What is a factor tree for 216?

The length of the diagonal is 5 in. The solution has been obtained by using the pythagoras theorem.

What is Pythagoras theorem?

The Pythagorean Theorem states that the square of the hypotenuse side of a right-angled triangle is equal to the sum of the squares of its other two sides.

We are given that the figure is a 12 in by 12 in square.

So, the lengths of the triangle come out to be 3 and 4.

Now, using the pythagoras theorem,

⇒Hypotenuse² = 3² + 4²

⇒Hypotenuse² = 9 + 16

⇒Hypotenuse² = 25

⇒Hypotenuse = 5

Hence, the length of the diagonal is 5 in.

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The step by step process of making the  8 by 10 frame consists of gather materials, measure the size and cut and screw it.

The first step in making a frame is to gather your materials. You'll need wood or other materials to construct the frame, as well as some tools like a saw and a hammer or nail gun.

To calculate the size of your frame, you'll need to add some extra length and width to the dimensions of your photo.

Once you have your dimensions, you'll need to cut your wood or other materials to size. You'll need four pieces of wood to create the frame - two longer pieces for the sides, and two shorter pieces for the top and bottom.

Next, you'll need to assemble your frame using nails or screws. Make sure the corners are flush and that the frame is square. You can use a carpenter's square to check your angles and make sure everything is aligned correctly.

Finally, you'll need to finish your frame. This could involve painting or staining the wood, adding decorative elements like beads or embellishments, or simply leaving the wood as-is for a more natural look. Once your frame is complete, you can insert your photo or artwork and enjoy your new creation!

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Answer:

The correct answer is (A) 96 and 84. When y is directly proportional to x, it means that the ratio of y to x remains constant. In this case, when x=9, y=108, which means that the ratio of y to x is 108/9. Since the ratio is constant, we can use that ratio to find the values of y when x=8 and x=7. When x=8, y = (108/9)x8 = 96 and when x=7, y = (108/9)x7 = 84.

Data can be divided on the basis of qualitative nature into two types as follows:

Thus, it is clear that nominal data can not be ranked or ordered but ordinal data are the type of qualitative data that are categorised and then ranked or ordered.

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Step-by-step explanation:

yes, they are, because both triangles have the same 3 angles :

the right angle = 90°

65°

25°

now, the side lengths can be different, but because of the same angles, the ratio between the corresponding side lengths will be the same for all sides (e.g. if one pair of sides has the scaling factor of 3 from the smaller to the larger triangle, then the other pairs will also have the same scaling factor 3).

that is the difference between equivalent and similar : for "equivalent" also the side lengths must be the same.

for "similar" only the angles need to be the same.

Answer: x = {41,42,43...}

Step-by-step explanation:

0.25x - 4 > 6

0.25x > 6 + 4

0.25x > 10

x > 10/0.25

x > 40

The possible values of x are {41,42,43...}

The size for a TV is determined as the diagonal length of the Television.

The Televisions that we see in our daily life are mostly of the rectangular shape.

A rectangular shape is a shape that has 4 sides in it, the opposite sides of the rectangular are parallel and equal. Two pairs of equal sides are formed in this type of shape.

If we connect the vertices that are directly opposite to each other than it is known as the diagonal of the rectangle . Often we see that the TV is of 32'' or 64''. This only means that the diagonal length of the TV is 32'' or 64''. This is how we measure the size of the TV.

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The y-coordinate for the solution to the system of equations is 6.

Equation is a physical and mathematical statement the describing physical phenomenon the relationship between different physical quantity typically consist of variable simple presenting physical quantity and then it personal variable maybe pointed search is the energy.

The y-coordinate for the solution to the system of equations is 6. This is calculated by substituting the given y-value (2/3) into the equation -x+3y=9 and solving for x. Specifically, -x+3(2/3) = 9, which reduces to -x = 3. Therefore, x = -3 and substituting this value into the first equation yields 3y = 9, which simplifies to y = 3. Therefore, the y-coordinate for the solution to the system of equations is 6.

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Therefore, the equations that represent circles with a diameter of 12 units and a center on the y-axis are: x² + (y - 3)²=36 and x² + (y + 8)²=36.

In mathematics, an equation is a statement that asserts the equality of two expressions. It consists of two expressions separated by an equals sign (=). The expression on the left side of the equals sign is called the left-hand side (LHS), and the expression on the right side of the equals sign is called the right-hand side (RHS). Solving an equation means finding the value of the variable that makes the equation true. I

Here,

A circle with diameter 12 units and center on the y-axis has its center at (0, c), where c is a constant. The radius of the circle is half the diameter, which is 6 units.

