If every 2 cm on a scale drawing is equal to 7 feet in real life, which lines on the drawing would be greater than 21 feet in real life? Select all that apply. A) 7 cm B) 5 cm C) 9 cm D) 12 cm

The value of x that satisfies this equation 4(2.5)2^x= 4 is x = -1.32

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

4(2.5)2^x= 4

This gives

(10)2^x= 4

Divide the equation by 10

So, we have the following

2^x = 0.4

Take the logarithm of both sides and evaluate

x = -1.32

Hence, the solution is x = -1.32

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if one of the end points of the diameter is at the origin and the radius is 3 then the the equation of the circle in general form is:x² + y² - 3x = 0

An equation is a statement that shows the relationship between two or more variables using mathematical symbols. It expresses the equality or inequality between the values of the variables on either side of the equation.

According to the given information :

Since one of the endpoints of the diameter is at the origin, we know that the center of the circle is also at the origin. Let (x, y) be any point on the circle. Then, using the distance formula, we have:

√(x² + y²) = 3

Squaring both sides, we get:

x² + y² = 9

So, the equation of the circle in standard form is:

x² + y² - 9 = 0

Another way to write the equation of the circle is in general form, which is:

x² + y² + Dx + Ey + F = 0

where D, E, and F are constants. To find the values of D, E, and F, we substitute the coordinates of one of the points on the circle into the general form equation:

(0)² + (0)² + D(0) + E(0) + F = 0

F = 0

So, the equation of the circle in general form is:

x² + y² + Dx + Ey = 0

To find the values of D and E, we substitute the coordinates of another point on the circle into this equation. Let's use the point (3, 0) since we know it lies on the circle. Substituting these values, we get:

(3)²+ (0)² + D(3) + E(0) = 0

9 + 3D = 0

D = -3

Therefore, the equation of the circle in general form is:

x² + y² - 3x = 0

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Answer:

1499.06 cm³

Step-by-step explanation:

volume = length × width × height

length = 22.5 cm

width = 10.25 cm

height = 6.5 cm

volume = 22.5 cm × 10.25 cm × 6.5 cm

volume = 1499.0625 cm³

Answer: 1499.06 cm³

Answer:-1/6

Step-by-step explanation:

Draw a line out in the 2nd quadrant.

Your y=[tex]\sqrt{35}[/tex]    hypotenuse=6  use pythagorean theorem to solve for x

6² = 35 + x²

x=1

so

cosΘ = -1/6

The equation of the line of best fit is y = x + 16 and the money spent on entertainment for a student who works 8 hours is $24

Drawing the line of best fit, we have the following points

(0, 6) and (16, 22)

The equation is represented as

y = mx + c

Where

c = y when x = 0

So, we have

y = mx + 6

Using the points, we have

16m + 6 = 22

So, we have

m =1

So, the equation is

y = x + 6

This means that

x = 8

So, we have

y = 8 + 16

y = 24

Hence, the amount is $24

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The valid conclusions about the data being surveyed is Option A: Of the students who attended the basketball game, fewer than half of them also attended the school play.

What is a survey?

Questioning a group of people in a survey is one way to collect information from them. Surveys can be carried out using a variety of methods, including paper and pencil, online forms, the telephone, or in-person interviews.

A. Of the students who attended the basketball game, fewer than half of them also attended the school play. (True)

To calculate this, we need to divide the number of students who attended both the basketball game and the school play (55) by the total number of students who attended the basketball game (118).

55/118 = 0.466 = 46.6%, which is less than half.

B. More than half of the students who were surveyed attended the school play and did not attend the basketball game. (False)

To calculate this, we need to add up the number of students who attended the school play and did not attend the basketball game (63) and divide by the total number of students surveyed (221).

63/221 = 0.285 = 28.5%, which is less than half.

C. Students who attended the school play were more likely not to attend the basketball game. (False)

To calculate this, we need to compare the number of students who attended the school play and did not attend the basketball game (63) to the number of students who did not attend the school play and did not attend the basketball game (15).

