Help me please with this

The expression for Jack's brother's age is x = 3 + w

It is important that we know algebraic expressions are defined as expressions which are composed of variables, coefficients, constants, factors and terms.

These algebraic expressions are also identified with mathematical operations, such as;

From the information given, we have that;

Jack is w years old

His brother is 3 years old than him

His brother's age is also x

This is represented as;

x = 3 + w

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Answer:

Step-by-step explanation:

There is no algebraic expression in the question????

The scale factor used to produce Figure 2 from Figure 1 is given as follows:

7/3.

A dilation happens when the coordinates of the vertices of an image are multiplied by the scale factor, changing the side lengths of a figure.

The side lengths are given as follows:

Hence the scale factor of the dilation is given as follows:

7/3.

(the scale factor is the division of the side length of the dilated figure by the equivalent side length of the original figure).

The problem asks for the scale factor used from figure 1 to figure 2.

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Answer:

C 7/3 because i got it right

Answer:

To calculate the probability that the winner of the gift certificate bought a printer from Super Electronics, we need to use the total number of customers who participated in the survey as the denominator and the number of customers who bought printers as the numerator.

The total number of customers who participated in the survey is:

Total Customers = Number of Customers who bought Laptops + Number of Customers who bought Desktops + Number of Customers who bought Printers

Total Customers = 88 + 52 + 64

Total Customers = 204

The number of customers who bought printers is 64.

Therefore, the probability that the winner of the gift certificate bought a printer from Super Electronics is:

P(Bought a Printer) = Number of Customers who bought Printers / Total Customers

P(Bought a Printer) = 64 / 204

P(Bought a Printer) = 0.3137 (rounded to 4 decimal places)

So, the probability that the winner of the gift certificate bought a printer from Super Electronics is 0.3137 or approximately 31.37%.

As a result, the spherical bοttle οffers the greatest value fοr the amοunt οf perfume cοntained in each cubic centimetre because it cοsts the least.

The measurement οf a three-dimensiοnal οbject's space filled is its vοlume. Mοst οften, it is expressed in cubic measures like cubic metres, cubic centimetres, οr cubic feet. The vοlume οf a cube, fοr instance, can be calculated by multiplying its length, breadth, and height. Calculating a cube's vοlume is as fοllοws:

Capacity is calculated using the fοrmula LWH.

given:

The fοrmula V = pi x r² x h, where r is the radius οf the circular base and h is the height οf the bοttle, must be used tο determine the perfume cοntainer's vοlume. Hοwever, we are unable tο determine the vοlume because we lack the values fοr r and h. The fοrmula V = 4/3 π x r³, where r is the radius οf the spherical cοntainer, must be used tο determine the vοlume οf the perfume bοttle. Hοwever, we are unable tο determine the vοlume because we lack the value fοr r.

Price per cubic centimetre = $54.00 / 282.74 cm³ = $0.191 per cm³ Vοlume οf cylindrical cοntainer = π x (3 cm)²x 10 cm = 282.74 cm³

Cοnical cοntainer vοlume equals 1/3 π x (2 cm) 2 x 8 cm = 16.76 cm³.

$20.00 divided by 16.76 cm3 (price per cubic centimetre) yields $1.19 per cm3.

The vοlume οf a sphere is equal tο 4/3 π  x (4 cm)³ = 268.08 cm³.

$35.00 divided by 268.08 centimetres squared equals $0.13 per centimetre.

As a result, the spherical bοttle οffers the greatest value fοr the amοunt οf perfume cοntained in each cubic centimetre because it cοsts the least.

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A. If a friend's kid has no curfew, what is the probability that they don't have chores? B. the probability that a friend's kid doesn't have chores given that they have no curfew is 1/3. C. I chose this question because it involves calculating a conditional probability based on a given set of data.

Probability can also be used to describe more complex events, such as the likelihood of a stock price increasing by a certain amount in a given period of time, or the probability of a medical treatment being effective for a certain disease.

My Conditional Frequency Question is:

If a friend's kid has no curfew, what is the probability that they don't have chores?

