the half-life of cobalt-60 (used in radiation therapy) is 5.26

The metric measurement will you use when telling your hairdresser how much to take off the ends is centimetres (cm).

The decimalized meter-based system of measurement that had been adopted in France in the 1790s was replaced by the metric system. The International System of Units (SI), which was invented/created in the middle of the 20th century with the help of an international standards body, was the historical culmination of the development of these systems.

The term "metrication" refers to the adoption of the metric system. The historical development of metric systems has led to the acceptance of a number of principles. A single base unit of measurement expresses all of nature's essential dimensions. More and more often now, natural principles rather than replicas of physical artifacts are used to define base units.

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The correct inequality representing the given conditions is option (d) "f ≤ 200".

This is because the combined weight of the stove and the freezer must be at least 370 pounds, and the weight of the stove is already known to be 170 pounds. This means that the weight of the freezer must be less than or equal to the remaining 200 pounds in order to satisfy the total weight requirement. In other words, the inequality that describes the conditions for the weight of the freezer is "f ≤ 200".

In mathematics, an inequality is a statement involving two values that are not equal.

It can be used to compare two values and determine the relationship between them. In this case, the inequality "f ≤ 200" is used to compare the weight of the freezer to the known weight of the stove, in order to determine the maximum possible weight of the freezer.

Therefore, the correct option is (d).

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Answer:

Step-by-step explanation

To make the problem easier, we are gonna have to change the denominator into 16

8*2=16 after we times 8 with 2 we now have to do the same 7

So this would show 7*2=14

Now it would be 6 14/16 - 6 15/16

All we have to do now is minus 14 with 15 which equals -1.

Now for the whole numbers, you can just minus the 6’s with eachother 6-6=0. Taking the denominator, we now have -1/16.

Hope this is the answer you are looking for.

Answer:

1 and 1/4 (1.25)

Step-by-step explanation:

So imagine you have 2 pizzas. Your friend wants to bring one home. Your pizzas are both in two pieces, and your friend wants to take one whole pizza and a half of the second one. In the first graph, that friend takes

1 and 1/2 (1/2 meaning one half) or 1.5 (.5 being half)

To get the fraction for one half you have to think:

- How many slices are there in each pizza?

- How can I make this a fraction?

- If it says “1” for a whole pizza how much is half going to be?

If there are 2 parts to one pizza, and only 1 of the 2 parts are taken, it is considered 1/2.

Another way you show “1/2” is by putting “.5 (0.5)” at the end of a number. You can find “.5” by doing “1 ÷ 2”

You divide one and two because there is 1 pizza and 2 parts of it.

Now that you know how to figure out the first one, the second one should be easy!

But.. for some reason, the “1/2 (.5)” that we got earlier of the second pizza is cut in half!

You can see that they took one full pizza, and half of “1/2” of a pizza!

There are two simple ways to find out what number “half of a half of a pizza” is!

For the first, you can count the blocks!

In this case, there are 4 blocks (4 slices), in a pizza. One pizza has all 4 blocks filled, meaning one whole pizza is taken by your friend, and only 1 block is filled in on the second pizza! You can say, for the second pizza, that your friend took “1/4” of a pizza.

You get this by seeing that out of 4 blocks that could be filled, only 1 is!

Which gives you the answer “1/4 (0.25)”

Or you could divide!

If you look you can see there are 2 parts where “1/2” was. If you want to find what half of “1/2” is, you could write the equation:

“1/2 ÷ 2”

The answer you get is also “1/4 (0.25)”

You divide “1/2” and “2” because you want to find what one of 2 parts of 1/2 is.

Now that you know that there is one full pizza and 1/4 of a pizza, your final answer comes out to be 1 and 1/4 (1.25) because you combine the two answers together.

D. No, because the probability of being left-handed is greater, x must count the number of left-handed adults.

The binomial probability formula can be used to calculate the probability of a certain number of successes (or left-handed individuals) in a given number of trials (100 adults). In order for the binomial probability formula to be used, the trials must be independent, meaning that the selection of one person does not affect the selection of the next one. Since the probability of being left-handed is greater, the binomial probability formula cannot be used in this case and x must count the number of left-handed adults.