63/78 = 0.808 = 80.8% and 15/78 = 0.192 = 19.2%. Since 80.8% is greater than 19.2%, we can conclude that students who attended the school play were more likely to attend the basketball game.

Therefore, valid conclusions is A.

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The value when x approaches to 0 the function approaches to 2.718.

In many different mathematical situations, particularly in calculus and analysis, the special number e is used. Although its precise number is an infinite decimal with no pattern, it is roughly equal to 2.71828. The limit of the formula as n approaches infinity is the definition of the constant e. The letter e stands for this limit, which is real and equivalent to a particular number. In many branches of mathematics and science, including the study of exponential and logarithmic functions, the constant e is crucial. It can be used in physics, probability theory, and mathematics, among other things.

The given function is: [tex]\ lim (x \to 0) \frac{2^x - 1}{x}[/tex].

Substituting the value of x = 0.01 we have:

[tex]\ lim (x \to 0) \frac{2^{0.01} - 1}{0.01}\\[/tex]

f(x) = 2.704

Similarly substituting the values of x from the table we have:

x                   f(x)

0.01            2.704

0.001          2.718

0.0001       2.7182

-0.0001      2.7181

-0.001         2.716

-0.01            2.669

Hence, as the x approaches to 0 the function approaches to 2.718.

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Accordingly, utilising name-brand microwave popcorn rather than store-brand microwave popcorn is anticipated to yield a higher percentage of popped kernels based on the results of this study.

A test statistic is a numerical summary of a sample used in statistics to evaluate the strength of the evidence presented by the data in support of a certain conjecture about the population from which the sample was taken. A test statistic determines how many standard errors the observed data deviates from the predicted value by comparing it to what would be expected under the null hypothesis. To ascertain if an observed effect or difference between groups is the result of chance or if it is statistically significant, test statistics are employed in hypothesis testing.

Here,

We can compare the mean percentage of popped kernels between the two groups using a hypothesis test to see if using name-brand microwave popcorn yields a higher proportion of popped kernels than store-brand microwave popcorn.

Let μ1 be the mean percentage of popped kernels for name-brand microwave popcorn and μ2 be the mean percentage of popped kernels for store-brand microwave popcorn.

The null hypothesis states that there is no distinction between store-brand and name-brand microwave popcorn in terms of the mean percentage of popped kernels:

H0: μ1 - μ2 = 0

The alternate theory is that name-brand microwave popcorn has a mean percentage of popped kernels that is higher than that of store-brand microwave popcorn:

Ha: μ1 - μ2 > 0

This hypothesis can be examined using a two-sample t-test with unequal variances. For a one-tailed test with 18 degrees of freedom and a significance threshold of 0.05, the crucial t-value is 1.734.

Based on the information provided, we can determine that the sample mean percentage of popped kernels for name-brand microwave popcorn is 90.9% with a sample standard deviation of 5.09% and the sample mean percentage of popped kernels for store-brand microwave popcorn is 85.9% with a sample standard deviation of 4.67%.

We can calculate the test statistic as follows:

t = (x1 - x2 - 0) / √(s1²/n1 + s2²/n2)

t = (90.9 - 85.9) / √((5.09²/10) + (4.67²/10))

t = 2.26

We can reject the null hypothesis and come to the conclusion that there is enough evidence to support the claim that using name-brand microwave popcorn results in a greater percentage of popped kernels than store-brand microwave popcorn at the 0.05 level of significance because the calculated t-value (2.26) is greater than the critical t-value (1.734).

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The area of the wooden platform built by Mr. Burns for the drama club at the school is 288 square feet.

What are the dimensions of a rectangle?

A rectangle has two dimensions: a length and a width that are both perpendicular to it. An oval's or a triangle's interior likewise has two dimensions.

The area of a rectangle is determined by dividing its length by its width. Accordingly, the platform's area can be determined as follows:

Area = Length x Width

Area = 24 feet x 12 feet

Area = 288 square feet

Therefore, the area of the wooden platform built by Mr. Burns for the drama club at the school is 288 square feet.

