City A and City B had two different temperatures on a particular day. On that day, five times the temperature of City A was 8° C more than three times the temperature of City B. The temperature of City A minus twice the temperature of City B was −4° C. The following system of equations models this scenario: 5x = 8 + 3y x − 2y = −4 What was the temperature of City A and City B on that day?

The properties of isosceles trapezoid are

The lengths of the left and right sides of an isosceles trapezoid are equal or identical hence the base angles are likewise equal.

Because lengths of the left and right sides are equal and base angels are equal, the diagonals are equal

Other types of trapezoid include

generally all trapezoid have two sides that are parallel to each other

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The force the road exerts on the car as the car passes the highest point of the bump n=mg−mv²/R

Newton's second law of motion defines the behavior of objects for which all existing forces are not balanced.

The second law states that the acceleration of an object is dependent upon two variables - the net force acting upon the object and the mass of the object.

The acceleration of an object depends directly upon the net force acting upon the object, and inversely upon the mass of the object.

The free-body diagram given below shows the forces on the car in the vertical direction. Newton’s second law then gives

∑F y=may = mv²/R

mg−n=mv²/R

n=mg−mv²/R

When n=0, mg=mv²/R​

Then, v= √gR

A more gently curved bump, with a larger radius, allows the car to have a higher speed without leaving the road. This speed is proportional to the square root of the radius.

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Equivalent equations are algebraic equations that are having identical roots or solutions

Equations in algebra with the same roots or solutions are said to be equivalent. An analogous equation is one that is created by adding or removing the identical number, symbol, or expression from both sides of an equation. We can also get an equivalent equation by multiplying or dividing both sides of an equation by the same nonzero value.

Expressions that are equivalent do the same thing even when they have distinct appearances. When we enter the same value(s) for the variable, two algebraic expressions that are equivalent have the same value (s).

To determine which complex expression is the simple expression's equivalence:

Give any coefficients a distribution:

a(bx±c)=abx±ac

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Answer: The marginal product is the change in total product that results from an additional unit of input. With the addition of the seventh unit of input, the marginal product can be calculated as follows:

Total product when 7 units of input is used: 58

Total product when 6 units of input is used: 55

Marginal product = Total product when 7 units of input is used - Total product when 6 units of input is used

Marginal product = 58 - 55 = 3

So with the addition of the seventh unit of input, the marginal product is 3 units.

Step-by-step explanation:

The  percentage of community service Joe still need to complete is 45%,

the correct option is C

Suppose the value of which a thing is expressed in percentage is "a'

Suppose the percent that considered thing is of "a" is b%

Then since percent shows per 100 (since cent means 100), thus we will first divide the whole part in 100 parts and then we multiply it with b so that we collect b items per 100 items(that is exactly what b per cent means).

We need to Write the percent as a fraction in simplest form

16.24%

So, we can rewrite it as;

16.24 / 100

16 and 24/100 or 16 6/25

So the percent as a fraction is 16 6/25.

Given;

Total number of hours joe has to perform= 40

Number of hours joe has already performed= 18

Now;

Percentage;

=18*100/40

=18*5/2

=45

Therefore, the percentage will be 45%

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The relationship between factors and multiples from the equation  6 x 7 = 42 are given below.

Factorization in mathematics is the process of dividing a large number into smaller ones that, when multiplied together, give you the original number. Factorization is the process of dividing a number into its components or divisors.

Given:

An equation,

6 x 7 = 42.

Multiples are what you receive after multiplying a factor, which is what you can multiply to produce a number.

1 x 42 = 42

2 x 21 = 42

3 x 14 = 42

6 x 7 = 42

So the factors of 42 are 1, 2, 3, 6, 7, 14, 21, 42

The multiples of 42 are 1,2,3,4,5,6 etc.

Therefore, the relationship between factors and multiples are given

above.

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The code chunk to add is summarize(mean(Rating)), and the mean rating is 3.185933 according to the ratings system, summarize(), and mean() functions.