The equation of a circle with center (0, c) and radius r is given by:

x² + (y - c)² = r²

Substituting r = 6 and simplifying, we get:

x² + (y - c)² = 36

The only two equations among the options given that match this form are:

x² + (y - 3)² = 36 (center at (0,3))

x² + (y + 8)² = 36 (center at (0,-8))

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Answer:

35.35 seconds

Step-by-step explanation:

The volume of the cylindrical glass can be calculated as:

V = πr²h

where r is the radius (half of the diameter), h is the height, and π is the mathematical constant π (approximately 3.14).

Since the diameter is 3 inches, the radius is 1.5 inches. The height is 10 inches. Therefore, the volume of the glass is:

V = π(1.5)²(10) ≈ 70.69 cubic inches

To fill the glass 50%, we need half of the volume:

V/2 ≈ 35.35 cubic inches

The faucet dispenses water at a rate of 1 cubic inch per second, so the time it takes to fill the glass 50% is:

t = (V/2) / (1 cubic inch per second) ≈ 35.35 seconds

Therefore, it takes approximately 35.35 seconds to fill the glass 50%. Rounded to two decimal places, the answer is 35.35 seconds.

Trigonometric functions derivative is a method for calculating how quickly trigonometric functions change in relation to a variable angle.

Differentiation of trigonometric functions refers to the process of determining a trigonometric function's derivatives. In other words, finding the rate of change of the function with respect to the variable is what is meant by the differentiation of trigonometric functions. There are differentiation formulas for the six trigonometric functions that can be applied to a variety of derivative application issues.

The sine (sin x), cosine (cos x), tangent (tan x), cotangent (cot x), secant (sec x), and cosecant are the six fundamental trigonometric functions (cosec x).

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The average rate of change of the cost from the 6th month to the 8th month is 1.

Rate of change is a major of house quickly one quantity change in relation to another it is parisu of the changing 122 the changing another quantity over specified time period.


The average rate of change from the 6th month to the 8th month can be calculated by taking the difference between the 6th and 8th month's cost and dividing it by the number of months between the two. In this case, the difference is 8.5 - 6.5 = 2, and the number of months is 2, so the average rate of change is 2/2 = 1. Therefore, the average rate of change of the cost from the 6th month to the 8th month is 1.

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Answer:

The maximum value of the function is 9/4.

The minimum value of the function is -1/4.

On the interval (0, pi/2), the function is strictly increasing.

The range of the function is [-1/4, 9/4].

Given function is:

y=5/4sin x + 1

:

The correct that represents the total amount of popcorn, in quarts, produced by x scoops of unpopped kernels

If 3 scoops of unpopped kernels produce 6 quarts of popcorn, we can find the rate of popcorn produced per scoop by dividing the total popcorn by the number of scoops:

6 quarts popcorn / 3 scoops = 2 quarts popcorn per scoop

We can use this rate to fill out the table for any number of scoops:

Number of scoops      Total amount of popcorn (in quarts)

1                                                             2

2                                                            4

3                                                            6

4                                                            8

5                                                            10

...                                                            ...

x                                                            2x

Therefore, the correct table that represents the total amount of popcorn, in quarts, produced by x scoops of unpopped kernels is:

Number of scoops    Total amount of popcorn (in quarts)

1                                                     2

2                                                    4

3                                                    6

4                                                    8

5                                                     10

...                                                     ...

x                                                      2x

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The mean of the distribution of  [tex]\bar{x}[/tex] and [tex]\bar{p}[/tex] are [tex]\mu_{\bar{x}}=\mu[/tex] and [tex]\mu_{\bar{p}}=p[/tex]. The standard deviation of the distribution of  [tex]\bar{x}[/tex] and [tex]\bar{p}[/tex] are [tex]\sigma_{\bar{x}}=\frac{\sigma}{\sqrt{n}}[/tex] and [tex]\sigma_{\bar{p}}=\sqrt{\frac{p(1-p)}{n}}[/tex]. So a suitable option is option D.

A distribution is the collection of all potential values for terms that reflect specified events in statistics. It is possible to calculate the expected value or mean of a statistical distribution by integrating the product of the variable's probability and the distribution's definition of that probability. This is represented by the symbol μ.

The term "standard deviation" refers to a measurement of the data's dispersion from the mean. A low standard deviation implies that the data are grouped around the mean and a higher standard deviation shows that the data are more dispersed. This is represented by the symbol σ.