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According to the question of drop factor, the answer is 53.3ml that will be infused per hour.

Drop factor is a mathematical concept related to the concept of rate. It is a unitless coefficient used to adjust a given rate. Drop factor is commonly used to represent the rate of change in a linear equation, and can be used to calculate the rate at which a given value decreases over time. The drop factor is calculated by subtracting the previous value from the current value and dividing it by the change in time. This value can then be used to calculate the rate of change over time.

The calculation for the amount of ml that will be infused per hour is as follows:

Volume (L) x Drop Factor (gtt/ml) = Total Drops

0.8 L x 60 gtt/ml = 480 drops

Total Drops / Time (hours) = Drops/Hour

480 drops / 9 hours = 53.3 drops/hour

Since 1 drop is equal to 1 ml, this means 53.3 ml of fluid will be infused per hour.

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Answer:

First account: $6380.

Second account: $4251.

Step-by-step explanation:

let the first account have $x at the start of the first year

So at the end of 1 year it had x + 0.1x = $1.1x

In the same we we calculate the amount in the second account

= $1.09(9700 - x)

So we have the following equation

1.1x + 1.09(9700 - x) = 9700 + 931

1.1x + 10573 - 1.09x = 10631

0.01x = 10631 - 10573 = 58

x = 58/0.01

   =$5800

So at the end of the year there was

5800 * 1.1 = $6380 in first account

and

the second account had

1.09 (9700 - 5800) = $4251.

The dimensions of the wooden platform are 24 feet long by 60 feet wide, making the area 1440 square feet and the perimeter 168 feet.

Area is a two-dimensional measurement of a surface, usually measured in square units, such as square feet or square meters. It is used to measure the size of a room, a piece of land, an object, or any other two-dimensional shape. Area is also used to calculate the perimeter, or distance around an object, or the volume of a three-dimensional object. It is an important concept in mathematics and helps us understand the world around us.

The wooden platform built by Mr Burns has a rectangular shape with a length of 24 feet and a width of 60 feet. This yields an area of 1440 square feet (24 x 60 = 1440). The perimeter of the platform is 168 feet (2 x 24 + 2 x 60 = 168).

The platform is large enough to accommodate the entire drama club. It is also big enough to accommodate other activities, allowing the drama club to have a larger space for their performances. The platform also provides a secure base for the club to perform on.

The dimensions of the wooden platform are 24 feet long by 60 feet wide, making the area 1440 square feet and the perimeter 168 feet. The size of the platform is suitable for the size of the drama club, and its sturdy construction will give them a secure and safe place to perform.

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Answer:

The answer is 13hours

Step-by-step explanation:

360miles------>5hours

936miles------->x hours

crossmultiply

x×360=936×5

360x=4680

divide both sides by 360

360x/360=4680/360

x=13hours

The percdentile is 69.15 for z=0.5.Next, take the two percentiles apart.

The normal distribution is an illustration of a continuous distribution of probabilities in which most data points are grouped in the middle of the range and the remaining ones taper off equally to either extreme. The middle of the range is sometimes referred to as the distribution's mean.

The mean, median, and mode are all equal in normal distributions, which are symmetric, unimodal, and asymptotically distributed. A normal distribution is perfectly symmetrical on both sides.

Percentage of data points with z=a and b between two supplied data points

Add the a% sign and subtract the table percentile for z=a from the table percentile for z=b.

The percentile for the data table for z=-0.5 is 30.85.

the percdentile is 69.15 for z=0.5.Next, take the two percentiles apart.

69.15-30.85= 38.3%

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Approximately 38.30% of data points in a normal distribution fall between z = -0.5 and z = 0.5.

A special kind of normal distribution called a "standard normal distribution" has a mean () of 0 and a standard deviation () of 1.

When comparing alternative normal distributions with arbitrary mean and standard deviation, the standard normal distribution is frequently used as a reference distribution in statistics and probability theory.

We employ a procedure called standardisation, which entails dividing by the standard deviation and removing the mean from any normal distribution to get a standard normal distribution.

The percentage of data items in a normal distribution that lie between z = -0.5 and z = 0.5 can be found using a standard normal distribution table or a calculator with normal distribution capabilities.

Using a standard normal distribution table, the value for z = -0.5 is 0.3085, and the value for z = 0.5 is 0.6915. Subtracting these values gives:

0.6915 - 0.3085 = 0.3830

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The inequality with the given solution set is given as follows:

D. -2 ≤ x + 5 < 6.

The four inequality symbols, along with their meaning on the number line and the coordinate plane, are presented as follows:

The solution to the compound inequality in this problem is given as follows:

-7 ≤ x < 1.

Hence the inequality can be obtained adding 5 to each term, as follows:

-7 + 5 ≤ x + 5 < 1 + 5 = -2 ≤ x + 5 < 6.

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There are 7,776 different outcomes when rolling five 6-sided dice.

In the game of Yahtzee, the dice used has 6 sides. This means that each dice has 6 possible outcomes.  

Dice 1 = 6outcomes  Dice 2 = 6 outcomes  dice 3 = 6outcomes

Dice 4 = 6outcomes dice 5 = 6outcomes

We multiply all the outcomes by the total number of the 6-sided dice will be used for the game, which is 5.

We can express it as follows

6 × 6 × 6 × 6 × 6

It can also be expressed as 6⁵, the power 5 being the number of times that 6 will be multiplied

= 7776

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The median, mean, range and mode will be 6, 5.4, 9 and 7.

What is median?

The median is the middle number in the data set when the data set is written from least to greatest.

The median is the number in the middle when arranged in an ascending order. The numbers will be:

0, 3, 4, 6, 6, 7, 7, 7, 9.

The median is 6.

The range is the difference between the highest and lowest number which is: = 9 - 0 = 9

The mode is the number that appears most which is 7.

The mean will be the average which will be:

= (0 + 3 + 4 + 6 + 6 + 7 + 7 + 7 + 9) / 9.

= 49/9

= 5.4

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On a fair 8-sided die, the probability of rolling a 3 is 1/8, or 0.125, which is equivalent to 12.5% in percentage terms.

The possibility or likelihood that an event will occur is measured by probability.

A number between 0 and 1, where 0 indicates that the occurrence is hypothetical and 1, meaning it is inevitable, is used to express it.

To put it another way, probability is the ratio of likely outcomes to real outcomes that pertain to a particular occurrence.

Every result (rolling any number from 1 to 8) is equally likely since the die is fair.

There are only two ways to roll a 3, and there are a total of eight outcomes.

As a result, the probability of rolling a 3 is:

P(rolling a 3) = 1/8

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Answer:

The motorist's rate is:

rate = distance / time

where distance is measured in kilometers and time is measured in hours.

We are given that the motorist travels 228 kilometers in 6 hours, so we can use this information to find the rate:

rate = distance / time = 228 km / 6 hours = 38 km/hour

To find how long it will take the motorist to travel an additional 247 kilometers at this rate, we can use the same formula and solve for time:

time = distance / rate = 247 km / 38 km/hour ≈ 6.5 hours

Therefore, it will take the motorist approximately 6.5 hours to travel an additional 247 kilometers at the same rate of 38 km/hour.

6 bottles would hold 3 liters of water.

In general, the total capacity of x bottles would be 0.5x liters, where x represents the number of bottles.

If nine bottles have a total capacity of 4.5 liters, we can determine the capacity of each bottle by dividing the total capacity by the number of bottles.

In this case, we have:

Capacity per bottle = Total capacity / Number of bottles

= 4.5 liters / 9 bottles

= 0.5 liters per bottle.

Now, if we want to find out how much x bottles would hold, we can simply multiply the capacity per bottle by the number of bottles (x). Therefore, the formula to calculate the total capacity of x bottles would be:

Total capacity of * bottles = Capacity per bottle *  Number of bottles

= 0.5  liters per bottle *  x  bottles

= 0.5x liters.

So, x bottles would hold 0.5x liters of water.

For example, if we wanted to find out how much 6 bottles would hold, we could substitute x with 6 in the formula:

Total capacity of 6 bottles = 0.5 * 6 liters

= 3 liters.

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On solving the equations the amount of 95% mixture required is obtained as 135 mL.

What is an equation?

A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("=").

Let's call the amount of 95% alcohol mixture we need to add "x".

We want to end up with a 50% alcohol solution, so the amount of pure alcohol in the final solution should be 50% of the total volume.

The amount of pure alcohol in the 405 mL of 35% alcohol mixture is -

0.35 × 405 = 141.75 mL

Let's set up an equation to solve for x -

0.95x + 141.75 = 0.5(x + 405)

First, let's distribute the 0.5 on the right side -

0.95x + 141.75 = 0.5x + 202.5

Subtract 0.5x and 141.75 from both sides -

0.45x = 60.75

Divide both sides by 0.45 -

x = 135

Therefore, you need to add 135 mL of the 95% alcohol mixture to obtain the desired 50% alcohol solution.

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The value of x in the right triangle is 5.6 units.

A right triangle is a triangle that has one of its angles as 90 degrees. The sum of angles in a triangle is 180 degrees.

Therefore, the side length x of the right triangle can be found using trigonometric ratios as follows:

tan 48 = opposite / adjacent

where

opposite side = x

adjacent side = 5

Hence,

tan 48 = x / 5

cross multiply

x = 5 tan 48

x = 5 × 1.11061251483

x = 5.55306257415

Therefore,

x = 5.6 units

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According to given fraction values, Harry used 4 gallons of paint in total.

What is fraction?

A fraction is a way of representing a part of a whole or a ratio of two numbers. It consists of a numerator (top number) and a denominator (bottom number) separated by a horizontal line.

To find the total amount of paint Harry used, we need to add the amount of paint he used for the living room and the amount of paint he used for his bedroom. We have:

2 1/4 gallons + 1 3/4 gallons

To add these two mixed numbers, we need to find a common denominator. The smallest common denominator of 4 and 4 is 4. So we can rewrite the mixed numbers as improper fractions:

2 1/4 = 9/4

1 3/4 = 7/4

Now we can add the two fractions:

9/4 + 7/4 = 16/4

Simplifying the fraction, we get:

16/4 = 4

Therefore, Harry used 4 gallons of paint in total.

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The amount in the account after 5 years would be $9555.42.

What is the formula for compound interest?

[tex]A = P(1 + \frac{r}{n} )^{(nt)}[/tex]

Where:

A = the amount of money in the account after t years

P = the principal amount (initial investment)

r = the annual interest rate (as a decimal)

n = the number of times the interest is compounded per year

t = the number of years

In this case, P = $6500, r = 8% = 0.08, n = 1 (compounded annually), and t is the number of years.

If no withdrawals are made from the account, then the amount of money in the account after t years will be

[tex]A = 6500(1 + \frac{0.08}{1})^{(1t)} \\ A = 6500(1.08)^t[/tex]

Now the amount of money in the account after a specific number of years,

A = 6500(1.08)⁵

A = 6500(1.469328)

A = $9555.42

So after 5 years, the amount in the account would be $9555.42

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Correct question is "Suppose Juan places $6500 in an account that pays 8% interest compounded each year. Assume that no withdrawals are made from the account.Then find What would be the amount in the account after 5 years?"

Answer:

15 = m

Step-by-step explanation:

10 − 3(m − 5) = 2(5 − m)

10 - 3m + 15 = 10 - 2m

25 - 3m = 10 - 2m

25 - 10 = - 2m + 3m

15 = m

__________

hope it helps!

Answer:

m=15

Step-by-step explanation:

10 − 3(m − 5) = 2(5 − m)

-3m+25=10-2m

-3m= -2m -15

-m=-15

m=15

For the given normal distribution a. We expect approximately 954 chicks to hatch between 25 and 33 days. b. We expect approximately 683 chicks to hatch between 27 and 31 days.