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A parabola equation calculator is an online tool used to find the equation of a parabola based on its vertex and focus points, or other given parameters.

A parabola equation calculator is a type of math calculator used to find the equation of a parabola based on certain given parameters. These parameters could include the vertex and focus points, the directrix, or the x- or y-intercepts. By inputting these parameters into the calculator, users can obtain the equation of the parabola, which is a quadratic function in the standard form y = ax² + bx + c.

Parabolas are widely used in physics and engineering applications, such as the trajectory of a projectile, the shape of a satellite dish, or the design of a parabolic solar collector.

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The length of each side of the octagon with area of 392 square centimeters and an apothem of 14 centimeters is  7  centimeters .

Compared to lower sided shapes, an octagon's area is a little more complicated. A normal octagon's area is equal to 4 as. Where "s" stands for the octagonal side and "a" for the apothem, which runs straight from the pentagon's center to one of its sides.

The formula for the area of a regular octagon is:

A = 4 × apothem × side

Using this formula and the given values, we can solve for the length of each side of the octagon:

392 = 4 × 14 × side

Dividing both sides by 4 × 14, we get:

side = 392 ÷ (4 × 14)

Simplifying the right-hand side, we get:

side = 392 ÷ 56 = 7 cm.

Therefore, the length of each side of the octagon is  7 cm .

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The approximate arc length of the circle of radius 1 unit is B. 0.785 units.

The circumference of a circle is the distance around the circle which is 2πr.

The diameter of a circle is the largest chord that passes through the center of a circle it is 2r.

We know, S = rФ, where S is the arc length, r is the radius and Ф is the measure of the angle in radians.

Therefore, When r = 1 and Ф = π/4,

S = 1×π/4.

S = 0.785 units.

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The required height of the triangle whose area and base are given is 9 yd.

The area of a triangle in a two-dimensional plane is the space that it completely encloses. A triangle is a closed shape with three sides and three vertices, as is pretty obvious.The area of a triangle is the total space occupied by its three sides. The general formula for determining the triangle's area is half of the product of its base and height.

In the given question, we have to find the height of the given triangle ,

we know that ,

Area of triangle = base x height x 1/2.

63.9 = 1/2 × 14.2 × height

Height = (63.9 × 2) ÷ 14.2

Height = 127.8 ÷ 14.2

Height = 9 yd

Therefore , the height of the triangle is 9 yd .

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Answer: C. $725

Step-by-step explanation: To find the answer, let's first calculate the increase. A 16% increase causes the cost to go up by 16% of its own value, so let's calculate that by doing 0.16 x 12.5, giving us 2. Next, we add 2 to 12.50, giving us 14.5. Finally, we multiply 14.5 by 50 to find the cost for 50 students, giving us $725. So, $725 is our answer.

Hope this helped :D

The following is a graph that illustrates the inequality system: (B) The graph displays a solid line with shading below it that goes through the points 0 commas 2, and 1 comma negative 3.

In mathematics, "inequality" refers to a relationship between two expressions or values that is not equal to each other.

Hence, inequality emerges from a lack of balance.

A mathematical statement that demonstrates the equality of two expressions is known as an equation, whereas a statement that demonstrates the greater or smaller value of one expression is known as an inequality.

For writing and comprehending an inequality plotted on a graph, there are two (2) main rules in mathematics, and these are as follows:

1. When the inequality symbol is (or), the line on a graph should be solid.

2. When the inequality symbol is (> or ), the line on a graph should be dashed (dotted).

The boundary line is dashed (dotted) and shaded above to indicate that the boundary is not part of the solution, and this must be indicated with the larger than (>) inequality sign.

Moreover, the y-value for this inequality graph meets the x-axis at -1.5.

Therefore, the following is a graph that illustrates the inequality system: (B) The graph displays a solid line with shading below it that goes through the points 0 commas 2, and 1 comma negative 3..

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Complete question:

The following inequalities represent a system.

y ≥ −5x + 2

y > 3x − 1.5

Which of the following graphs represents the system?

