Rob Is saving to buy a new MP3 player. For every $15 he earns babysitting, he saves $5. On Saturday, Rob
earned $60 babysitting. How much money did he save?
he eamed $60, he saved $

Answer:

[tex]f(x) = \frac{6}{x^2} -8[/tex] or [tex]f(x) = -\frac{6}{x^2} + 4[/tex]

Step-by-step explanation:

Given

[tex](x,y) = (1,-2)[/tex] --- Point

[tex]\int\limits^6_2 {(1 + 144x^{-6})} \, dx[/tex]

The arc length of a function on interval [a,b]:  [tex]\int\limits^b_a {(1 + f'(x^2))} \, dx[/tex]

By comparison:

[tex]f'(x)^2 = 144x^{-6}[/tex]

[tex]f'(x)^2 = \frac{144}{x^6}[/tex]

Take square root of both sides

[tex]f'(x) =\± \sqrt{\frac{144}{x^6}}[/tex]

[tex]f'(x) = \±\frac{12}{x^3}[/tex]

Split:

[tex]f'(x) = \frac{12}{x^3}[/tex] or [tex]f'(x) = -\frac{12}{x^3}[/tex]

To solve fo f(x), we make use of:

[tex]f(x) = \int {f'(x) } \, dx[/tex]

For: [tex]f'(x) = \frac{12}{x^3}[/tex]

[tex]f(x) = \int {\frac{12}{x^3} } \, dx[/tex]

Integrate:

[tex]f(x) = \frac{12}{2x^2} + c[/tex]

[tex]f(x) = \frac{6}{x^2} + c[/tex]

We understand that it passes through [tex](x,y) = (1,-2)[/tex].

So, we have:

[tex]-2 = \frac{6}{1^2} + c[/tex]

[tex]-2 = \frac{6}{1} + c[/tex]

[tex]-2 = 6 + c[/tex]

Make c the subject

[tex]c = -2-6[/tex]

[tex]c = -8[/tex]

[tex]f(x) = \frac{6}{x^2} + c[/tex] becomes

[tex]f(x) = \frac{6}{x^2} -8[/tex]

For: [tex]f'(x) = -\frac{12}{x^3}[/tex]

[tex]f(x) = \int {-\frac{12}{x^3} } \, dx[/tex]

Integrate:

[tex]f(x) = -\frac{12}{2x^2} + c[/tex]

[tex]f(x) = -\frac{6}{x^2} + c[/tex]

We understand that it passes through [tex](x,y) = (1,-2)[/tex].

So, we have:

[tex]-2 = -\frac{6}{1^2} + c[/tex]

[tex]-2 = -\frac{6}{1} + c[/tex]

[tex]-2 = -6 + c[/tex]

Make c the subject

[tex]c = -2+6[/tex]

[tex]c = 4[/tex]

[tex]f(x) = -\frac{6}{x^2} + c[/tex] becomes

[tex]f(x) = -\frac{6}{x^2} + 4[/tex]

You can use the formula for finding the arc length on specified interval on x axis.
The curves whose arc length on the given interval is described are

[tex]f(x) = 6x^{-2} -8[/tex]

and

[tex]f(x) = -6x^{-2} + 4[/tex]

If the function is differentiable in the given interval, then we have:

[tex]s = \int_a^b\sqrt{(1 + (f'(x))^2)}\:dx[/tex]

where s denotes the length of the arc of the given function from x = a to x = b

Using the above formula, as we're already given the arc length, thus,

[tex]\int_a^b\sqrt{(1 + (f'(x))^2)}\:dx = \int_2^6\sqrt{(1 +144x^{-6})}\:dx[/tex]

This gives us

[tex]f'(x) = \pm \sqrt{144x^{-6}} = \pm 12x^{-3}[/tex]

Integrating both sides with respect to x, we get:

[tex]f(x) = \pm \int 12x^{-3}\\\\f(x) = \pm 6x^{-2} + c[/tex]

where c is constant of integration.

