -> -2, and use the L'Hopital theorem.

Because we have zero over zero at that point, we need to look at the quotients of the derivatives of both numerator and denominator.

Then the function does not diverge, then the function has no discontinuity.
We also could look at the graph of f(x) to see it:
Our function is a linear function, and this is because the numerator is x times the denominator, then the function is:
f(x) = x.
35-15 i think dont hate me if im wrong
Use the formula d= x2-x1^2+y2-y1^2
X2 would be -3+5 ^2+ 7+1^2
7=y2
1=y1
Now calculate
-3+5=2
2^2 +4^2 Since negative 3 and negative 1 = positive 4
Now square 2 which is for and 4 squared is 16
Add them up and it will be = 20 square which can simplify to 4/5
Answer:
The 95% confidence interval would be given (0.622;0.644).
We are confident (95%) that the true proportion of people that said that they change their nail polish once a week is between 0.622 and 0.644
Step-by-step explanation:
Data given and notation
n=7000 represent the random sample taken
X=4431 represent the people that said that they change their nail polish once a week
estimated proportion of people that said that they change their nail polish once a week
represent the significance level
Confidence =0.95 or 95%
p= population proportion of people that said that they change their nail polish once a week
Solution to the problem
The confidence interval would be given by this formula
For the 95% confidence interval the value of
and
, with that value we can find the quantile required for the interval in the normal standard distribution.
And replacing into the confidence interval formula we got:
And the 95% confidence interval would be given (0.622;0.644).
We are confident (95%) that the true proportion of people that said that they change their nail polish once a week is between 0.622 and 0.644
Answer:
12 1/5
Step-by-step explanation:
5 can go into itself one time and 5 can go into 25 5 times hope that makes sense