Find the height of a right circular cylinder whose height is equal to its base radius length and its volume is 64 π cm³​

The linear regression equation for the data is given as follows:

y = 0.55x + 0.3.

The prediction of Adam's shoe size when he is 14-years-old is given by the following option:

A. 8.

The equation for the line of fit is obtained inserting the points of the data-set into a linear regression calculator.

From the table, the points are given as follows:

(6,3), (8, 4.5), (10,5), (12, 7.5).

Inserting these points into a calculator, the regression equation predicting the shoe size at an age of x is given as follows:

y = 0.55x + 0.3.

Then the estimate for the shoe size at an age of 14 is found when x = 14, hence:

y = 0.55(14) + 0.3 = 8.

Meaning that option A is correct.

More can be learned about linear regression at brainly.com/question/29613968

#SPJ1

Answer:

17

Step-by-step explanation:

You need to use the formula for Arithmetic Sequences.

[tex]a_{n}=a_{1}+(n-1)d[/tex]

You need to plug in the value for [tex]a_{1}[/tex] which is just the first value in your sequence. As well as [tex]n[/tex] which is the term your looking for, in this case it's 48. Lastly [tex]d[/tex] which is the amount that the pattern is increasing or decreasing by. If the sequence is increasing then the [tex]d[/tex] is positive but if the sequence is decreasing then the [tex]d\\[/tex] is negative.

Using the AAS rule.

ST ≅ UT (given)

∠SRT≅∠UVT (given)

∠RTS ≅ ∠UVT (opposite angles)

∠RST ≅ ∠VUT (AAS rule)

Proved.

It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.

We have,

AAS rule:

When two angles and a non-included side of one triangle are equal to two angles and a non-included side of another triangle, then the triangles are congruent.

From the figure we have,

ST ≅ UT (given)

∠SRT≅∠UVT (given)

∠RTS ≅ ∠UVT (opposite angles)

∠RST ≅ ∠VUT (AAS rule)

Thus,

∠RST is congurent to ∠VUT using the AAS rule.

Learn more about triangles here:

https://brainly.com/question/25950519

#SPJ1

Answer:

Step-by-step explanation:

I'm sorry, but I'm not sure what you're asking. It's not clear to me what you mean by "point (3'6)" or "(3-5)." Could you please provide more information or clarify your question

All the possible lengths for the third side lie between 13 to 35 feet.

What is a triangle Inequality Theorem?

In Euclidean geometry, the theorem is that the sum of any two sides of a triangle is greater than or equal to the third side; in symbols, a + b ≥ c. In essence, the theorem states that the shortest distance between two points is a straight line.

The Triangle Inequality theorem states that the sum of any 2 sides of a triangle must be greater than the measure of the third side.

So, a difference of two sides <x< sum of two sides, will give you the possible length of a triangle.

Therefore, 24 − 11 < x < 24 + 11

13 < x < 35 is the possible length of the third side of a triangle.

13 < x < 35 satisfies the triangle inequality theorem.

Hence, all the possible lengths for the third side lie between 13 to 35 feet.

To learn more about the Triangle Inequality theorem, visit:

https://brainly.com/question/1163433

#SPJ1

If Group 1 trees produce 25 percent more coconuts than Group 2, proportionately, Group 2 trees produce 120 coconuts.

Proportion refers to the two ratios equated to each other.

Proportion shows how much quantity or value is contained in another.

We depict proportions using fractional values, such as fractions, decimals, and percentages.

The number of coconuts produced by Group 1 trees = 150

The percentage by which Group 1 trees produce more than Group 2 = 25%

Let Group 1's production compared to Group 2's = 1.25 (100% + 25%)

Let Group 2's production = 100% = 150/125 x 100

= 120 coconuts

Thus, Group 2 trees would produce 120 coconuts compared to Group 1 trees that produced 150, which was proportionately, 25% more.

Learn more about proportions at https://brainly.com/question/1496357

#SPJ1

The quadratic equation (x + 1)² / 46.667 - (y - 5)² / 56 = 1 represents the hyperbola in standard form.

In this question we find the equation of a hyperbola in general form, that is, a quadratic equation of the form A · x² + B · y² + C · x + D · y + E = 0, and we need to obtain the standard form of the hyperbola:

(x - h)² / a² - (y - k)² / b² = 1

Where:

We can switch from general form into standard form by completing the square, an application of algebra properties:

6 · x² - 5 · y² + 12 · x + 50 · y - 149 = 0

(6 · x² + 12 ·  x) - (5 · y² - 50 · y) = 149

6 · (x² + 2 · x) - 5 · (y² - 10 · y) = 149

6 · (x² + 2 · x + 1) - 5 · (y² - 10 · y + 25) = 149 + 6 + 125

6 · (x + 1)² - 5 · (y - 5)² = 280

(x + 1)² / 46.667 - (y - 5)² / 56 = 1

The equation of the hyperbola in standard form is (x + 1)² / 46.667 - (y - 5)² / 56 = 1.