A. The graph shows a solid line that passes through 0 comma 2 and 1 comma negative 3, with shading above the line. There is also a dashed line that passes through 0 comma negative 1.5 and 1 comma 1.5, with shading above the line.

B. The graph shows a solid line that passes through 0 comma 2 and 1 comma negative 3, with shading below the line. There is also a dashed line that passes through 0 comma negative 1.5 and 1 comma 1.5, with shading above the line.

C. The graph shows a solid line that passes through 0 comma 2 and 1 comma negative 3, with shading above the line. There is also a dashed line that passes through 0 comma negative 1.5 and 1 comma 1.5, with shading below the line.

D> The graph shows a solid line that passes through 0 comma 2 and 1 comma negative 3, with shading below the line. There is also a dashed line that passes through 0 comma negative 1.5 and 1 comma 1.5, with shading below the line.

Answer: $1.9

Step-by-step explanation:

To convert 8 cups to quarts, you can divide the number of cups by 4 to get 2 quarts.

To convert cups to quarts, you can use the following conversion factor:

1 quart = 4 cups

Therefore, to convert 8 cups to quarts, you can divide the number of cups by 4:

8 cups ÷ 4 = 2 quarts

So, 8 cups is equal to 2 quarts.

It's important to keep in mind that cups and quarts are units of volume measurement commonly used in cooking and baking. Cups are often used to measure smaller amounts of liquid or dry ingredients, while quarts are used for larger amounts.

In many recipes, the measurements are given in cups, but in some cases, you may need to convert from cups to quarts or other units.

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Answer:

75 degrees

Step-by-step explanation:

since this figure has four sides we can figure out the measure of the interior angles by using the formula, (n-2)*180, where 'n' = number of sides

(4-2)180 = 2(180) = 360

also, we know that since AB is parallel to DC that the figure is a rhombus where adjacent angles are supplementary

therefore, we can find 'x' by writing this equation:

12x - 3 + 9x - 6 = 180

simplify:

21x - 9 = 180

21x = 189

x = 9

also, we know that opposite angles in a rhombus are equal so if we substitute '9' for 'x' in angle C we will know the measure of angle A:

m<A = 9(9)-6

m<A = 81-6

m<A = 75 degrees

Answer:

Step-by-step explanation:

The conversion of 180 centimetres in feet is equals to the 5.90 feet. Thus, conversion factor for conversion of units, centimetres to feet is 5.90/180 = 0.032.

A conversion is defined as to convert one set of units into another set of units by multiplication or division. A number or value which used in conversion is called conversion factor. If conversion is necessary, a conversion factor suitable for equivalent value must be used. For example, to convert meters to centimetres, the appropriate conversion value is 100 centimetres equal 1 meter. It includes converting a value from inches to millimeters, for distance from miles to kilometers, feet or other units. How to convert centimeters to feet : One meter is a measure of length and equals approximately 3.28 feet. Thus conversion factor is 3.28 feet. So, 180 meters

= 180 × 3.28 feet

= 590.4 feet --(1)

But we need to convert 180 centimeters to feet. So, change meters to centimeters. As you know, 1 meter = 100 centimeters, so 180 meters = 18000 centimeters --(2). Now from equations (1) and (2),

18500 centimeters = 590.4 feet,

Divide both parts by 100,

=> 180 centimetres = (590.4/100 ) feet

= 5.90 feet

Hence required value is 5.90.

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A critical t-value calculator is an online tool that helps you determine the critical value for the t-distribution for a given level of significance (alpha) and degrees of freedom (df). The critical t-value is the value that separates the area under the t-distribution curve into the rejection region and the non-rejection region for a two-tailed hypothesis test.

In statistical hypothesis testing, the t-distribution is used when the sample size is small, and the population standard deviation is unknown. The t-distribution is a family of distributions that depend on the degrees of freedom (df) and is bell-shaped, with a mean of 0 and a standard deviation of 1.

To use a critical t-value calculator, you need to input the significance level (alpha) and the degrees of freedom (df) and select whether the test is one-tailed or two-tailed. The calculator will then provide you with the critical t-value that separates the rejection and non-rejection regions for the given alpha and df.