Solution:

The conditional probability of a kid not having chores given that they have no curfew can be found using the formula:

P(No Chores | No Curfew) = P(No Chores and No Curfew) / P(No Curfew)

From the table, we can see that the number of kids who have no curfew and no chores is 2, and the total number of kids who have no curfew is 6. Therefore:

P(No Chores | No Curfew) = 2/6 = 1/3

So the probability that a friend's kid doesn't have chores given that they have no curfew is 1/3.

I chose this question because it involves calculating a conditional probability based on a given set of data. This is a common type of question in statistics and probability, and it requires an understanding of the basic concepts of probability such as conditional probability and independence. The table provided gives us the data we need to calculate the conditional probability, and the solution involves applying the formula for conditional probability and simplifying the fraction.

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The true number sentence is expression B: 3 + 4 = 7.

We must analyse each expression and contrast them in order to determine which number statement is correct.

Expression A: Paste the formula 5 + 8 = 12 – 1.

Taking into account the left-hand side of the equation:

The formula is 5 + 8 = 13.

Following is an evaluation of the right-hand side of the equation:

12 – 1 to get 11.

Expression A is incorrect since 13 and 11 are not equivalent.

B Expression

3 + 4 = 7

This is a straightforward addition equation, and the answer is that 3 + 4 = 7. As a result, expression B is accurate.

C expression

2 x 2 = 5 - 1

Taking into account the left-hand side of the equation:

2 x 2 = 4

Following is an evaluation of the right-hand side of the equation:

5 - 1 = 4

Expression C is accurate since 4 and 4 are equal.

D Expression

the formula 9 + 2 Equals 6 x 2.

Taking into account the left-hand side of the equation:

9 + 2 = 11 to copy

Following is an evaluation of the right-hand side of the equation:

6 x 2 =

Expression D is incorrect since 11 and 12 are not equal.

Hence, expression B—3 + 4 = 7—is the correct number expression.

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he correct answer is d. 4/ x^2 -2x+1 + 1.

To find f(g(x)), we need to substitute g(x) into f(x).

f(x) = x^2

g(x) = 2/x-1

So, f(g(x)) = (2/x-1)^2

= 4/x^2 - 4/x + 1

Therefore, the correct answer is d. 4/ x^2 -2x+1 + 1.

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Answer:

x = 0

Step-by-step explanation:

3(3x+5) - 8 =7

9x + 15 - 8 = 7

9x + 7 = 7

9x = 0

x = 0

Let's check

3(3(0) + 5) - 8 = 7

3(0 + 5) - 8 = 7

3(5) - 8 = 7

15 - 8 = 7

7 = 7

So, x = 0 is the correct answer.

Heather runs 3 miles in 28 minutes, so at the same rate, she would run 4.494 miles in 42 minutes.

To find out how many miles Heather would run in 42 minutes at the same rate, we use the concept of unit rate. Unit rate is a comparison of two different quantities when they are combined together. In this case, we need to find the unit rate of Heather's running speed in miles per minute.

Step 1: Find the unit rate of Heather's running speed in miles per minute.

To do this, we divide the distance she ran by the time she took to run it:

3 miles ÷ 28 minutes = 0.107 miles per minute

Step 2: Use the unit rate to find out how many miles Heather would run in 42 minutes.

To do this, we multiply the unit rate by the time she runs:

0.107 miles per minute × 42 minutes = 4.494 miles

Therefore, Heather would run 4.494 miles in 42 minutes at the same rate.

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.

Answer: 9/4

Step-by-step explanation:

Answer:

15/4 feet

Step-by-step explanation:

When given a mixed number like [tex]3\frac{3}{4}[/tex], you multiply the denominator by the whole number and add the numerator.

In this case, multiply 3 x 4 and then add 3. After finding that value, put it over the original denominator, giving 15/4

The original piece of cardboard should be approximately 32.86 inches by 16.43 inches.

To find the size of the original piece of cardboard, we can use the formula for the volume of the box, which is V = l × w × h. Since the box is open-topped, the height will be the size of the square that was removed from each corner, which is 3 inches. Also, given that the length of the original piece of cardboard is twice the width, we can substitute l = 2w in the formula. Therefore, the formula becomes:

V = (2w) × w × 3

Now, we can plug in the given volume of 1,620 in3 and solve for w:

1,620 = (2w) × w × 3

540 = 2w^2

270 = w^2

w = √270

w ≈ 16.43 inches

Now, we can use the value of w to find the length of the original piece of cardboard:

l = 2w = 2(16.43) = 32.86 inches

Therefore, the original piece of cardboard should be approximately 32.86 inches by 16.43 inches.

