Kaitlyn uses conkainers shaped like a cylinder to catch rainwater. The dimensions of the containers are 12 ft in diameter and 9 ft in height. How much
rainwater can she collect if she has 6 containers?

Given :

Sum of all angles in a triangle = 180°

Which means :

[tex] = \tt61 + 15x - 1 = 180[/tex]

[tex] =\tt 61 - 1 + 15x = 180[/tex]

[tex] =\tt 60 + 15x = 180[/tex]

[tex] = \tt15x = 180 - 60[/tex]

[tex] =\tt 15x = 120[/tex]

[tex] = \tt \: x = \frac{120}{15} [/tex]

[tex] =\tt x = 18[/tex]

Measure of angle 15x-1 :

[tex] = \tt15 \times 8 - 1[/tex]

[tex] =\tt120 - 1[/tex]

[tex] =\tt 119[/tex]

Thus, the measure of angle 15x-1 = 119°

Let us place 8 in the place of x to see if we have found out the correct measure of the angles :

[tex] = \tt40 + 21 + 119 = 180[/tex]

[tex] = \tt61 + 119 = 180[/tex]

[tex] =\tt 180 = 180[/tex]

Since the measures of all the angle sum up to form 180°, we can conclude that we have found out the correct measure of each of the angles.

Therefore, the value of x = 8

[tex]\boxed{\color{plum}\bold{x = 8}}[/tex]

Answer:

1a. 3y = 18

1b. y + 7 = 18

1c. 2y + 4 = 18

Step-by-step explanation:

In each case, let's take the red boxes to be constant why the the green boxes represents the variable, y.

Thus,

1a. There are only 3 green boxes which gives us 18, therefore, the equation that expresses this would be:

3y = 18

1b. We have 7 red boxes which represents the constant, 7.

We also have 1 green box which represents the variable, y. Therefore, the equation that expresses this would be:

y + 7 = 18

1c. We have 4 red boxes = 4

We have 2 green boxes = 2y

Therefore, we would have:

2y + 4 = 18

Answer:

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

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Answer:

all you have to do is graph i dont see what i can help you with im

sorry

Step-by-step explanation:

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: positive force → balanced force → negative force

Step-by-step explanation: I just did it

Answer:

A

Step-by-step explanation:

edg

Answer:

-4 5/12

Step-by-step explanation:

-23/3 + (-11/2) + 35/4

Find a common denominator (12).

-92/12 + (-66/12) + 105/12

Reform the equation to have this as a single fraction.

(-92 + (-66) + 105)/12

Subtract 66 from -92 to get -158.

(-158 + 105)/12

Add 105 to -158 to get -53.

-53/12

Convert into a mixed number by dividing by 12.

-4 5/12 (Choice A) is your answer.

Answer:

The scale factor would be 3

Step-by-step explanation:

do 12/4 and get 3

Answer: A

Step-by-step explanation:

26/400 = x/56,000

6.5% of the products are defective so you can just use that information to find the total defective.

.065 x 56,000 = 3,640

Answer:

3,640

Step-by-step explanation:

First find the percent of products that were defective out of 400.

26 ÷ 400 = 0.065 or 6.5%

Then find 6.5% of 56,000.

56,000 × .065 = 3640

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:

I believe you are correct

Step-by-step explanation:

hope I am right

perimeter = 72 cm

width = x

length = x+8

perimeter of rect. = 2(l+b)

2(x+x+8) = 72

2(2x+8) = 72

4x + 16 = 72

4x = 56

x = 56|4

x= 14

hence width is 14 so ,length will

14+ 8 = 22

hope it helps and your day will full of happiness

Answer:

So I think its either 75 or 3

Step-by-step explanation:

for 80% of 15 its 3. 20% is fifteen. 20 times 5 is 100 so I did 15 times 5 to get the answer 75. I hope this helps!

Answer:

=12r2+5

Step-by-step explanation:

3² + (12r2) - 16 / 4

9+12r2+−4

Combine like terms

(12r2)+(9+−4)

12r2+5

Answer:

false

Step-by-step explanation:

I assume this is a true/false question.

The answer would be 'false'.

For 3 segments to make a triangle, each single side must be LESS than the sum of the other two.

Here, that is not the case. The '10' side is not less than 3+7.

Answer:

35

Step-by-step explanation:

Hope this helps

==========================================================

Explanation:

There are currently 8,427 trees. Triple this value to get 3*8427 = 25,281

Add this result onto the previous number of trees to get 25,281+8,427 = 33,708

-----------

An alternative approach:

if we started off with x number of trees, and then added on three times as much, then we add on 3x more trees. This gets us x+3x = 4x trees total.

In this case, x = 8427, so that leads to 4*x = 4*8427 = 33,708

Answer:

200 slices

28.125 bottles and if you need to round it is 28

Step-by-step explanation:

Answer:

x = 12

y = 12√3

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:

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

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:

[tex](-6,\, -5)[/tex] is outside the circle of radius of [tex]12[/tex] centered at [tex](3,\, 3)[/tex].

Step-by-step explanation:

Let [tex]J[/tex] and [tex]r[/tex] denote the center and the radius of this circle, respectively. Let [tex]F[/tex] be a point in the plane.

Let [tex]d(J,\, F)[/tex] denote the Euclidean distance between point [tex]J[/tex] and point [tex]F[/tex].

In other words, if [tex]J[/tex] is at [tex](x_j,\, y_j)[/tex] while [tex]F[/tex] is at [tex](x_f,\, y_f)[/tex], then [tex]\displaystyle d(J,\, F) = \sqrt{(x_j - x_f)^{2} + (y_j - y_f)^{2}}[/tex].

Point [tex]F[/tex] would be inside this circle if [tex]d(J,\, F) < r[/tex]. (In other words, the distance between [tex]F\![/tex] and the center of this circle is smaller than the radius of this circle.)

Point [tex]F[/tex] would be on this circle if [tex]d(J,\, F) = r[/tex]. (In other words, the distance between [tex]F\![/tex] and the center of this circle is exactly equal to the radius of this circle.)

Point [tex]F[/tex] would be outside this circle if [tex]d(J,\, F) > r[/tex]. (In other words, the distance between [tex]F\![/tex] and the center of this circle exceeds the radius of this circle.)

Calculate the actual distance between [tex]J[/tex] and [tex]F[/tex]:

[tex]\begin{aligned}d(J,\, F) &= \sqrt{(x_j - x_f)^{2} + (y_j - y_f)^{2}}\\ &= \sqrt{(3 - (-6))^{2} + (3 - (-5))^{2}} \\ &= \sqrt{145} \end{aligned}[/tex].

On the other hand, notice that the radius of this circle, [tex]r = 12 = \sqrt{144}[/tex], is smaller than [tex]d(J,\, F)[/tex]. Therefore, point [tex]F[/tex] would be outside this circle.

Answer:

outside the circle

Step-by-step explanation:

khan

Answer:

14

Step-by-step explanation:

x = -14

and

y = - x

so you put the -14 instead of x

y = --14

y = +14

Answer:

Step-by-step explanation:

65

Answer:

True

Step-by-step explanation:

They are the same dimensions

Answer:

I think its true because there both the same shape and dimension