It's important to note that the critical t-value depends on the level of significance (alpha) and the degrees of freedom (df). As the level of significant increases or the degrees of freedom decrease, the critical t-value also changes. Therefore, it's essential to use a critical t-value calculator to obtain the correct value for your hypothesis test.

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A critical t-value calculator is a tool used to calculate the critical value of t in a Student's t-test for a given significance level (alpha) and degrees of freedom (df).

When the sample size is small or the population standard deviation is unknown, the t-distribution is used to estimate the population mean.

The critical t-value in a Student's t-test is the value of t that separates the rejection region from the non-rejection region in a t-distribution. The null hypothesis is rejected if the calculated t-value is greater than the critical t-value, indicating that there is a significant difference between the sample mean and the population mean.

To use a critical t-value calculator, enter the t-significance test's level (alpha) and degrees of freedom (df). The degrees of freedom are defined as the number of observations minus one and are proportional to the sample size. The calculator will output the critical t-value for the given significance level and degrees of freedom once you enter these values.

For example, the degrees of freedom for a two-tailed t-test with a sample size of 20 and a significance level of 0.05 would be 20-1=19. The critical t-value at a significance level of 0.05 and 19 degrees of freedom is approximately 2.093, according to a critical t-value calculator.

Knowing the critical t-value is useful in hypothesis testing because it allows you to compare the calculated t-value from the sample data to the critical t-value to determine whether the null hypothesis should be rejected

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A) 500

B) 54 minutes

C) 68cents and 60 cents

D)

E) $40.95

A proportion is a statement that says that two ratios are equal. They can be used in many everyday situations like comparing sizes, cooking, calculating percentages, and more.

Proportions can be written as equivalent fractions or as equal ratios.

A) 42% = 210

100% = (210 x 100)/42

= 500 people

B) 135 berries = 15 minutes

    486 berries = ??minutes

= (486 x 15)/135

= 54 minutes

C) unit price = $6.75/10 = 0.675cents or 68cents

    ii) unit price = $7.25/12 = 0.604cents or 60cents

D) Inconclusive question.

E) 40% of 65 = $26

65 - 26 = $39

Tax = 5% = $1.95

Total = $39 + 1.95

Final Price of jacket = $40.95

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The given function,[tex]y=20(0.8)^x[/tex] is an exponential decay.

What is an exponential function?

An exponential function is a mathematical function of the form [tex]f(x) = a^x[/tex], where "a" is a constant and "x" is the input variable. These functions are commonly used to model situations that involve continuous growth or decay.

The function ,[tex]y=20(0.8)^x[/tex]  represents exponential decay.

In the given function, a = 20 and b = 0.8, which is between 0 and 1. Therefore, the function represents exponential decay. This means that as x increases, the value of y decreases, getting smaller and smaller. In this case, the base 0.8 represents the decay factor, and 20 represents the initial value or the y-intercept of the function.

Hence, the given function,[tex]y=20(0.8)^x[/tex]  is an exponential decay.

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Each child would get 7/8 of a pound of candy from each pinata.

To find out how much candy each child would get, we need to first determine the total amount of candy in all four pinatas, and then divide that amount by the total number of kids who will be sharing the candy.

To start, we can convert the 10 1/2 pounds of candy into a mixed fraction:

10 1/2 = 10 + 1/2 = 20/2 + 1/2 = 21/2

So the Pickle Family had 21/2 pounds of candy to fill the pinata.

To find out how much candy each piñata would have, we can divide the total amount of candy by the number of piñatas:

21/2 ÷ 4 = 21/2 × 1/4 = 21/8

So each pinata would have 21/8 pounds of candy.

Now we need to determine how much candy each child would get. Since each pinata will be shared among 6 kids, we can divide the amount of candy in each pinata by 6:

21/8 ÷ 6 = 21/8 × 1/6

= 7/8

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Answer:

Step-by-step explanation:

The answer is 15/40

Because 3 times 5 is 15 and 8 times 5 is 40

Answer:

15/40

Step-by-step explanation:

the equivalent fraction for 3/8 using 5 as a multiplier is :

3 x 5 / 8 x 5

= 15 / 40

One milliliter (mL) is equal to 0.033814 fluid ounces (fl oz). Therefore, to convert milliliters to fluid ounces, you need to divide the number of milliliters by 29.5735.