A probability distribution that is frequently used in statistics is the normal distribution, usually referred to as the Gaussian distribution. The majority of the data are within one standard deviation of the mean, resulting in a bell-shaped curve that is symmetrical around the mean.

In a normal distribution, the mean, median, and mode are all equal, and the mean and standard deviation serve as the two parameters that define the curve. While the standard deviation reflects the distribution's spread, the mean represents the distribution's centre.

The z-score is given by the formula:

z = (x - mu) / sigma

a. For 25 to 33 days:

z = (25 - 29) / 2

z = -2

and

z = (33 - 29) / 2

z = 2

Thus, P(z < 2) = 0.9772.

Now, we have:

P(25 < x < 33) = P(z < 2) - P(z < -2)

P(25 < x < 33) = 0.9772 - 0.0228

P(25 < x < 33) = 0.9544

Expected number of chicks = 0.9544 x 1000 = 954.4

Hence, we expect approximately 954 chicks to hatch between 25 and 33 days.

b. For 27 to 31 days:

P(27 < x < 31) = P(z < 1) - P(z < -1)

P(27 < x < 31) = 0.8413 - 0.1587

P(27 < x < 31) = 0.6826

Expected number of chicks = 0.6826 x 1000 = 682.6

Therefore, we expect approximately 683 chicks to hatch between 27 and 31 days.

c. For 29 days or fewer:

P(x <= 29) = P(z <= 0) = 0.5

Expected number of chicks = 0.5 x 1000 = 500

d. In 23 to 35 days:

P(23 < x < 35) = P(z < 3) - P(z < -3)

P(23 < x < 35) = 0.9987 - 0.0013

P(23 < x < 35) = 0.9974

Expected number of chicks = 0.9974 x 1000 = 997.4

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Answer:

No solution

Step-by-step explanation:

12(2x+11) = 12(2x+12)

24x + 132 = 24x + 144

0 + 132 = 144

0 = 12

This is not true, 0 ≠ 12, so there is no solution.

no value of x will make the equation true.

The equation [tex]12(2x+11)=12(2x+12)[/tex] 12(2x+11)=12(2x+12) is linear in one variable (x) with coefficients and constants that are real numbers. It can be simplified by performing basic algebraic operations, such as distributing and simplifying, to solve for the value of x.

To solve for x in the equation[tex]12(2x+11)=12(2x+12)[/tex] 12(2x+11)=12(2x+12), we will follow the steps of algebraic manipulation:

First, we will simplify both sides of the equation by distributing the 12 on each side:

[tex]12(2x+11)=12(2x+12)[/tex] 12(2x+11) = 12(2x+12)

[tex]24x + 132 = 24x + 144[/tex] 24x +132 = 24x + 144

Next, we will simplify further by subtracting 24x from both sides:

[tex]24x - 24x + 132 = 144[/tex] 24x - 24x + 132 = 144

[tex]132 = 144[/tex] 132 = 144

Since this is not a true statement, the equation has no solution. Therefore, no value of x will make the equation true.

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The equivalent fractions when paired up would be:

We must first simplify each fraction before categorizing them according to their simplified form in order to couple equivalent fractions. Since 2/4 and 4/8 may both be reduced to 1/2, they are equal.

The same is true of 2/3 which may be reduced to 4/6, they are both equivalent. 3/4 is the same as 6/8, they are equivalent.

Since 1/3 may be simplified to 2/6, they are equivalent.

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According to the information, the classification of the fractions would be: 3/4 = 6/8, 1/3 = 2/6, 4/6 = 2/3

To classify the fractions in the correct option box we can carry out two procedures. The first one is to simplify the fractions to identify which ones are equivalent to those in the boxes. On the other hand, we can do the divisions of the fractions and those that have the same results go in the same box. According to the above, the fractions are classified as follows:

Note: This question is incomplete. Here is the complete information:

Attached image

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