What is the constant of variation for the quadratic variation?
10y = 6x2

6

0.6

10

The simplified from of expression; which is obtained by performing mathematical operations to the expression and convert it to its standard form. Hence, the simplified form of 135(z^{0} ) is 135.

Usually, simplification involves proceeding with the pending operations in the expression. Like, 5 + 2 is an expression whose simplified form can be obtained by doing the pending addition, which results in 7 as its simplified form. Simplification usually involves making the expression simple and easy to use later.

We need to find the simplified form of this equation :

135(z^{0} )

Since we know that any power of 0 is 1. So, z to the power of 0 is going to be one.

135(z^{0} ) = 135(1 )

135^1 = 135

The simplified from of expression; which is obtained by performing mathematical operations to the expression and convert it to its standard form. Hence, the simplified form of 135(z^{0} ) is 135.

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The Sun produces energy through nuclear fusion in its core. Visiting the Sun is not possible due to high temperatures and intense radiation. Scientists use special instruments to observe the Sun safely.

The Sun produces energy through the process of nuclear fusion. In the Sun's core, hydrogen atoms combine to form helium atoms, releasing a tremendous amount of energy in the process. This energy is then radiated outwards in the form of light and heat. However, visiting the Sun is not feasible due to its extremely high temperatures and intense radiation. If one were to approach the Sun, they would burn up before reaching it.

As an analogy, imagine you are attending a crowded rally and need to work your way through the dense crowd to reach the edge. Photons in the Sun's core behave similarly, constantly bumping into atoms and changing direction as they make their way outwards. They only become visible when they reach the Sun's atmosphere, where the density of atoms is low enough to allow their outward progress.

To observe the Sun and learn about its characteristics, scientists use instruments like telescopes equipped with special filters that block harmful radiation and enable safe observations. These observations help us understand the Sun's behavior and its impact on Earth.

Final answer:

The Sun produces energy via nuclear fusion in its core, where hydrogen atoms fuse to create helium, emitting light and heat. The photosphere, just over 400 kilometers thick, is the layer from which visible light is emitted. Physically visiting the Sun would be impossible due to its extreme conditions, yet exploring its energy production and photonic behavior is intriguing.

Explanation:

To address the question of how the Sun produces so much energy for such an extended period, one must understand that the Sun has been generating energy for about 4.5 billion years through nuclear fusion processes. In the Sun's core, hydrogen atoms fuse to form helium under extreme temperatures and pressures, releasing vast amounts of energy in the form of light and heat. This process is similar to having an incredibly long-lasting 'nuclear battery' that provides the energy that we see as sunlight.

An interesting analogy to understand the journey of a photon from the Sun's core to the outside is by imagining being in a crowded rally and trying to get from the center to the edges; you would constantly bump into people, change direction, and only gradually make your way out. Photons behave the same way inside the Sun, constantly interacting with atoms and only becoming visible when they reach the Sun's atmosphere where atom density is low. This atmosphere, or photosphere, is about 400 kilometers thick, relatively thin compared to the Sun's diameter, and it's from this layer that the bulk of the Sun's visible light we see is emitted.

The cost of each box of strawberries is $14.

Division is breaking a number up into an equal number of parts.

Given that, 3 boxes of strawberries sold for $42,

3 boxes = $42

1 box = $42/3 = $14

Hence, The cost of each box of strawberries is $14.

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Answer:

The Answer is -1 1/3 (A.)

-1 2/3 is equal to -1.666 so -1 1/3 equals -1.3, it would make the number locate on the right of -1 2/3 on the horizontal number line

The mixed fraction number - 1 ²/₃ is lesser than the mixed fraction number - 1 ¹/₃. Then the correct option is A.

A number line refers to a straight line in mathematics that has numbers arranged at regular intervals or portions along its width. A number line is often shown horizontally and can be postponed in any direction.

The mixed fraction number is given below.

⇒ - 1 ²/₃

Convert the mixed fraction number into a decimal number. Then we have

⇒ - 1 ²/₃

⇒ - (1 + 0.667)

⇒ - 1.667

The value of the mixed fraction number - 1 ¹/₃ will be given as,

⇒ - 1 ¹/₃

⇒ - (1 + 0.333)

⇒ - 1.333

The mixed fraction number - 1 ²/₃ is lesser than the mixed fraction number - 1 ¹/₃. Then the correct option is A.

The number line is given below.

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The complete question is given below.

Which number is located to the right of -1 2/3 on the horizontal number line?

A. -1 1/3

B. -2 1/3

C. - 2

D. - 3

To find the length of the job that costs the same regardless of the moving company used, solve the equation 840 + 17x = 760 + 22x. The job would need to be 16 hours long.

To determine the length of the job that costs the same regardless of the moving company used, we need to solve the equation 840 + 17x = 760 + 22x, where x represents the number of hours.

