6% service charge for 200 boxing ticket

Most dermatologists recommend using sunscreens that have a Sun Protection Factor (SPF) of at least 30. One of the authors wanted

Vikentia [17]

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 : u ≤ 30

Ha : u > 30 ( claim )

95% confidence interval for mean SPF level ( df = 51 )

= mean value ± $(2.0076 + \frac{20.12}{\sqrt{52} } )$

95% confidence interval = ( 28.9485, 40.1515 )

we cannot reject H0

4 0

3 years ago

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 in

Marina86 [1]

Answer:

$\lim_{n\to\infty} (1+ \frac{2}{n} +\frac{1}{n^2})$

And when we apply the limit we got that:

$\lim_{n\to\infty} (1+ \frac{2}{n} +\frac{1}{n^2}) =1$

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:

$\lim_{n\to\infty} \sum_{n=1}^{\infty} i^3$

We can express this formula like this:

$\lim_{n\to\infty} \sum_{n=1}^{\infty}i^3 =\lim_{n\to\infty} [\frac{n(n+1)}{2}]^2$

And using this property we need to proof that: 1^3+2^3+3^3+...+n^3=[n(n+1)/2]^2

$\lim_{n\to\infty} [\frac{n(n+1)}{2}]^2$

If we operate and we take out the 1/4 as a factor we got this:

$\lim_{n\to\infty} \frac{n^2(n+1)^2}{n^4}$

We can cancel $n^2$ and we got

$\lim_{n\to\infty} \frac{(n+1)^2}{n^2}$

We can reorder the terms like this:

$\lim_{n\to\infty} (\frac{n+1}{n})^2$

We can do some algebra and we got:

$\lim_{n\to\infty} (1+\frac{1}{n})^2$

We can solve the square and we got:

$\lim_{n\to\infty} (1+ \frac{2}{n} +\frac{1}{n^2})$

And when we apply the limit we got that:

$\lim_{n\to\infty} (1+ \frac{2}{n} +\frac{1}{n^2}) =1$

3 0

3 years ago

TUZ.U410)

ICE Princess25 [194]

Answer:

Part A: 15

Part B:

Point slope form: $y-400=15(x-5)$

Slope intercept form: $y =15x+325$

Standard Form: $15x-y+325=0$

Part C: $g(x) =15x+325$

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

$x_1 = 5\\x_2 = 10\\y_1 = 400\\y_2 = 475$

Part A: Slope of the function:

$m=\dfrac{y_2-y_1}{x_2-x_1} \\\Rightarrow m = \dfrac{475-400}{10-5}\\\Rightarrow m = \dfrac{75}{5} = 15$

So, slope of the line = 15

It has a positive slope and the function will be increasing with the increasing value of 'x'.

Part B:

Point slope form of a line is given as:

$y-y_1=m(x-x_1)$

Putting $(x_1, y_1)\ as\ (5, 400)$ :

$y-400=15(x-5)$

Slope intercept form:

$y=mx+c$ where c is the intercept.

$y =15x+c$

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

$400=15\times5+c\\\Rightarrow c = 325$

So, the equation in slope intercept form:

$y =15x+325$

Standard form of line:

$Ax+By+C=0$

Rewriting the slope intercept form:

$15x-y+325=0$

Part C:

Using the function notation, putting y = g(x) in slope intercept form:

$g(x) =15x+325$

Part D:

Balance after 12 days = ?

i.e. g(x) = ? at x = 12

Putting x = 12 in $g(x) =15x+325$

$g(12) =15\times 12+325\\\Rightarrow g(12)=505$

7 0

3 years ago

****PLEASE HELP**** Meghan spends 25% more each year for auto insurance than Scott, and together they spend $1237.50 per year. H

s344n2d4d5 [400]

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

6 0

4 years ago

I NEED HELP ASAP PLEASE

kipiarov [429]

Answer:

1679616

Step-by-step explanation:

6*6

36*36*36*36

6 0

3 years ago

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