So, the value of 75 mL is equal to 2.53605 fluid ounces.

The metric system uses millilitres as the unit of volume, denoted by the letters ml or mL. One cubic centimetre, or one thousandth of a litre, is equivalent to one millilitre.

Fluid ounces is a measure of liquid; in Britain, 0.0284 of a litre.

Here, we want to convert the 75 mL into fluid ounces.

To convert milliliters (mL) to fluid ounces (oz), you can use the conversion factor of 0.033814.

So to convert 75 mL to ounces:

75 mL x 0.033814 oz/mL

= 2.53605 oz (rounded to five decimal places)

Therefore, 75 mL is approximately equal to 2.53605 fluid ounces.

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As per the line segment, the location point of M is option (c) (16/5,19/5)

To answer the question, it is important to understand what a line segment is. A line segment is a part of a line that connects two points, usually denoted by X and Y.

Here we have consider that in this case, the line segment XY is divided by Point M such that XM/MY is equal to 2/3.

As we all know that this means that the ratio between the two parts of the line segment is 2:3. Therefore, the location point of M is (-16/5,19/5).

Therefore, the correct option is (c).

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As a result, the rectangular pyramid has two conceivable dimensions: a base of 3 inches by 3 inches with a height of 3 inches, and a base of 1 inch by 9 inches with a height of 9 inches.

Volume is a fundamental physical quantity that measures the amount of three-dimensional space occupied by an object or a substance. In simpler terms, it refers to the amount of space that an object takes up or occupies. The standard unit of measurement for volume is the cubic meter (m3), which is defined as the amount of space occupied by a cube that has edges that measure one meter in length. However, in everyday life, other units of measurement are commonly used, such as liters, gallons, or cubic feet.

Here,

The volume of the rectangular prism is:

V = lwh = 6 * 1 * 1/2 = 3 cubic inches.

Let's call the base of the rectangular pyramid "b" and its height "h". The volume of a pyramid is given by:

V = (1/3)bh.

We want the volume of the pyramid to be the same as that of the rectangular prism, so we can set the two expressions for V equal to each other and solve for h:

3 = (1/3)bh

h = 9/b

Now we can choose any value for b and calculate the corresponding value for h that would result in the same volume as the original rectangular prism.

For example, we could choose b = 3, which would give us:

h = 9/b = 9/3 = 3

So one set of possible dimensions for the rectangular pyramid is a base of 3 inches by 3 inches, with a height of 3 inches.

Another set of possible dimensions could be b = 1, which would give us:

h = 9/b = 9/1 = 9

So another set of possible dimensions for the rectangular pyramid is a base of 1 inch by 9 inches, with a height of 9 inches.

Therefore, two sets of possible dimensions for the rectangular pyramid are: A base of 3 inches by 3 inches, with a height of 3 inches, A base of 1 inch by 9 inches, with a height of 9 inches.

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The figure W has one Rotational symmetries. This can be observed by rotating the figure by 0 or 180 degrees and noting that the shape remains unchanged. so the correct option is (b).

The letter W has one vertical line of symmetry that divides it into two identical halves. However, it does not have any rotational symmetry of order 2 or higher because there is no way to rotate the letter by a certain angle and have it look the same as before the rotation. Therefore, the answer is (b) 1, as W has only one line of symmetry and no rotational symmetry of order 2 or higher. In other words, if you rotate the letter by any angle other than 0 or 180 degrees, it will look different than before the rotation.

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______The given question is incomplete, the complete question is given below:

How many rotational symmetries does W alphabet have?

a. 0

b. 1

c. 2

d. 3

We have verified the identity [tex]csc^2(x)cos^2(x) = csc^2(x) - 1.[/tex]

What is trigonometry?

Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles, as well as the functions derived from these relationships. The most common trigonometric functions are sine, cosine, and tangent, which are abbreviated as sin, cos, and tan, respectively. These functions are used to model periodic phenomena such as sound waves, ocean tides, and the motion of planets.