Here, the expected value for [tex]\bar{x}[/tex] is written as    [tex]\mu_{\bar{x}}=\mu[/tex] , and the standard deviation for [tex]\bar{x}[/tex] is written as [tex]\sigma_{\bar{x}}=\frac{\sigma}{\sqrt{n}}[/tex]. Similarly, the expected value for [tex]\bar{p}[/tex] is written as [tex]\mu_{\bar{p}}=p[/tex], and the standard deviation for [tex]\bar{p}[/tex] is written as  [tex]\sigma_{\bar{p}}=\sqrt{\frac{p(1-p)}{n}}[/tex]. Therefore, the correct option for this will be D.

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The complete question is -

Which answer shows

i. The mean of the distribution of [tex]\bar{x}[/tex].

ii. The standard deviation of the distribution of [tex]\bar{x}[/tex].

iii. The mean of the distribution of [tex]\bar{p}[/tex].

iv. The standard deviation of the distribution of [tex]\bar{p}[/tex].

A.

i. [tex]\mu_{\bar{x}}=np[/tex]

ii. [tex]\sigma_{\bar{x}}=\sqrt{\frac{p(1-p)}{n}}[/tex]

iii. [tex]\mu_{\hat{p}}=np[/tex]

iv. [tex]\sqrt{np(1-p)}[/tex]

B.

   i. [tex]\mu_{\hat{p}}=np[/tex]

ii. [tex]\sigma_{\bar{x}}=\sqrt{np(1-p)}[/tex]

iii. [tex]\mu_{\hat{p}}=\sqrt{np(1-p)}[/tex]

iv. [tex]\sigma_{\bar{p}}=\sqrt{\frac{p(1-p)}{n}}[/tex]

C.

i. [tex]\mu_{\bar{x}}=p[/tex]

ii. [tex]\sigma_{\bar{x}}=\frac{\sigma}{\sqrt{n}}[/tex]

iii. [tex]\mu_{\hat{p}}=\bar{x}[/tex]

iv. [tex]\sigma_{\hat{p}}=\sqrt{\frac{p(1-p)}{n}}[/tex]

D.

i. [tex]\mu_{\bar{x}}=\mu[/tex]

ii. [tex]\sigma_{\bar{x}}=\frac{\sigma}{\sqrt{n}}[/tex]

iii. [tex]\mu_{\bar{p}}=p[/tex]

iv. [tex]\sigma_{\bar{p}}=\sqrt{\frac{p(1-p)}{n}}[/tex]

E.

i. [tex]\mu_{\bar{x}}=\mu[/tex]

ii. [tex]\sigma_{\bar{x}}=\sqrt{\frac{p(1-p)}{n}}[/tex]

iii. [tex]\mu_{\bar{p}}=p[/tex]

iv. [tex]\sigma_{\hat{p}}=\frac{\sigma}{\sqrt{n}}[/tex]

The value of fluid ounce in millimeter can be calculated by mutliplyin by 29.574 so 12 fluid ounce is 354.882 millileters.

Unit conversion is the process of converting the measurement of a given amount between various units, often by multiplicative conversion factors that alter the value of the measured quantity without altering its effects.

Per ounce, there are 29.5735296 millilitres (ml) (oz). As a result, the conversion formula for oz to ml is as follows:

ounce x 29.5735296 = ml

The following is the response to the question "What is 12 oz to ml?" when we enter 12 oz into our formula:

12 x 29.5735296

= 354.8823552 12 oz

≈ 354.882 ml

We have also changed the answer to "12 oz to ml?" into a fraction for your convenience. The fractional response to "12 oz to ml?" is as follows:

12 oz ≈ 354 15/17 ml

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The converted value representing in grams and ounce is given by 30 grams is equal to 1.05822 ounce.

Conversion factor representing the relation between ounce and grams is given by :

28 grams equal to one ounce

Substitute the required grams value to be converted into ounce we have,

⇒ 28 grams = 1 ounce

⇒ 1gram = ( 1 / 28 ) ounce

⇒ 30 gram = ( 30 ) × ( 1 / 28 ) ounce

⇒ 30 gram =  ( 1.05822 ) ounce

Therefore, the value after conversion grams into ounce is given by            30 gram =  ( 1.05822 ) ounce .

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Answer:

f(n)= f( n-1 ) + 6

Therefore , the solution of the given problem of unitary method comes out to be  $1,320, $3,960, and $5,280, respectively.

After determining the dimensions of one tiny slice, multiply the sum by two to complete a work using unitary procedure. The unit variable methodology, which just requires an expression, can be used to equation a coded unit from a certain group or set of groups. 40 pens, for example, might cost Rs. 4,000, which would be equal to $1.01 and 4000 pounds. It's possible that one country will have total control over the method employed to do this. Virtually every living creature has a distinctive quality.

Here,

In 2016, the prices for 1, 3, or 4 gold ounces were $1,320, $3,960, and $5,280, respectively.

In 2016, 2 gold ounces would cost $2,640.

1 ounce of gold costing $2 in 2016 is equal to $2 divided by 2 ounces of gold. in 2016.

= $2,640 ÷ 2

= $1,320

The price of 3 grams of gold for 2016 equals the price of One ounce of gold. multiplied by 3.

= $1,320 × 3

= $3,960

cost of one ounce of gold. in 2016 multiplied by 4 to get the price of 4 ounces of gold. in 2016.

= $1320 × 4

= $5,280

The price of 1, 3, and 4 gold ounces each in 2016 is therefore $1,320, $3,960, and $5,280, respectively.

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One centimeters is equal to 0.01 meters. Centimeter (cm) and meter (m) are both units of length in the International System of Units (SI).

One centimeter is equal to 0.01 meters.

This can be derived by using the conversion factor that 1 meter is equal to 100 centimeters:

1 meter = 100 centimeters

Dividing both sides by 100, we get:

1 centimeter = 1/100 meters

Simplifying this, we get:

1 centimeter = 0.01 meters

Therefore, one centimeter is equal to 0.01 meters.

A centimetre is a metric length unit that equals one tenth of a metre. It is typically used to measure short distances, such as an object's length or width, or a person's height.

A metre, on the other hand, is the SI system's base unit of length and is defined as the distance travelled by light in a vacuum in 1/299,792,458 of a second. Larger distances, such as the length of a room, a building, or a road, are measured with it.

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Answer:

Step-by-step explanation:

Since the hexagon is regular, all of its sides have the same length. Therefore, each side has a length of 57 inches / 6 = 9.5 inches.

To find the area of the hexagon, we can use the formula:

Area = (3√3 / 2) × s^2

where s is the length of a side.

Substituting s = 9.5 inches, we get:

Area = (3√3 / 2) × (9.5 inches)^2

Area ≈ 244.3 square inches

Rounding to the nearest tenth, the area of the hexagon is 244.3 square inches.

For a regular pentagon, the apothem is the distance from the center of the pentagon to the midpoint of one of its sides. We can use the formula for the area of a regular pentagon to find the apothem:

Area = (5/4) × apothem × side length

Substituting the given values, we get:

118.25 square meters = (5/4) × apothem × (4.3 meters)

apothem = 118.25 square meters / (5/4) / (4.3 meters)

apothem ≈ 8.4 meters

Therefore, the length of the apothem is approximately 8.4 meters.

Since the hexagon is regular, all of its sides have the same length. Therefore, each side has a length of 90 feet / 6 = 15 feet.

To find the area of the hexagon, we can use the same formula as in the first problem:

Area = (3√3 / 2) × s^2

Substituting s = 15 feet, we get:

Area = (3√3 / 2) × (15 feet)^2

Area ≈ 1161.4 square feet

Rounding to the nearest tenth, the area of the hexagon is 1161.4 square feet.

We can estimate that about 98 million more megawatt hours were generated from wind in 2020 than in 2016.

What is Division?

Division is a mathematical operation that involves splitting a quantity into equal parts or groups. It is the inverse operation of multiplication and is represented using the division symbol ÷ or the forward slash /.

Solution:

To estimate how many more megawatt hours were generated from wind in 2020 than in 2016, we need to make some assumptions and approximations since the problem only provides data for 2009 and 2017.

Assuming that the wind energy generation continued to increase at the same constant rate between 2017 and 2020, we can estimate the amount of wind energy generated in 2020 as follows:

1. From 2009 to 2017, the wind energy generation increased by 254 million - 74 million = 180 million megawatt hours.

2. The time period between 2009 and 2017 is 8 years, so the average annual increase in wind energy generation is 180 million / 8 years = 22.5 million megawatt hours per year.

3. Therefore, we can estimate the wind energy generation in 2020 as 254 million + 3 years x 22.5 million = 322.5 million megawatt hours.

4. Similarly, we can estimate the wind energy generation in 2016 as 74 million + 7 years x 22.5 million = 224.5 million megawatt hours.

5. The difference in wind energy generation between 2020 and 2016 is then:

322.5 million - 224.5 million = 98 million megawatt hours.

Therefore, we can estimate that about 98 million more megawatt hours were generated from wind in 2020 than in 2016.