Since the curve passes through (1,-2), thus, putting f(x) = -2, x = 1, we get:

[tex]f(x) = \pm 6x^{-2} + c\\-2 = \pm 6 + c\\c = -2 \mp 6 = -8, or ,4[/tex]

c = -8 when we have [tex]f(x) = 6x^{-2} + c[/tex]

c = + 4 when we have [tex]f(x) = -6x^{-2} + c[/tex]

The curves whose arc length on the given interval is described are

[tex]f(x) = 6x^{-2} -8[/tex]

and

[tex]f(x) = -6x^{-2} + 4[/tex]

Learn more about length of the arc of a curve here:

https://brainly.com/question/14319881

Answer:

25 adult tickets and 75 student tickets were sold.

Step-by-step explanation:

Given that the tickets for the school play are $ 7.00 for adults and $ 5.00 for students, and that there were 100 tickets sold generating a total profit of $ 550.00, to determine how many of each were sold the following calculation must be performed:

100 x 5 = 500

550 - 500 = 50

7 - 5 = 2

50/2 = 25

100 - 25 = 75

(25 x 7) + (75 x 5) = X

175 + 375 = 550

Therefore, 25 adult tickets and 75 student tickets were sold.

Answer:

5) $82

6) 300

Step-by-step explanation:

If y=x is your linear regression equation, and if x = temperature and y = $ of ice cream sales, then...

5) x = 82, and given that y=x, then y = $82

6) y = $300, and given that y=x, then x = 300

This doesn't really require algebraic calculation, so I wonder if the linear regression equation obtained from the scatter plot is correct.

Answer:

x = 13

Step-by-step explanation:

We have the expression -26 - 2x = 13 - 5x and are asked to solve for x.

To solve we need to isolate x.

-26 -2x = 13 - 5x

Add 26 to both sides :

-2x = 39 - 5x

Add 5x to both sides :

3x = 39

Divide 3 from both sides :

x = 13

Answer:

Your answer is 140 degree

Hope that this is helpful. Tap the crown button, Like & Follow me

Answer:

≈ 1.77

Step-by-step explanation:

So we are looking for x in 44(x) = 78.

All we have to do is isolate the variable, get x by itself.

Divide 44 by both sides :

[tex]\frac{44x}{44} = \frac{78}{44}[/tex]

[tex]x = 1.772727272723[/tex]

Which can be rounded to ≈ 1.77

Answer:

8 divided by 1/4 = 2

12 divided by 1/4 = 3

more cows were put in the barn

Step-by-step explanation:

8 horses 1/4= 2

12 horses 1/4= 3

angle EFB= 75°= Angles on a straight line add up to 180°

x= 75°= Corresponding angles.

Answer:

See Explanation

Step-by-step explanation:

The question has missing details as no link is provided to the "question 3".

However, I'll give a worked solution on how to calculate the equation of a regression line.

Using the following data:

[tex]\begin{array}{cc}x & {y} & {43} & {99} & {21} & {65} \ \\ {25} & {79} & {42} & {75} \ \end{array}[/tex]

Calculate the equation of the regression line.

The equation is calculated using:

[tex]y = mx + b[/tex]

Where:

[tex]m = \frac{n(\sum xy ) - (\sum x)(\sum y)}{n(\sum x^2) - (\sum x)^2}[/tex]

and

[tex]b = \frac{(\sum y)(\sum x^2) - (\sum x)(\sum xy)}{n(\sum x^2) - (\sum x)^2}[/tex]

So, first we fill in the table with columns x^2, y^2 and xy

[tex]\begin{array}{ccccc}x & {y} & {xy} & {x^2} & {y^2 }& {43} & {99} & {4257} & {1849} & {9801} & {21} & {65} &{1365} &{441} & {4225}\ \\ {25} & {79} & {1975} & {625} & {6241}& {42} & {75} &{3150} & {1764} & {5625}\ \end{array}[/tex]

From the above table.

[tex]\sum x = 43+21+25+42[/tex]

[tex]\sum x = 131[/tex]

[tex]\sum y = 99+65+79+75[/tex]

[tex]\sum y = 318[/tex]

[tex]\sum xy = 4257+1365+1975+3150[/tex]

[tex]\sum xy = 10747[/tex]

[tex]\sum x^2 = 1849 + 441 + 625 + 1764[/tex]

[tex]\sum x^2 = 4679[/tex]

[tex]\sum y^2 = 9801 + 4225 + 6241 + 5625[/tex]

[tex]\sum y^2 = 25892[/tex]

[tex]n =4[/tex]