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If the matrix A = [a1 a2 a3 a4 a5] has reduced row echelon form [1−10​2​][00031​][00001​][00000​], then a basis for Col(A) is [a1−a2a3a4].

Reduced row echelon form is a way of representing a matrix that has been transformed into a more simplified version. It is commonly used in linear algebra and has many applications.

The columns of a matrix that contain at least one non-zero element in the reduced row echelon form are known as pivot columns. Pivot columns can be used to form a basis for the column space of the matrix.

The number of pivot columns determines the rank of the matrix. Since in the given matrix A has three pivot columns, therefore, the rank of the matrix is 3. Since there are three pivot columns in the reduced row echelon form, a basis for Col(A) must consist of the first three columns of A.

Hence, the required basis for Col(A) is [a1−a2a3a4].

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The value of f(3) using synthetic division is 72.

To find f(3) using synthetic division, we need to divide the polynomial f(v) by the factor (v - 3). This will give us the quotient and the remainder, which will help us find the value of f(3).

Write the coefficients of the polynomial in a row: 12 -40 4 17 21

Write the value of the factor we are dividing by to the left of the row: 3 | 12 -40 4 17 21

Bring down the first coefficient: 3 | 12 -40 4 17 21
          ------------------
             12

Multiply the first coefficient by the factor and write the result under the second coefficient: 3 | 12 -40 4 17 21
          ------------------
             12  36

Add the second coefficient and the result from step 4: 3 | 12 -40 4 17 21
          ------------------
             12  -4

Repeat steps 4 and 5 for the remaining coefficients: 3 | 12 -40 4 17 21
          ------------------
             12  -4  0  51

The last number in the bottom row is the remainder. This is the value of f(3): 3 | 12 -40 4 17 21
          ------------------
             12  -4  0  51  72

So, f(3) = 72.

Therefore, the value of f(3) using synthetic division is 72.

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Answer:

$948.34

Step-by-step explanation:

35% = .35

.35 x $2299

= $804.65

That is the total before the sales tax and after the sale.

6.25% = .0625

.0625 x $2299

= $143.69, and because that is 6.25% of the total, it must be added onto that as tax.

That means the total is $804.65 + $143.69

= $948.34

As a result, a new rectangle is created by increasing the breadth by 5 cm, making the οriginal rectangle 12 by 8 cm in size.

A rectangle is a flat, fοur-sided shape that is made by twο sets οf parallel lines at each οf its fοur right angles (angles οf 90 degrees). A rectangle's diagοnals and οppοsing sides have equal lengths and are bisected by its οppοsite sides. The perimeter οf a rectangle is equal tο the sum οf the lengths οf its fοur sides, and its area is calculated by multiplying its length by its breadth. Rectangles are frequently seen in daily living, including οn cοmputer screens, bοοk cοvers, and dοοrs and windοws.

given:

Let L represent the initial rectangle's length in centimetres.

Therefοre, the width οf the initial rectangle can be expressed as L – 4 cm, which is 4 cm less than its length.

The οriginal rectangle's area is equal tο the sum οf its length and breadth, sο:

Area οf the initial parallelοgram is equal tο L(L-4) = L2 - 4L.

The new rectangle's size is specified as 117 cm2, sο:

New rectangle's surface area Equals (L - 3)

(L + 1) = L² - 2L - 3 = 117

When we simplify this sοlutiοn, we οbtain:

L² - 2L - 120 = 0

Using the quadratic fοrmula, we can answer this quadratic equatiοn:

L is equal tο (-b √(b² - 4ac)) / 2a.

where (a, b, and c) are (1, 2, and -120)

As a result, there are twο οptiοns:

L = 12 οr L = -10

Rectangles cannοt have negative lengths, sο we rule οut the negative sοlutiοn and determine that the initial rectangle's length was 12 cm.

We can determine the breadth by using the fοrmula fοr the width οf the initial rectangle:

Original rectangle's width is equal tο L – 4 (12 – 4), οr 8 centimetres.

As a result, a new rectangle is created by increasing the breadth by 5 cm, making the οriginal rectangle 12 by 8 cm in size.

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Due to the formation of two identical rectangles, the streetlight is consequently twice as large as the individual.

A triangle is a polygon with three vertices and three angles that has three sides. It is one of the fundamental geometric shapes and has numerous uses in fields like engineering, physics, architecture, and more. The lengths of a triangle's sides and angles can be calculated using a variety of geometric formulas. Triangles come in a variety of shapes, including equilateral, isosceles, scalene, right-angled, acute-angled, and obtuse-angled triangles, each of which has unique attributes.

given

Let x represent the person's height.

Let x represent the streetlight's height.

Let d represent the distance between an individual and a streetlight.

Let s be the size of the shade cast by the subject.

According to the facts provided, x equals 6 feet (height of the person)

d Equals 15 feet (distance from the person to the streetlight)

The shadow's extent, s, is 15 feet.

Finding y's number, or the streetlight's height, is necessary.

The following ratios can be written using the comparable triangles property:

y / (d + s) Equals x / s

Inputting the numbers provided yields:

By condensing and figuring out x, we arrive at:

y = 12 feet

Consequently, the streetlight has a 12 foot height.

We can divide the streetlight's height by the person's height to determine how many times higher the streetlight is:

y / x = 12 / 6 = 2

Due to the formation of two identical rectangles, the streetlight is consequently twice as large as the individual.

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The number of broken eggs will give you an idea of how well the new package design protects the eggs from impacts. If there are no broken eggs, the package design may be effective. However, if there are several broken eggs, the package design may need to be improved to provide better protection.

When testing a new package design, it is important to simulate real-world conditions as much as possible. In this case, dropping a carton of a dozen eggs from a height of 1 foot is a good way to simulate the types of impacts that the package may experience during shipping and handling.

To conduct the test, you will need to follow these steps:

The number of broken eggs will give you an idea of how well the new package design protects the eggs from impacts. If there are no broken eggs, the package design may be effective.

However, if there are several broken eggs, the package design may need to be improved to provide better protection.

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The Mean, Mode, and Median for the number of wins are 37.8; 29, 42; 38 respectively. The standard deviation and variation are 11.15 and 124.26 respectively. 9 teams had over 41 wins. 16.67% of teams scored below 30 wins. Our data set for age does not represent a normal curve, it is positively skewed. The lowest and highest Z-score for wins are -1.78 and 1.99 respectively. The Z-score for the number of wins for 37 is -0.07.

To create a frequency table, we need to categorize the number of wins into intervals and count the number of teams in each interval. We can use the following intervals: 15-24, 25-34, 35-44, 45-54, 55-64.

| Interval | Frequency |
|---------|----------|
| 15-24   | 3        |
| 25-34   | 5        |
| 35-44   | 8        |
| 45-54   | 5        |
| 55-64   | 2        |

To calculate the mean, we add up all the values and divide by the number of values:

Mean = (60 + 44 + 39 + 29 + 23 + 57 + 50 + 43 + 37 + 27 + 49 + 42 + 37 + 29 + 19 + 56 + 51 + 40 + 33 + 26 + 48 + 42 + 31 + 25 + 18 + 53 + 44 + 40 + 29 + 23)/30 = 37.8

To find the mode, we look for the value that appears most often. In this case, it is 29 and 42, both appearing twice.

Mode = 29, 42

To find the median, we need to order the values from smallest to largest and find the middle value. If there is an even number of values, we take the average of the two middle values.

Ordered values: 18, 19, 23, 23, 25, 26, 27, 29, 29, 31, 33, 37, 37, 39, 40, 40, 42, 42, 43, 44, 44, 48, 49, 50, 51, 53, 56, 57, 60

Median = (37 + 39)/2 = 38

To calculate the standard deviation, we first find the variance by subtracting the mean from each value, squaring the result, and then taking the average of those squared differences. The standard deviation is the square root of the variance.

Variance = [(60-37.8)^2 + (44-37.8)^2 + ... + (23-37.8)^2]/30 = 124.26

Standard deviation = sqrt(124.26) = 11.15

To find the number of teams with over 41 wins, we can count the values that are greater than 41:

Number of teams with over 41 wins = 9

To find the percent of teams with below 30 wins, we can count the values that are less than 30 and divide by the total number of teams:

Percent of teams with below 30 wins = (5/30)*100 = 16.67%

To create a histogram, we can use the intervals and frequencies from the frequency table and plot them on a graph with the intervals on the x-axis and the frequencies on the y-axis. We can also add a normal curve by calculating the mean and standard deviation and using a normal distribution function.

The data set for the number of wins does not represent a normal curve, as it is slightly positively skewed (there are more values on the lower end of the distribution).

The lowest Z-score is for the value 18, which is (18-37.8)/11.15 = -1.78. The highest Z-score is for the value 60, which is (60-37.8)/11.15 = 1.99.

The Z-score for the value 37 is (37-37.8)/11.15 = -0.07. This means that the value 37 is 0.07 standard deviations below the mean.

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Sinusoidal (periodic) functions, also known as sine and cosine functions, are ubiquitous in our daily lives. They are used to model a wide range of phenomena in fields such as engineering, physics, and mathematics.

One of the most common applications of sinusoidal functions is in the field of electronics, where they are used to model alternating current (AC) circuits.

Sinusoidal functions are also used in signal processing, audio and image compression, and speech recognition. In addition, they are used in the design of various mechanical and electrical systems, such as engines, turbines, and power generators.

Sinusoidal functions also play an important role in wave motion, such as ocean waves and sound waves. They are used to model the behavior of waves and to predict their properties, such as wavelength and frequency.

Furthermore, sinusoidal functions are used in the field of optics to model the behavior of light waves. They are used to describe the properties of light waves, such as amplitude, frequency, and phase.

In conclusion, sinusoidal functions have a wide range of applications in various fields, from electronics and signal processing to mechanics and optics. Their versatility and accuracy make them an essential tool for modeling and predicting real-world phenomena.

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Answer: Let x = 0.727272...

Then, 100x = 72.727272...

Subtracting x from 100x gives:

100x - x = 72.727272... - 0.727272...

99x = 72

x = 72/99

We can simplify this fraction by dividing both the numerator and denominator by their greatest common factor, which is 9. Therefore:

x = (72/9) / (99/9) = 8/11

So, a = 8 and b = 11. Therefore, the recurring decimal 0.727272... can be expressed as the fraction 8/11.

Step-by-step explanation:

The answer of the question based on the to represent the area of the figure the answer is given below,

A rectangle is four-sided polygon with opposite sides that are parallel and congruent (equal) in the length.

a) The figure is a rectangle with a length of 2x + 3 and a width of x - 2. The area of the rectangle is:

Area = length x width

Area = (2x + 3)(x - 2)

Using the distributive property of multiplication, we can simplify this expression:

Area = 2x² - 4x + 3x - 6

Area = 2x² - x - 6

Therefore, the expression for the area of the figure is 2x² - x - 6.

The figure is a trapezoid with a height of 3 and two parallel sides of length x + y and x - y. average of lengths of the two sides are:

(x + y + x - y)/2 = 2x/2 = x

So, the area of the trapezoid is:

Area = (1/2) x height x (sum of parallel sides)

Area = (1/2)(x)(3)(x + y + x - y)/2

Area = (3/2) x²

Now, we need to subtract the area of the triangle from the trapezoid. The triangle has a height of 3 and a base of y, so its area is:

(1/2)(y)(3) = (3/2)y

Therefore, the expression for the area of the figure is:

Area = (3/2)x² - (3/2)y.

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Answer:

Step-by-step explanation

So first do 12-6=6 then multiply 14x6 which is 84 so 84 bags in 14 weeks is 3 and a half months.

The probability that Ann's score is above 600 is 1 - 0.6628 = 0.3372.

(a) The shape of the sampling distribution of the sample means will be approximately normal. This is because of the Central Limit Theorem, which states that the sampling distribution of the sample means will be approximately normal if the sample size is large enough, regardless of the shape of the population distribution. In this case, the sample size of 35 is large enough for the Central Limit Theorem to apply.

(b) The mean of the sampling distribution of the sample means will be equal to the mean of the population, which is 550. The standard deviation of the sampling distribution of the sample means will be equal to the standard deviation of the population divided by the square root of the sample size, which is 120/√35 ≈ 20.28.

(c) To find the probability that the average score of the 35 selected students is above 600, we need to find the z-score for 600 using the mean and standard deviation of the sampling distribution of the sample means. The z-score is (600 - 550)/20.28 ≈ 2.47. Using a z-table, we can find the probability that the z-score is less than 2.47, which is 0.9932. Therefore, the probability that the average score of the 35 selected students is above 600 is 1 - 0.9932 = 0.0068.

(d) To find the probability that Ann's score is above 600, we need to find the z-score for 600 using the mean and standard deviation of the population. The z-score is (600 - 550)/120 ≈ 0.42. Using a z-table, we can find the probability that the z-score is less than 0.42, which is 0.6628.

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The sum of the two vectors is a vector with length 26.56 and an angle of 12.72°.

The vector ü can be represented in Cartesian coordinates as (16cos5°, 16sin5°) and the vector ü can be represented as (11cos25°, 11sin25°).

To find the sum of these two vectors, we add their corresponding coordinates:
(16cos5° + 11cos25°, 16sin5° + 11sin25°)

Using a calculator, we can approximate these values:
(25.82, 5.81)

Therefore, the sum of the two vectors is approximately (25.82, 5.81) in Cartesian coordinates. To find the length and angle of this vector, we can use the Pythagorean theorem and the inverse tangent function:

Length = √(25.82² + 5.81²)

≈ 26.56

Angle = tan⁻¹(5.81/25.82)

≈ 12.72°

So the sum of the two vectors is a vector with length 26.56 and an angle of 12.72°.

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Answer:

  75 seconds

Step-by-step explanation:

You want to know how long it took Sean to drink his slushy, given a graph of amount remaining versus time.

Sean will have finished his slushy when the amount remaining is zero. That point on the graph occurs when the time is 75 seconds.

It takes 75 seconds for Sean to finish the slushy.

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The graph and the solution to the system of inequalities are added as attachments

System 1

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

x ≤ -3

y < 5/3x + 2

The above system is a system of inequalities that contain two linear inequalities

Next, we plot the graph

One of the points in the shaded region is (-4, -5)

System 2

Here, we have the following system

y ≤ -5/2x - 2

y < -1/2x + 2

The above system is a system of inequalities that contain two linear inequalities

Next, we plot the graph

One of the points in the shaded region is also (-4, -5)

System 3

Here, we have the following system

y ≥ 2/3x + 3

y > -4/3x - 3

The above system is a system of inequalities that contain two linear inequalities

Next, we plot the graph

One of the points in the shaded region is also (4, 7)

See attachment for the graph of the inequalities

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Louise has 2 1/4 feet more of green yarn than white yarn.

What is the fractions ?

A fraction is a way to represent a part of a whole or a ratio between two quantities.

To compare the amounts of green and white yarn, we need to express the amounts in the same units. Let's convert 2/4 yards of white yarn to feet, since the green yarn is already measured in feet.

1 yard = 3 feet

2/4 yard = 2/4 * 3 feet/yard = 1.5 feet

Now we can compare the amounts of green and white yarn in feet:

Amount of green yarn = 3 3/4 feet

Amount of white yarn = 1.5 feet

To find how many more feet of green yarn Louise has than white yarn, we can subtract the amount of white yarn from the amount of green yarn:

3 3/4 feet - 1.5 feet = 2 1/4 feet

Hence, Louise has 2 1/4 feet more of green yarn than white yarn.

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The positive solution for x in the equation log_x(1)/256 = -4/3 is x = 4.57

To solve the logarithm problem for the positive solution for x, we can use the following steps:

1. First, we can rewrite the equation in exponential form:
x^(-(4)/(3)) = 1/256

2. Next, we can raise both sides of the equation to the power of -(3)/(4) to isolate x:
(x^(-(4)/(3)))^(-(3)/(4)) = (1/256)^(-(3)/(4))

3. Simplify the left side of the equation:
x = (1/256)^(-(3)/(4))

4. Simplify the right side of the equation:
x = 256^((3)/(4))

5. Take the fourth root of both sides of the equation:
x = (256^((3)/(4)))^(1/4)

6. Simplify the right side of the equation:
x = 256^((3)/(16))

7. Simplify the exponent:
x = 256^(3/16)

8. Calculate the value of x:
x ≈ 4.57

Therefore, the positive solution for x is approximately 4.57.

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