To learn more on hyperbolas: https://brainly.com/question/7098764

#SPJ1

There are no local extrema since there isn't any x value that causes the first derivative to be equal to 0.

z = 5x + 3 y

Discover the function's first derivative.

By applying the Sum Rule, the derivative of 5 x + 3 y with respect to x is d d x [ 5 x ] + d /d x [ 3 y ].

d/d x [ 5 x] + d /d x [ 3 y]

Analyze d /d x [ 5 x ].

Tap to take other actions...

5 + d /d x [ 3 y]

Because 5 is independent of x, its derivative is 5 d d x [ x ] since 5 is constant with respect to x.

5 d/ d x [ x ] + d /d x [ 3 y]

The Power Rule, which asserts that d d x [ x n ] is n x n 1 where n = 1. 5 1 + d d x [ 3 y ] is a method of differentiation, says that you should differentiate.

Subtract 1 from 5 and multiply the result by 5 + d /d x [ 3 y ]

The Constant Rule can be used to differentiate.

Because 3 y is constant in relation to x, its derivative in relation to x is 0 (5 + 0).

Subtract 5 from 0 to get 5.

Since 5 is constant in relation to x, its derivative in relation to x is 0 (f " (x ) = 0).

By setting the derivative to 0, you can solve the problem and discover the function's local maximum and lowest values.

5 = 0

There are no local extrema since there isn't any x value that causes the first derivative to be equal to 0.

To Learn more About first derivative refer to:

https://brainly.com/question/10023409

#SPJ1

The parameters of the absolute value function g(x) = -|2x| + 5 are given as follows:

The standard definition of the absolute value function is given as follows:

f(x) = a|bx + c| + d.

The meaning of each parameter is given as follows:

In this problem, the function is defined as follows:

g(x) = −|2x| + 5.

Compared with the standard absolute value function, the values of these parameters are given as follows:

a = -1, b = 2, c = 0, d = 5.

More can be learned about the absolute value function at https://brainly.com/question/3381225

#SPJ1

Answer:

Ordered pair: (- 8, 1)

x = - 8,y = 1

Step-by-step explanation:

[tex]1.5x-9y=-21\\-1.5x-3y=9[/tex]

Add together.

- 12y = - 12

y = 1

1.5x - 9(1) = - 21

1.5x - 9 = - 21

1.5x = - 12

x = - 8

when me I would say the 1st one but who knows lol

The graph of the function C = 49 + 20m is a discrete function and is represented by vertical lines for whole numbered values of 'm'.

An equation is written in the form of variables and constants separated by the operation of multiplication and division,

An equation states that terms in different forms on both sides of the equality sign are equal.

Multiplication and division do not separate the terms of an equation.

Given, That no. of months is a whole month and hence it is discrete as it can not take decimal values.

The graph of the equation C = 49 + 20m would have vertical lines at each whole value of 'm'.

learn more about discrete functions here :

https://brainly.com/question/28386066

#SPJ1

Answer:

Mr. Conners will use 144 fence posts.

Step-by-step explanation:

Given question is incomplete; please find the question attached herewith.

As we can see from the attachment, Mr Corner's yard is in the rectangular shape.

Total distance around the yard = Perimeter of a rectangle = 2(Length + width)

Length of the yard = 330 ft

And width of the yard = 102 ft

So perimeter of the yard = 2(330 + 102                                         = 864 f

Mr. Conners wants to put a fence post at every 6 feet.

So number of posts used =

                                   =

                                         = 144

The system of equation is 45x+75y=1455.

The number of small boxes is 14 and large boxes is 11.

In the given question,

The paper will be shipped in small boxes and large boxes.

Each small box of paper weights 45 pounds.

Each large box of paper weights 75 pounds.

There were 3 more small boxes shipped than large boxes and the total weight of all boxes was 1455 pounds.

We have to write a system of equations that could be used to determine the number of small boxes shipped and the number of large boxes shipped.

We also have to define the variables that we use to write the system.

Let x be the number of small boxes.

Let y be the number of large boxes.

There were 3 more small boxes shipped than large boxes.

So x = y+3

Weight of x number of small boxes = 45x

Weight of y number of small boxes = 75y

Total weight of boxes = 1455

So; 45x+75y=1455

Now putting the value of x to this system of equation

45(y+3)+75y=1455

45y+135+75y=1455

120y+135=1455

Subtract 135 on both side, we get

120y=1320

Divide by 120 on both side, we get;

y=11

Now putting the value of y in x=y+3

x = 14

Hence, the number of small boxes is 14 and large boxes is 11.

To learn more about solving the system of equation link is here

brainly.com/question/1440592

#SPJ4

Answer:

Ax + By = C is standard form.