Solving for m

[tex]m = \frac{n(\sum xy ) - (\sum x)(\sum y)}{n(\sum x^2) - (\sum x)^2}[/tex]

[tex]m = \frac{4 * 10747 - 131*318}{4*4679 -(131)^2}[/tex]

[tex]m = \frac{1330}{1555}[/tex]

[tex]m = 0.86[/tex] --- approximated

Solving for b

[tex]b = \frac{(\sum y)(\sum x^2) - (\sum x)(\sum xy)}{n(\sum x^2) - (\sum x)^2}[/tex]

[tex]b = \frac{318*4679 - 131*10747}{4*4679-131^2}[/tex]

[tex]b = \frac{80065}{1555}[/tex]

[tex]b = 51.49[/tex]

The equation becomes:

[tex]y = mx + b[/tex]

[tex]y = 0.86x + 51.49[/tex]

Apply the above steps and you will arrive at a solution.

Answer:

I believe you are correct

Step-by-step explanation:

hope I am right

Answer: he was a stranger or a hunter

Step-by-step explanation: I think this because it says that they covered him with their muskets and muskets are obviously kind of gun, so it had to be a stranger or hunter.    hope this helped if not sorry

Answer: = -2x-5

Step-by-step explanation:

Answer:

A hope its right!!

Step-by-step explanation:

Have a good day!

Answer:

......

Step-by-step explanation:

Answer

11 inches by 8.5 inches

Step-by-step explanation:

We can use proportions to solve this problem, drawing on top, real life on bottom

1/2 inch           x inches

-------------- = ----------

1 ft                  22ft

Using cross products

1/2 * 22 = x*1

11  =x

11 inches

1/2 inch           x inches

-------------- = ----------

1 ft                  17ft

Using cross products

1/2 * 17 = x*1

8.5 =x

Answer:

200 slices

28.125 bottles and if you need to round it is 28

Step-by-step explanation:

Answer:

113335800

Step-by-step explanation:

solve it step by step

10 x 5/2 is 25

25 x 4533432= 113335800

Answer:

113335800

Step-by-step explanation:

10x5=50

2x4533432=9066864

9066864+50=113335800

Answer:

1325/10000

Explain Step By Step Answer

Answer:

Step-by-step explanation:

From the given information:

sample size n = 100

Since the population is assumed to be normal. then:

[tex]\overline X _{state} - \overline X_{private} \sim N(\overline X _{state}-\overline X _{private, SD^2_{state} + SD^2_private} -2\times Cov(\overline X _{state} - \overline X_{private}})}[/tex]

[tex]\overline X _{state} - \overline X_{private} \sim N(4.5-4.1, 0.8^2 + 0.2^2 -2\times 0})}[/tex]

[tex]\overline X _{state} - \overline X_{private} \sim N(0.4, 0.68})}[/tex]

The test statistics:

[tex]z = \dfrac{\overline X_{state} - \overline X_{private} }{ \sqrt{\dfrac{\sigma^2_{state}}{n } + \dfrac{\sigma^2_{private}}{n } } }[/tex]

[tex]z = \dfrac{0.4 }{ \sqrt{\dfrac{1.5811^2}{100 } + \dfrac{1^2}{100 } } }[/tex]

z = 2.138

Using the z tables;

P-value = (Z> 2.138)

P-value = 1 - (Z<2.138)

P-value = 1 - 0.9837

P-value = 0.0163

Decision rule: to reject the null hypothesis if the p-value is less than the significance level

Conclusion: We reject the null hypothesis and conclude that there is enough evidence to conclude that the average time it requires for the students to graduate from a private university is lesser than that of the time it takes such student to graduate from the California state university system.

Answer:      B=1.75

jhgvfcdszdftgyhujikolp

Answer:

1.75

Step-by-step explanation:

Answer:

= 9x−7

Step-by-step explanation:

=(2)(3x)+(2)(−5)+3x+3

=6x+−10+3x+3

Combine Like Terms:

=6x+−10+3x+3

=(6x+3x)+(−10+3)

=9x+−7

Answer:

57 for the way you wrote it. -10 if you write it backwards.

Step-by-step explanation:

Answer:

Alex I think

Step-by-step explanation:

Answer:

The scale factor would be 3

Step-by-step explanation:

do 12/4 and get 3