Now, According to the question:

The full code should be trimmed flavors df%>% summarize(mean(Rating)) to determine the mean rating.

In order to present summary statistics, this code combines the summarize() and mean() functions to show the mean rating of your data.

The statistic that will be displayed due to the "mean()" method is the mean rating, which in this instance would be 3.185933.

The mean scale score represents the overall effectiveness of a group of students on a test. A mean scale score is calculated specifically by adding up the scores of each individual student and dividing that total by the number of scores. It is additionally known as an average.

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Answer:

y = 1/3x +2

Step-by-step explanation:

when x =o, y=2

when x= -6, y=0

so slope is always the difference between the Ys divided by diff b/w the Xs

so the slope is (2-0)/(0-(-6)) =  1/3

the intercept by definition is when x=0, so it's 2

so Y = 1/3 X +2

The scale will register a weight greater than 80 pounds due to Newton’s Third Law

Given that there is a 1-liter container filled with 500 milliliters of water placed on top of a scale displaying 80 pounds.will register a weight greater than 80 pounds

When a body is submerged in a water an upward force acts on the body known as buoyant force which is equal to weight of the water displaced by the body. Since water exerts Buoyant force on the body and according to Newton's third law there must be equal and opposite force exerted by the body on the water. This additional force equal and opposite to the Buoyant force will cause the reading of the scale to increase. Therefore the scale will register a weight greater than 80 pounds due to Newton’s Third Law.

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The complete question is :

There is a 1-liter container filled with 500 milliliters of water placed on top of a scale displaying 80 pounds. When a metal cube is submerged tied to a string end into the container, which of the following statements accurately describes the result?

The cube’s density must be provided to predict what will happen

The scale will remain at 80 pounds until the cube is floating on top of the water fully submerged.

The scale will register a weight greater than 80 pounds due to Newton’s Third Law

The scale will register a weight greater than 80 pounds due to Newton’s Third Law

Answer:

D. {x | x > 2}

Step-by-step explanation:

Separately solve inequalities:

[tex]\displaystyle{3x-2 > -11 \ \: \text{and} \ \: -2x+1 < -3}[/tex]

For left inequality, add 2 both sides. For right inequality, subtract 1 both sides:

[tex]\displaystyle{3x-2 +2 > -11+2 \ \: \text{and} \ \: -2x+1-1 < -3-1}\\\\\displaystyle{3x > -9 \ \: \text{and} \ \: -2x < -4}[/tex]

For left inequality, divide both sides by 3. For right inequality, divide both sides by -2 and also switch from < to > since the coefficient of x is negative:

[tex]\displaystyle{\dfrac{3x}{3} > \dfrac{-9}{3} \ \: \text{and} \ \: \dfrac{-2x}{-2} > \dfrac{-4}{-2}}\\\\\displaystyle{x > -3 \ \: \text{and} \ \: x > 2}[/tex]

Since both are in form of x > a and x > b, consider for highest value (since putting value below than 2 would make the other inequality false but if we put value higher than 2 then it'd make both inequalities true) which is x > 2.

All of the trains scheduled to leave from the Concert Hall station are listed in Keiko's record for the population, and a random selection of 70 train records are listed in Keiko's record for the sample. As a result, statement II is true for the population, whereas statement I is true for the sample. The total population or all trains is regarded as a parameter, while the random group is regarded as a statistic.

In statistics, when we talk about population, we are talking about the entire population from which we want to draw a conclusion about. And when we talk about sample, we are talking about a particular or specific group from which we want to collect data from. So the size of sample will be less compared to the total size of the population.

a) In the given scenario, when we discuss population, we are referring to all of the trains that were scheduled to depart the Concert Hall station in the previous year. So statement II is correct.

And, when we discuss samples, we are referring to the random sample of 70 train records that Keiko audited. So statement I is correct.

b) When we talk about parameters, we are talking about the data of an entire population or all trains. And, when we are talking about statistics, we are talking about the sample data or random group.

The complete question is -

The records for all trains scheduled to depart from the Concert Hall train station last year showed that the average delay for these trains was 13.1 minutes, 18.6% of the trains had been delayed, and 12 trains had been canceled. Keiko is a traffic engineer helping the Concert Hall station improve its performance. She audited a random group of 70 records of trains scheduled to depart from the Concert Hall station last year. In her group the trains were late an average of 22.5 minutes, 30% of the trains had been delayed, and 4 trains had been canceled.

a. For Keiko's audit of train records, identify the population and the sample

Population:

I. The random group of 70 records of trains audited by Keiko.

II. The records of all the trains scheduled to depart from the Concert Hall station last year.

Sample:

I. The random group of 70 records of trains audited by Keiko.

II. The records of all the trains scheduled to depart from the Concert Hall station last year

b. Choose whether each number described below is a parameter or a statistic for Keiko's audit.

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True, The Laffer curve shows the exclusively direct relationship that exists between tax rates and tax revenues

The Laffer Curve was developed by Arthur Laffer. Arthur, a supply side economist used this curve to show the relationship that existed between tax rates and also the amount of tax revenue which the government takes or collects. This curve provides an illustration to his argument that sometimes when tax rates are cut there could be increase in total tax revenue.

True, The Laffer curve shows the exclusively direct relationship that exists between tax rates and tax revenues

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The solution for the expression is (35y - 22)/(5y-8)(10y+1). The solution has been obtained by solving the algebraic expression.

What is algebraic expression?

An algebraic expression is one that uses variables, constants, and algebraic operations (addition, subtraction, etc.).

The four primary categories of expressions are as follows:

We are given

⇒(2/5y -8)+ (3/10y+1)

⇒(2(10y+1) + 3(5y -8))/(5y-8)(10y+1)

⇒(20y + 2 + 15y - 24)/(5y-8)(10y+1)

⇒(35y - 22)/(5y-8)(10y+1)

Hence, the solution for the expression is (35y - 22)/(5y-8)(10y+1).

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The roof of the barn measures 4701 square feet. (This is equivalent to saying that the barn has a roofing area of 4701 square feet.)

What is integration ?

Integration is a fundamental concept in calculus. It refers to the process of finding the integral of a function, which gives the total amount of change of a quantity over a given interval. The process of integration is the reverse of differentiation, which is the process of finding the rate of change of a quantity. The symbol for integration is ∫.

A barn is 100 feet long and 40 feet wide.

Find the first derivative of the given function:

dy/dx = -10[1/20e^x/20 - 1/20 e^-x/20]

1 + (dy/dx)^2 = 1/4[e^x/20 - e^-x/20]^2

The arc length:

= ∫ √1/4[e^x/20 - e^-x/20]^2 dx

After solving the above integration:

= 20(e - 1/e)

The roofing = 100(20(e - 1/e))

= 4701 square feet,

The roof of the barn measures 4701 square feet. (This is equivalent to saying that the barn has a roofing area of 4701 square feet.)

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The order of rotational symmetry of a square about its center is 4.

Geometrically speaking, a shape has rotational symmetry when it retains its appearance following a small amount of rotation by a partial turn. The number of different orientations in which an object appears exactly the same for each rotation is known as the degree of rotational symmetry.

The number of times a square fits onto itself during a full rotation of 360 degrees determines a square's rotational symmetry. The square in the images above can be seen to fit four times on top of itself during a full 360-degree rotation.

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Taking k as a common factor on the first expression, we can rewrite that into the second one, thus, the expressions are equivalent.

Two expressions are equivalent only of we can, using algebra, rewrite one of the expressions into the other one.

The two given expressions are:

k + 0.10k

and

1.1k

Now let's take the first expression:

k + 0.10k

We can take k as a common factor, then we will get:

k + 0.10k = (1 + 0.10)k = 1.1k

So yea, the two expressions are equivalent.

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The ratios equivalent to 7:6 can be expressed as a) 14 : 12

The concept that will be used here is ratio. The proportion is an equation that demonstrates how two ratios are equivalent, but the notion of ratio defines us to compare two quantities.

A ratio in mathematics demonstrates how many times one number is present in another. For instance, if a dish of fruit contains eight oranges and six lemons, the ratio of oranges to lemons is eight to six. The ratio of oranges to the overall amount of fruit is 8:14, and the ratio of lemons to oranges is 6:8.

From the  ratios equivalent to 7:6 which can be written as 7/6

Then we consider option A , 14/12 = 7/6 ( divide the denominator and numerator by factor of 2.

Option B; 2 : 18 = 2/18 = 1/9

option C : 28 : 26 = 16/ 13

option D : 30 : 25 = 6/5

Therefore, option A is correct.

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Missing options:

a) 14 : 12

b) 2 : 18

c) 28 : 26

d) 30 : 25

Answer:

yes

Step-by-step explanation:

9(b_5)

multiply 9 with everything in the bracket:

9×b=9b

9×5=45

:9(b-5)

It will take them 28 minutes to fill the tank.

The fractional bar is a horizontal bar that divides the numerator and denominator of every fraction into these two halves.

Given:

The first pipe alone can fill the tank in 84 minutes.

So, the rate at which the first pipe fills the tank = 1/84

and, The second pipe can fill the tank in 42 minutes by itself.

So, the rate at which the second pipe fills the tank =1/42

If they work together, they would work simultaneously and their individual rates are additive.

= 1/84 + 1/42

let it takes t hours for both pipes to fill the tank working together, the working rate per minute would be 1/t. Therefore,

1/84 + 1/42 = 1/t

3/84 = 1/t

t = 84/3

t = 28 minutes

Hence, 28 minutes will take to fill.

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The bearing of B from S = 63.8 + 180 = 243.8°

To calculate the distance that the boys walked, you would need to know their speed and the duration of their walk.

Speed is typically measured in units such as miles per hour (mph) or kilometers per hour (kph). If you know the speed of the boys and the duration of their walk in hours, you can calculate the distance they walked using the formula: distance = speed x time.

To calculate the bearing of S from B, you can use the following steps:

Calculate the distance between S and B using the Pythagorean theorem. The distance is the hypotenuse of a right triangle, where one side is 8.6 km (the north-south distance) and the other side is 12.5 km (the east-west distance).

Calculate the angle formed by the distance between S and B and the north-south line. To do this, you can use the arctangent function (atan), which returns the angle in radians.

To convert radians to degrees, multiply by 180/π

The bearing of S from B = atan(12.5/8.6) x 180/π = 63.8°

To calculate the bearing of B from S, you just need to add 180 degrees to the bearing of S from B

The bearing of B from S = 63.8 + 180 = 243.8°

b. 243.8

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Complete question:

A bank B is 8.6 km north and 12.5 km west of a school S.

Calculate correct to 3 significant figures:

a the bearing of S from B

b the bearing of B from S.

Using the quadratic equation the distance of point B from the ground level is D. 3 units

An equation is a mathematical function that shows the relationship between two variables.

Since an archway is modeled by the equation y = -2x² + 8x.

A rod is to be placed across the archway at an angle defined by the equation x − 2.23y + 10.34 = 0.

If the rod is attached to the archway at points A and B, such that point B is at a higher level than point A, we desire to find the distance of point be from the ground. To do this , we proceed as follows.

Since we have the equations

Substituting y into the second equation, we have

x - 2.23y + 10.34 = 0

x - 2.23(-2x² + 8x) + 10.34 = 0

x + 4.46x² - 17.84x + 10.34 = 0

4.46x² - 16.84x + 10.34 = 0

To find the points a and B, we solve for x where both equations intersect.

So, using the quadratic formula, we solve for x

[tex]x = \frac{-b +/-\sqrt{b^{2} - 4ac} }{2a}[/tex] where a = 4.46, b = -16.84 and c = 10.34

So, substituting the values of the variablers into the equation, we have that

[tex]x = \frac{-(-16.84) +/-\sqrt{(-16.84)^{2} - 4\times4.46\times10.34} }{2\times4.46}\\= \frac{16.84 +/-\sqrt{283.5856 - 184.4656} }{8.92}\\= \frac{16.84 +/-\sqrt{99.12} }{8.92}\\= \frac{16.84 +/-9.96 }{8.92}\\x = \frac{16.84 + 9.96 }{8.92} or x = \frac{16.84 - 9.96 }{8.92}\\x = \frac{26.8}{8.92} or x = \frac{6.88}{8.92}\\x = 3.004 or x = 0.771[/tex]

Since B is higher, we take the higher value x = 3.

So, the distance of point B from the ground level is D. 3 units

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Using the quadratic equation the distance of point B from the ground level is D. 3 units

An equation is a mathematical function that shows the relationship between two variables.

Since an archway is modeled by the equation y = -2x² + 8x.

A rod is to be placed across the archway at an angle defined by the equation x − 2.23y + 10.34 = 0.

If the rod is attached to the archway at points A and B, such that point B is at a higher level than point A, we desire to find the distance of point be from the ground. To do this , we proceed as follows.

Since we have the equations

Substituting y into the second equation, we have

x - 2.23y + 10.34 = 0

x - 2.23(-2x² + 8x) + 10.34 = 0

x + 4.46x² - 17.84x + 10.34 = 0

4.46x² - 16.84x + 10.34 = 0

To find the points a and B, we solve for x where both equations intersect.

So, using the quadratic formula, we solve for x

[tex]x = \frac{-b +/-\sqrt{b^{2} - 4ac} }{2a}[/tex] where a = 4.46, b = -16.84 and c = 10.34

So, substituting the values of the variablers into the equation, we have that

[tex]x = \frac{-(-16.84) +/-\sqrt{(-16.84)^{2} - 4\times4.46\times10.34} }{2\times4.46}\\= \frac{16.84 +/-\sqrt{283.5856 - 184.4656} }{8.92}\\= \frac{16.84 +/-\sqrt{99.12} }{8.92}\\= \frac{16.84 +/-9.96 }{8.92}\\x = \frac{16.84 + 9.96 }{8.92} or x = \frac{16.84 - 9.96 }{8.92}\\x = \frac{26.8}{8.92} or x = \frac{6.88}{8.92}\\x = 3.004 or x = 0.771[/tex]

Since B is higher, we take the higher value x = 3.

So, the distance of point B from the ground level is D. 3 units

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Answer:

$155.56

Step-by-step explanation:

S.I=(PRT)÷100

$144=(P×9×1)÷100

crossmultiply

$144×100=9P

P=$14400÷9

P=$155.56

The inequality that represents the situation in this problem is given as follows:

x + 3 < 16

The inequality symbols are given as follows:

In three years, your friend's age is given as follows:

x + 3.

To apply for the driver's license, an age of 16 is needed, and your friend will be younger than 16, as he/she cannot apply, hence the inequality is:

x + 3 < 16

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The length of the road after D days of construction (L) is equal to the original length of the road (10 miles) plus the number of miles added by the construction crew each day (1 mile/day) times the number of days the construction has been going on (D).

So the equation relating L to D is:

L = 10 + 1D

This equation can be graph on a Cartesian plane with D on the x-axis and L on the y-axis. The graph will be a straight line passing through the point (0,10) and having a slope of 1, meaning that for every one increase in D there is a one increase in L.

It will look like this:

graph{10+x [-12, 12, -6, 6]}

Where D=x and L=y.

Answer: L - 10 = D

Step-by-step explanation:

1 Day = 1 Mile
After 1 Day of construction a 1 Mile is added to the road
Original length is 10 miles
Length (e.g. 11 miles) - 10miles = Day 1
So:
L - 10 = D

The answer for the blank is we can use a dive table or computer.

When planning a subsequent dive, it is important to take into account the dive time, depth, and surface interval from the previous dive in order to safely plan for the next dive. To determine the required surface interval, one can use a dive table or a dive computer.

A dive table is a printed or electronic table that provides information about the safe amount of time that can be spent at certain depths, based on the previous dive. The table will take into account the dive time, depth, and surface interval from the previous dive, and provide a recommended surface interval to ensure safe diving.

A dive computer, on the other hand, is an electronic device that is worn by the diver and calculates the safe amount of time that can be spent at a certain depth, based on the diver's previous dive. The dive computer takes into account the dive time, depth, and surface interval from the previous dive, and provides a recommended surface interval to ensure safe diving.

In summary, to determine the required surface interval before returning to the same site and depth for another 60 minutes dive, one can use a dive table or a dive computer. These tools will give you the recommended time for your surface interval, based on your previous dive profile, so you can ensure you have enough no-stop time for your next dive.

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A two-sample z-interval for a population proportion. This method is used to create an estimate of the percentage of trees in a large forest that are infested with a certain beetle by taking a random sample of trees to inspect.

A two-sample z-interval for a population proportion is the most appropriate method for creating an estimate of the percent of trees in a large forest that are infested with a certain beetle. This method involves taking a random sample of trees from the forest and inspecting them to determine the proportion of infested trees. The sample size chosen should be large enough to provide a reliable estimate of the proportion of trees in the population that are infested. A two-sample z-interval is then used to calculate a confidence interval for the population proportion, which can be used to estimate the overall percent of trees in the forest that are infested with the beetle. This method can provide a reliable estimate of the percent of trees in the forest that are infested with the beetle, allowing environmentalists to make informed decisions regarding management of the forest.

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The larger angle between the pair of supplementary angles is 126 degrees.

Supplementary angles are simply angles that sum up to 180 degrees.

Given the data in the question;

Since, they both form a supplementary angle, their sum gives a total of 180 degree.

Angle 1 + Angle 2 = 180

(4x+30) + (2x+6) = 180

Solve for x

4x + 2x + 30 + 6 = 180

6x + 36 = 180

6x = 180 - 36

6x = 144

x = 144 / 6

x = 24

Now, we determine the measure of the angles.

Angle 1 = (4x+30)

Angle 1 = 4(24) + 30

Angle 1 = 126 degrees

Angle 2 = (2x+6)

Angle 2 = 2(24) + 6

Angle 2 = 54 degrees.

Therefore, the larger angles measures 126 degree.

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Harris ate (n - 4)/4 number of  slices of pizza.

An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.

Given:

4 friends evenly divided up an n-slice pizza.

That means,

n / 4.

One of the friends, Harris, ate 1 fewer slice than he received.

That means,

n/4 - 1

= (n - 4)/4

Therefore, Harris ate  (n - 4)/4.

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Answer:

32%

Step-by-step explanation:

1552 / 4850 = 0.32

The expression of (9 * 10⁶)(8 * 10⁸) in scientific notation is; 72 * 10¹⁴

Scientific notation is defined as a way of writing very large or very small numbers. A number is usually written in scientific notation when a number between 1 and 10 is multiplied by a power of 10. For example, 750,000,000 can be written in scientific notation as 7.5 * 10⁸.

We want to multiply the expression given as;

(9 * 10⁶)(8 * 10⁸)

Now, we can rewrite this as;

(9 * 8) * (10⁶ * 10⁸)

According to laws of exponents, x² × x³ = x²⁺³

Thus;

(9 * 8) * (10⁶ * 10⁸) = 72 * 10⁶⁺⁸

= 72 * 10¹⁴

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