Step-by-step explanation:

It is standard form because slope intercept is y = mx + b and point slope is y-y₁=m(x-x₁)

Hope this helps

Answer:

Standard form.

Step-by-step explanation:

y=mx + b is the slope-intercept form.

The new coordinates are X'(8, 7), Y'(5, -2), Z'(7, 0).

The coordinates of the triangle are given as

X(-7, 8), Y(2, 5), Z(0,7).

The rotation is given as r(90,0) XYZ

This means that

We have (x, y) ⇒ (y, -x)

Substitute X(-7, 8), Y(2, 5), Z(0,7) in (x, y) ⇒ (y, -x)

So, we have

X'(8, 7), Y'(5, -2), Z'(7, 0).

Hence, the coordinates of the image are X'(8, 7), Y'(5, -2), Z'(7, 0).

Read more about rotation at

brainly.com/question/12508456

#SPJ1

Answer:

A.124

Step-by-step explanation:

Because it's like that

Answer:

A. 124

Step-by-step explanation:

<3

By ASA, the two triangles are congruent.  They share 2 angles and the line in between them.

Answer:

y=x-1

Is the line equation.

Step-by-step explanation:

As we know that general equation of line is given by

y=mx + c

M is the slope and C is is Y intercept

Know m = 1 and point (x,y) as (5,4)

So plug in the values and solve for c

4=1*(5)+c

c=-1

So, equation of the line is

y=x-1

Answer:

If Doug has $100,000 in a savings account that earns 13% interest per year and the interest is not compounded, then after four years he will earn $52,000 in interest. This is because 13% of $100,000 is $13,000, and since the interest is not compounded, this amount will remain constant for each year. Therefore, after four years Doug will earn a total of $13,000 + $13,000 + $13,000 + $13,000 = $52,000 in interest.

In general, if a savings account earns x% interest per year and the initial amount in the account is y dollars, then after n years the account will earn n * (x/100) * y dollars in interest. For example, if the interest rate is 13% and the initial amount is $100,000, then after four years the account will earn 4 * (13/100) * $100,000 = $52,000 in interest.

Step-by-step explanation:

Answer: He will earn about $3,756.66

Step-by-step explanation:

Answer:

81

Step-by-step explanation:

81 * 1 = 81

If the 81x1 is = 81 * 1 then it should be 81.

If its not I will redo my answer.

Answer:

81 x 1 is 81

81

x 1

81

On the graph, the graph equation has been drawn, crossing the y and x-axis points (0, 10) and (20, 0).

To calculate the slope m and the y-intercept, write the equation y = MX + b.

The slope and y-intercept can then be used to graph the equation (0, b).

The three primary forms of linear equations are point-slope, standard, and slope-intercept.

So, the equation is as follows:

8x+16y=160

Now,

The short sleeves are symbolized by an x.

y is a symbol for the long sleeves.

The equation must now be plotted as follows:

(Please see the graph below.)

As a result, the y and x-axis points (0, 10) and (20, 0) intersected by the equation.

Therefore, on the graph, the graph equation has been drawn, crossing the y and x-axis points (0, 10) and (20, 0).

Know more about graph equations here:

brainly.com/question/29464771

#SPJ1

To find the side x, we can use the Law of Cosines, which states that in any triangle, the square of the length of any side is equal to the sum of the squares of the lengths of the other two sides minus twice the product of those two sides and the cosine of the angle between them. In symbols, if a, b, and c are the lengths of the sides of a triangle, and C is the measure of the angle opposite the side of length c, then we have the equation:

c^2 = a^2 + b^2 - 2ab * cos(C)

In our case, we are given the lengths of two sides (a = 10 and b = 6) and the measure of the angle opposite the unknown side (C = 0 degrees), so we can plug those values into the equation to solve for c:

x^2 = 10^2 + 6^2 - 2 * 10 * 6 * cos(0)

x^2 = 100 + 36 - 120

x^2 = 16

x = sqrt(16) = 4

Therefore, the length of the side x is 4.

To find the indicated angle, we can use the Law of Sines, which states that in any triangle, the ratio of the length of a side to the sine of the angle opposite that side is constant. In symbols, if a, b, and c are the lengths of the sides of a triangle, and A, B, and C are the measures of the angles opposite those sides, then we have the equations:

a/sin(A) = b/sin(B) = c/sin(C)

In our case, we are given the lengths of two sides (a = 10 and c = 12) and the measure of the angle opposite one of those sides (A = 0 degrees), so we can use those values to solve for the measure of the angle opposite the other side:

10/sin(0) = 12/sin(C)

sin(C) = 0

Therefore, the measure of the angle C is 0 degrees.

this is original answer

To find the side x, we can use the Law of Cosines, which states that in any triangle, the square of the length of any side is equal to the sum of the squares of the lengths of the other two sides minus twice the product of those two sides and the cosine of the angle between them. In symbols, if a, b, and c are the lengths of the sides of a triangle, and C is the measure of the angle opposite the side of length c, then we have the equation:

c^2 = a^2 + b^2 - 2ab * cos(C)

In our case, we are given the lengths of two sides (a = 10 and b = 6) and the measure of the angle opposite the unknown side (C = 0 degrees), so we can plug those values into the equation to solve for c:

x^2 = 10^2 + 6^2 - 2 * 10 * 6 * cos(0)

x^2 = 100 + 36 - 120

x^2 = 16

x = sqrt(16) = 4

Therefore, the length of the side x is 4.