To verify the identity [tex]csc^2(x)cos^2(x) = csc^2(x) - 1[/tex], we will start with the left-hand side and manipulate it until we get the right-hand side. Here's the full work:

[tex]csc^2(x)cos^2(x)[/tex] (given)

[tex]= (1/sin^2(x))(cos^2(x))[/tex] (definition of csc)

[tex]= (cos^2(x))/sin^2(x)[/tex] (multiply by reciprocal)

[tex]= (cos^2(x))/(1 - cos^2(x))[/tex](Pythagorean identity)

[tex]= (cos^2(x))/(1 - cos^2(x)) * [(1 + cos^2(x))/(1 + cos^2(x))][/tex] (multiply by conjugate)

[tex]= (cos^2(x)(1+cos^2(x)))/((1 - cos^2(x))(1 + cos^2(x)))[/tex](multiply and simplify)

[tex]= cos^2(x) * (1 + cos^2(x)) / (1 - cos^4(x))[/tex] (expand denominator)

[tex]= cos^2(x) / (1 - cos^2(x))[/tex] (cancel common factor of [tex]1 + cos^2(x))[/tex]

[tex]= csc^2(x) - 1[/tex](definition of csc and simplify)

Therefore, we have verified the identity [tex]csc^2(x)cos^2(x) = csc^2(x) - 1.[/tex]

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The expression that can be used to determine if she has enough money to purchase the jeans would be discussed below.

The total amount of money given to Natalie by her mom= $40.

The original price of the jeans = $45

The discount percentage = 20% of 45

= 20/100 ×45/1

= 900/100 = $9

The price of the jeans after discount = $36

The percentage of tax deduction = 8% of 45

= 8/100 × 45

= 360/100

= $3.6

The price of the jeans after tax = 36+ 3.6 = $39.6

Therefore, the amount of money that the money gave to Natalie to purchase jeans will be enough.

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Answer: the discount in dollars and cents was $10.40.

Step-by-step explanation: Austin bought some belts online for $26. With a 40% discount, the price of the belts is reduced by:

Discount = 40% x $26 = $10.40

So the new price after the discount is:

$26 - $10.40 = $15.60

Then a 10% processing fee is applied to the discounted price of $15.60, so the final price paid by Austin is:

Final price = $15.60 + 10% x $15.60 = $17.16

Therefore, the discount in dollars and cents was $10.40.

ANSWER : Austin got discount of 8.84 $ and 34% of price of belt.

EXPLANATION

Price of belts is $26.

Price of belts after discount of 40% = $15.6

(60% of 26 is 15.6)

Price of belt after processing fee of 10% = 17.16

(110% of 15.6 is 17.16)

Final discount in $ = Price of belt - Price of belt after processing fee

26-17.16=8.84

Final discount in % = (8.84*100)/26 =34%

The value of euros can be converted to dollars by simply multiplying euro by 1.06 so 120 euros be 127.89 dollars.

Unit conversion is the process of converting the dimension of a given quantum between colorful units, frequently by multiplicative conversion factors that alter the value of the measured volume without altering its goods.

The sanctioned currency of 20 of the EU's 27 member countries is the euro( symbol€; law EUR)( EU). By of 2023, this group of countries — officially known as the eurozone or euro area — will have around 344 million residers. One euro is equal to one hundred cents.

The United States bone ( symbol$; law USD; frequently shortened asUS$ orU.S. Bone to separate it from other bone - nominated currencies; also known as the bone ,U.S. bone , American bone , or informally buck) is the sanctioned coin of the United States and multitudinous other nations.

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The value on conversion of 300 Fahrenheit to Celsius will be equal to 148.8 Celsius depending on the relation.

The temperature in degree celsius is calculated using the formula -

Celsius = 5/9 (F - 32)

Now we need to keep the value of fahrenheit in the formula where F represents Fahrenheit

Celsius = 5/9 (300 - 32)

Firstly solving the bracket where subtraction sign is present. So, performing the subtraction first.

Celsius = 5/9 × 268

Performing division and multiplication on Right Hand Side of the equation

Temperature in Celsius = 148.8

Therefore, the temperature in Celsius is 148.8.

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