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Step-by-step explanation:

This is the correct answer

There are 0.625 (or approximately 5/8) gallons in 80 fluid ounces. It's worth noting that the conversion factor between fluid ounces and gallons can vary depending on the system of measurement used

There are 128 fluid ounces in a gallon in the US customary system of measurement. Therefore, to find out how many 80-ounce containers are in a gallon, you can use the following formula:

number of 80-ounce containers in a gallon = 128 / 80

Simplifying this expression, we can perform the division:

number of 80-ounce containers in a gallon = 1.6

This means that there are 1.6 (or approximately 1 and 3/5) 80-ounce containers in a gallon.

Alternatively, you can convert the 80 ounces to gallons using the following formula:

number of gallons in 80 fluid ounces = 80 / 128

Again, simplifying this expression, we can perform the division:

number of gallons in 80 fluid ounces = 0.625

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We know that a statistical technique that allows a researcher to cluster such traits as being talkative, social, and adventurous with extroversion is known as the Factor analysis.

Factor analysis is most likely a statistical procedure that identifies clusters of related items also known as factors which are on a test; used to identify different dimensions of performance that underlie one's total score.

We can say that factor analysis is more like a technique which is used in mathematics for reducing a larger number into a smaller number.

In other words, its a method for reducing a large variable into a smaller variable factor also this technique takes out the maximum ordinary variance from all of the variables and then puts them in the common score.

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Answer:

180 degrees

......................

The rate of change of the area of a circle with respect to its radius when r = 3 cm is 6π cm2/cm, and the rate of change of the area of a circle with respect to its radius when r = 4 cm is 8π cm2/cm.

The area of a circle can be calculated using the formula, A = πr^2, where A is the area of the circle and r is the radius.The rate of change of the area of a circle with respect to its radius r can be calculated using the derivative of the equation. By taking the derivative of A with respect to r, we get the equation, dA/dr = 2πr.This equation signifies that the rate of change of the area of a circle with respect to its radius is proportional to the radius. As the radius increases, the rate of change of the area of the circle also increases.To calculate the rate of change of the area of a circle with respect to its radius when r = 3 cm and r = 4 cm, we can substitute the corresponding values of r in the equation, dA/dr = 2πr.

For r = 3 cm, the rate of change of the area of the circle with respect to its radius is dA/dr = 2π(3) = 6π cm2/cm.

For r = 4 cm, the rate of change of the area of the circle with respect to its radius is dA/dr = 2π(4) = 8π cm2/cm.

Therefore, the rate of change of the area of a circle with respect to its radius when r = 3 cm is 6π cm2/cm, and the rate of change of the area of a circle with respect to its radius when r = 4 cm is 8π cm2/cm.

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Inverse trigonometric integrals involve inverse trigonometric functions and are used to evaluate integrals containing trigonometric functions and their derivatives

Inverse trigonometric integrals are a group of integrals that include inverse trigonometric functions like arcsine, arccosine, and arctangent. These functions are utilized to assess integrals that include expressions containing trigonometric functions and their derivatives.

Inverse trigonometric functions are the Inverse of their respective trigonometric functions and can be utilized to find the point that compares to a given ratio of sides in a right triangle. Inverse trigonometric integrals are generally experienced in analytics and are helpful in different fields like physics, engineering, and statistics. They are ordinarily assessed utilizing algebraic manipulation, substitution, and integration by parts

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The value of her kinetic energy is,

Kinetic energy = 3,388 J

Multiplication means to add number to itself a particular number of times. Multiply will be viewed as a process of repeated addition.

Given that;

A student rides her bicycle down a hill. Together, she and the bicycle have a mass of 56 kilograms.

And, She is moving at 11 meters per second.

We know that;

Kinetic energy = 1/2 (mv²)

Where, m is mass and v is velocity.

Substitute all the values , we get;

Kinetic energy = 1/2 (mv²)

Kinetic energy = 1/2 (56 × 11²)

Kinetic energy = 1/2 × 56 × 121

Kinetic energy = 3,388 J

Thus, The value of her kinetic energy is,

Kinetic energy = 3,388 J

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The angle of depression from point R to point S is ∠1.

The angle of elevation from point S to point R is ∠2.

∠2 is the angle of elevation from S to R.

∠1 is the angle of depression from point R to point S.

What is an angle of depression?

If the line of sight is directed downward from the horizontal line, then an angle is created with the horizontal line. The angle formed between the horizontal line and the observer's line of sight is known as the angle of depression if the object being observed is below the observer's level.

There is an angle of elevation from point R to S. Thus point R is lie above S.

The angle of depression from point R to point S is ∠1.

The angle of elevation from point S to point R is ∠2.

∠2 is the angle of elevation from S to R.

∠1 is the angle of depression from point R to point S.

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