To find the indicated angle, we can use the Law of Sines, which states that in any triangle, the ratio of the length of a side to the sine of the angle opposite that side is constant. In symbols, if a, b, and c are the lengths of the sides of a triangle, and A, B, and C are the measures of the angles opposite those sides, then we have the equations:

a/sin(A) = b/sin(B) = c/sin(C)

In our case, we are given the lengths of two sides (a = 10 and c = 12) and the measure of the angle opposite one of those sides (A = 0 degrees), so we can use those values to solve for the measure of the angle opposite the other side:

10/sin(0) = 12/sin(C)

sin(C) = 0

Therefore, the measure of the angle C is 0 degrees.

The height of the flagpole in this problem is calculated as follows:

12.9 feet.

The height of the flagpole in this problem is obtained using similar triangles, as shown by the image given at the end of the answer.

Similar triangles are used because the equivalent sides have proportional side lengths.

From the image given at the end of the answer, the equivalent sides of each triangle are given as follows:

Then the proportional equation is given as follows:

8/20 = 5.1667/x

Applying cross multiplication, the height of the flagpole is calculated as follows:

8x = 20 x 5.1667

x = 20 x 5.1667/8

x = 12.9 feet.

More can be learned about similar triangles at brainly.com/question/11920446

#SPJ1

Answer:

=(3,-4)

Step-by-step explanation:

The product of the polynomials (4 + 2x³)(4 − 2x³) is 16 - 4x⁶

From the question, we have the following parameters that can be used in our computation:

Polynomial products: (4 + 2x3 )(4 − 2x3 )

Rewrite the above product properly

So, we have the following representation

Polynomial products = (4 + 2x³)(4 − 2x³)

Using the difference of two squares identity

We have the following representation

Polynomial products = (4)² - (2x³)²

Evaluate the exponents

Polynomial products = 16 - 4x⁶

Hence, the product is 16 - 4x⁶

Read more about polynomials at

https://brainly.com/question/17517586

#SPJ1

Domain - the set of possible x-coordinates of a function.

Range - the set of possible y-coordinates of a function.

Domain is:

Range is:

This is not a function as it fails the vertical line test.

Domain is:

Range is:

This is not a function as it fails the vertical line test.

Domain is:

Range is:

This is not a function as it fails the vertical line test.

Domain is:

Range is:

This is a function as it passes the vertical line test.

The solution is 42 : 98 : 105

The ratio of the number of songs Gerald , Harold and James downloaded is in the ratio 42 : 98 : 105

What is Proportion?

The proportion formula is used to depict if two ratios or fractions are equal. The proportion formula can be given as a: b::c : d = a/b = c/d where a and d are the extreme terms and b and c are the mean terms.

Given data ,

Let the ratio of number of songs downloaded by Gerald and Harold be =

3 : 7

Let the ratio of number of songs downloaded by Harold and James be =

14 : 15

So , the number of songs downloaded by Gerald = 3x

The number of songs downloaded by Harold = 7x

And ,

The number of songs downloaded by Harold = 14y

The number of songs downloaded by James = 15y

So , substituting the values in the equation , we get

7x = 14y

x = 2y

And ,

The number of songs downloaded by Gerald = 3 x 14 z

The number of songs downloaded by Gerald = 42z

The number of songs downloaded by Harold = 7 x 14z

The number of songs downloaded by Harold = 98z

The number of songs downloaded by James = 7 x 15z

The number of songs downloaded by James = 105z

So , the ratio of the number of songs Gerald , Harold and James downloaded = 42z : 98z : 105z

On simplifying the proportion , we get

The ratio will be = 42 : 98 : 105

Hence , The ratio of the number of songs Gerald , Harold and James downloaded is in the ratio 42 : 98 : 105

To learn more about proportion click :

https://brainly.com/question/7096655

#SPJ1

Answer:

D) 4, H) 14

Step-by-step explanation:

D) both angles form a linear pair so 101-5x + 2x+70 = 180

Simplify

171-3x = 180

-3x = 9

x = -3

H) 11x-23 = 41 + 90 because they are opposite angles

Simplify

11x = 154

x = 14