Answer:
95% confidence interval = ( 28.9485, 40.1515 )
Step-by-step explanation:
sample size( n ) = 52
mean value ( x )= 34.55
std ( б ) = 20.12
H0 : <em>u </em>≤ 30
Ha : u > 30 ( claim )
95% confidence interval for mean SPF level ( df = 51 )
= mean value ± 
95% confidence interval = ( 28.9485, 40.1515 )
we cannot reject H0
Answer:

And when we apply the limit we got that:

Step-by-step explanation:
Assuming this complete problem: "The following formula for the sum of the cubes of the first n integers is proved in Appendix E. Use it to evaluate the limit . 1^3+2^3+3^3+...+n^3=[n(n+1)/2]^2"
We have the following formula in order to find the sum of cubes:

We can express this formula like this:
![\lim_{n\to\infty} \sum_{n=1}^{\infty}i^3 =\lim_{n\to\infty} [\frac{n(n+1)}{2}]^2](https://tex.z-dn.net/?f=%20%5Clim_%7Bn%5Cto%5Cinfty%7D%20%5Csum_%7Bn%3D1%7D%5E%7B%5Cinfty%7Di%5E3%20%3D%5Clim_%7Bn%5Cto%5Cinfty%7D%20%5B%5Cfrac%7Bn%28n%2B1%29%7D%7B2%7D%5D%5E2)
And using this property we need to proof that: 1^3+2^3+3^3+...+n^3=[n(n+1)/2]^2
![\lim_{n\to\infty} [\frac{n(n+1)}{2}]^2](https://tex.z-dn.net/?f=%20%5Clim_%7Bn%5Cto%5Cinfty%7D%20%5B%5Cfrac%7Bn%28n%2B1%29%7D%7B2%7D%5D%5E2)
If we operate and we take out the 1/4 as a factor we got this:

We can cancel
and we got

We can reorder the terms like this:

We can do some algebra and we got:

We can solve the square and we got:

And when we apply the limit we got that:

Answer:
Part A: 15
Part B:
Point slope form: 
Slope intercept form: 
Standard Form: 
Part C: 
Part D: 505
Step-by-step explanation:
We are given the following
x g(x)
5 $400
10 $475
We can see that these are two points on the line.
i.e. (5, 400) and (10, 475)
OR

<u>Part A: </u>Slope of the function:

So, slope of the line = 15
<em>It has a positive slope and the function will be increasing with the increasing value of 'x'.</em>
<em></em>
<u>Part B:</u>
Point slope form of a line is given as:

Putting
:

Slope intercept form:
where c is the intercept.

Putting (x,y) as (5, 400) to find c:

So, the equation in slope intercept form:

Standard form of line:

Rewriting the slope intercept form:

<u>Part C:</u>
Using the function notation, putting y = g(x) in slope intercept form:

<u>Part D:</u>
Balance after 12 days = ?
i.e. g(x) = ? at x = 12
Putting x = 12 in 

Answer: Meghan spent $687.5 per year.
Step-by-step explanation:
Let x represent the amount of money that Scott spends per year for auto insurance.
Meghan spends 25% more each year for auto insurance than Scott. The value of 25% of the amount that Scott spends per year is
25/100 × x = 0.25 × x = 0.25x
Therefore, the amount that Meghan spends would be
x + 0.25x = 1.25x
If the amount that they spent together is $1237.50 per year, it means that
x + 1.25x = 1237.5
2.25x = 1237.5
x = 1237.5/2.25
x = 550
The amount that Meghan spent per year would be
1.25 × 550 = 687.5
Answer:
1679616
Step-by-step explanation:
6*6
36*36*36*36