First, we subtract 760 from both sides: 840 + 17x - 760 = 760 + 22x - 760, which simplifies to 80 + 17x = 22x.

Next, we subtract 17x from both sides: 80 + 17x - 17x = 22x - 17x, resulting in 80 = 5x.

Finally, we divide both sides by 5 to solve for x: 80 ÷ 5 = 5x ÷ 5, giving us x = 16. Therefore, the job would need to be 16 hours long to cost the same regardless of the moving company used.

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Answer:

$10.32

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The 16 oz bottle of fruit punch, costing $0.15 per ounce, is a more economical choice compared to the 24 oz bottle, which costs $0.16 per ounce.

To determine which size of fruit punch costs less per ounce, we need to calculate the cost per ounce for each bottle size. For the 16 oz bottle costing $2.40, we divide $2.40 by 16 oz, giving us $0.15 per ounce. For the 24 oz bottle costing $3.84, we divide $3.84 by 24 oz, resulting in $0.16 per ounce. Thus, we can see that the 16 oz bottle has a lower cost per ounce compared to the 24 oz bottle.

To further clarify, here are the calculations:

Comparing the two, the 16 oz bottle's cost per ounce is $0.01 less than the 24 oz bottle, making it the more economical choice.

The decimal 0.79 as a fraction in simplest form is 79/100, which cannot be simplified further.

To convert the decimal 0.79 into a fraction in simplest form, we have to write it as a fraction with a denominator that reflects the decimal's place value. Since 0.79 has two decimal places, it equates to 79/100. This fraction cannot be simplified further since 79 and 100 have no common divisors other than 1, thus 79/100 is the fraction in simplest form.

Answer:

80 units by 18 units

Step-by-step explanation:

Find the number of feet represented by 1 unit in the drawing.

1 unit ÷ 1

5 feet ÷ 1

 =  

1 unit

5 feet

1 unit in this model is about 5 feet in the actual room.

Find the width of the scale model represented by 90 feet in the actual room.

1 unit × 18

5 ft × 18

 =  

18 units

90 ft

The width of the scale model represented by 90 feet in the actual room is 18 units.

Find the length of the scale model represented by 400 feet in the actual room.

1 unit × 80

5 ft × 80

 =  

80 units

400 ft

The length of the scale model is 80 units.

The scale model is 80 units by 18 units.

The value of the missing number in the given ratio 63:27= 49:? is 21.

The ratio is the division of the two numbers.

For example, a/b, where a will be the numerator and b will be the denominator.

As per the given ratio,

63:27= 49:?

Let's assume the missing number is x.

63/27 = 49/x

Multiply both side by x.

x(63/27) = 49

Multiply both side by 27/63

x = 49(27/63)

x = 21

Hence "The value of the missing number in the given ratio 63:27= 49:? is 21".

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The sign of the product is negative because a positive multiplied by a negative is a negative.

Significance starts with the word sign for a reason. An item's significance is a sign of its importance.

Here, Product of positive and negative term will always gives us negative result.

356864 is positive and -194758 is negative then the result of their product will always be negative number.

Thus, the sign of the product is negative because a positive multiplied by a negative is a negative.

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Micah has 33 red marbles and 22 blue marbles.

To find out how many red and blue marbles Micah has, we first need to divide the total number of marbles by the sum of the parts of the ratio (which is 3 + 2 = 5), and then multiply each part of the ratio by this result.

First, let's find the value of each part of the ratio:

- Each part represents a fraction of the total: [tex]\( \frac{55}{5} = 11 \)[/tex] marbles per part.

- Since the ratio of red to blue marbles is 3:2, we have:

 - Red marbles: [tex]\( 3 \times 11 = 33 \)[/tex] marbles

 - Blue marbles: [tex]\( 2 \times 11 = 22 \)[/tex] marbles

So, Micah has 33 red marbles and 22 blue marbles.

The practical domain of the function f(x)=−85x+3145, which represents the number of unprinted pages x minutes after the printing begins, is from 0 to 37. Here, the value of 'x' are whole numbers since it represents time in minutes, and in this context, fractions or decimal amounts of minutes do not apply.

In Mathematics, particularly in the topic of functions, the practical domain refers to the set of all possible values of x, for which the function is defined. In this particular problem, the function f(x)=−85x+3145f(x)=−85x+3145 represents the number of unprinted pages x minutes after the printing begins.

Given that the printer prints 85 pages per minute and there are 3145 pages to print in total, it will take the employee 3145/85 = 37 minutes to print all the pages. Therefore, the practical domain of this function f is all whole numbers from 0 to 37 inclusive.

Keep in mind, these are whole minutes. It may not make practical sense to consider fractions or decimals of minutes in this problem context as the printer operates at set whole minute intervals. So, the practical domain does not include real numbers between 0 and 37, only whole numbers.

So the practical domain of function f is all whole numbers from 0 to 37.

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Answer

She paid 17.99 in sales tax

Step-by-step explanation: