compute the zeros of the polynomial 4x2 - 4x - 8

The probability that an 18-year-old man selected at random is between 70 and 72 inches tall is approximately 0.0793 and the probability that the mean height of a sample of eight 18-year-old men is between 70 and 72 inches is approximately 0.9057 and the probability in part (b) is much higher because the standard deviation is smaller for the x distribution.

What do you mean by normally distributed data?

In statistics, a normal distribution is a probability distribution of a continuous random variable. It is also known as a Gaussian distribution, named after the mathematician Carl Friedrich Gauss. The normal distribution is a symmetric, bell-shaped curve that is defined by its mean and standard deviation.

Data that is normally distributed follows the pattern of the normal distribution curve. In a normal distribution, the majority of the data is clustered around the mean, with progressively fewer data points further away from the mean. The mean, median, and mode are all the same in a perfectly normal distribution.

Calculating the given probabilities :
(a) The probability that an 18-year-old man selected at random is between 70 and 72 inches tall can be found by standardizing the values and using the standard normal distribution table. First, we find the z-scores for 70 and 72 inches:

[tex]z-1 = (70 - 71) / 5 = -0.2[/tex]

[tex]z-2 = (72 - 71) / 5 = 0.2[/tex]

Then, we use the table to find the area between these two z-scores:

[tex]P(-0.2 < Z < 0.2) = 0.0793[/tex]

So the probability that an 18-year-old man selected at random is between 70 and 72 inches tall is approximately 0.0793.

(b) The mean height of a sample of eight 18-year-old men can be considered a random variable with a normal distribution. The mean of this distribution will still be 71 inches, but the standard deviation will be smaller, equal to the population standard deviation divided by the square root of the sample size:

[tex]\sigma_x = \sigma / \sqrt{n} = 5 / \sqrt{8} \approx 1.7678[/tex]

To find the probability that the sample mean height is between 70 and 72 inches, we standardize the values using the sample standard deviation:

[tex]z_1 = (70 - 71) / (5 / \sqrt{8}) \approx -1.7889[/tex]

[tex]z_2 = (72 - 71) / (5 / \sqrt{8}) \approx 1.7889[/tex]

Then, we use the standard normal distribution table to find the area between these two z-scores:

[tex]P(-1.7889 < Z < 1.7889) \approx 0.9057[/tex]

So the probability that the mean height of a sample of eight 18-year-old men is between 70 and 72 inches is approximately 0.9057.

(c) The probability in part (b) is much higher because the standard deviation is smaller for the x distribution. When we take a sample of eight individuals, the variability in their heights is reduced compared to the variability in the population as a whole. This reduction in variability results in a narrower distribution of sample means, with less probability in the tails and more probability around the mean. As a result, it becomes more likely that the sample mean falls within a given interval, such as between 70 and 72 inches.

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Answer:

a=1/3

Step-by-step explanation:

First, expand the brackets by doing multiplication:

2+6a+3=3a+6

Then, move the unknown to the left and the numbers to the right:

3a=6-5

3a=1

a=1/3

The solution to the given equation is -1.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

The solution of an equation is the set of all values that, when substituted for unknowns, make an equation true.

The given equation is 2+3(2a+1)=3(a+2)

2+6a+3=3a+2

6a+5=3a+2

6a-3a=2-5

3a=-3

a=-1

Therefore, the solution to the given equation is -1.

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Answer:

The answer to 1 + 1 is 2.

Very complicated problem, please mark brainliest!

Answer:

1+1 = 2

Or, 1=2-1

1=1

we know value of one is one

so,

1+1=11

The slopes are,

1) 7/6

2)7/2

3) -1

4) -2

5) 10/9

What is slope?

Calculated using the slope of a line formula, the ratio of "vertical change" to "horizontal change" between two different locations on a line is determined. The difference between the line's y and x coordinate changes is known as the slope of the line.Any two distinct places along the line can be used to determine the slope of any line.

1) The given points , [tex](x_1,y_1) =(0,1)[/tex] and [tex](x_2,y_2) = (6,8)[/tex] then,

=> slope  = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex] = [tex]\frac{8-1}{6-0} = \frac{7}{6}[/tex]

2) The given points [tex](x_1,y_1) =(-1,10)[/tex] and [tex](x_2,y_2) = (-5,-4)[/tex] then,

=> Slope = [tex]\frac{-4-10}{-5+1} = \frac{-14}{-4}=\frac{7}{2}[/tex]

3)  The given points [tex](x_1,y_1) =(-10,2)[/tex] and [tex](x_2,y_2) = (-3,-5)[/tex] then,

=> slope = [tex]\frac{-5-2}{-3+10} = \frac{-7}{7}=-1[/tex]

4)  The given points [tex](x_1,y_1) =(-3,-4)[/tex] and [tex](x_2,y_2) = (-1,-8)[/tex] then,

=> slope = [tex]\frac{-8+4}{-1+3} = \frac{-4}{2}=-2[/tex]

5)The given points [tex](x_1,y_1) =(0,1)[/tex] and [tex](x_2,y_2) = (-9,-9)[/tex] then,

=> slope = [tex]\frac{-9-1}{-9+0} = \frac{-10}{-9}=\frac{10}{9}[/tex]

Hence the slopes are,

1) 7/6

2)7/2

3) -1

4) -2

5) 10/9

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An assignment of probabilities to events in a sample space must obey all of the following: They must obey the addition rule for disjoint events, They must sum to 1 when adding over all events in the sample space, and The probability of any event must be a number between 0 and 1, inclusive. Hence, the correct option is All of the above.

Probability is the branch of mathematics that deals with the likelihood of a random event occurring. Probability is concerned with quantifying the probability of different results in a certain event.

The possibility that a specific event will occur is calculated using probability. Probability is calculated using several methods in mathematics, including axioms, probability spaces, events, random variables, and expectation values.

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The power dissipated by the heater is 1260 watts (W).

What is a polynomial?

A polynomial is a mathematical expression consisting of variables (also known as indeterminates) and coefficients, which are combined using only the operations of addition, subtraction, and multiplication.

Given:

Current (I) = 10.5 A

Potential Difference (V) = 120 V

Unknown:

Power (P) = ?

The formula to calculate the power is:

P = VI

Substituting the given values:

P = 120 V × 10.5 A

P = 1260 W

It's important to note that the number of significant digits should be based on the precision of the given values. In this case, both values have three significant digits, so the answer should also have three significant digits. Thus, the final answer should be:

P = 1260 W (rounded to three significant digits).

Therefore, the power dissipated by the heater is 1260 watts (W).

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The equation in standard form for the circle with center (5,0) passing through (5, 9/2) is 4x² + 4y² - 40x + 19 = 0

Given that

Center = (5, 0)

Point on the circle = (5. 9/2)

The equation of a circle can be expressed as

(x - a)² + (y - b)² = r²

Where

Center = (a, b)

Radius = r

So, we have

(x - 5)² + (y - 0)² = r²

Calculating the radius, we have

(5 - 5)² + (9/2 - 0)² = r²

Evaluate

r = 9/2

So, we have

(x - 5)² + (y - 0)² = (9/2)²

Expand

x² - 10x + 25 + y² = 81/4

Multiply through by 4

4x² - 40x + 100 + 4y² = 81

So, we have

4x² + 4y² - 40x + 19 = 0

Hence, the equation is 4x² + 4y² - 40x + 19 = 0

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The percentiles for the standard normal distribution

a. 0.93

b. -0.88

c. 0.67

d. -0.65

e. -1.28

To determine the percentiles for the standard normal distribution, use the standard normal distribution table. Percentiles for standard normal distribution are given by the standard normal distribution table.

The standard normal distribution is a special type of normal distribution with a mean of 0 and a variance of 1.

Step 1: Write down the given percentiles as a decimal and round to two decimal places.

For example, for the 81st percentile, 0.81 will be used.

Step 2: Use the standard normal distribution table to find the corresponding z-score.

Step 3: Round off the obtained answer to two decimal places.

a) 81st percentile:

The area to the left of the z-score is 0.81.

The corresponding z-score is 0.93.

Hence, the 81st percentile for the standard normal distribution is 0.93.

b) 19th percentile:

The area to the left of the z-score is 0.19.

The corresponding z-score is -0.88.

Hence, the 19th percentile for the standard normal distribution is -0.88.

c) 76th percentile:

The area to the left of the z-score is 0.76.

The corresponding z-score is 0.67.

Hence, the 76th percentile for the standard normal distribution is 0.67.

d) 24th percentile:

The area to the left of the z-score is 0.24.

The corresponding z-score is -0.65.

Hence, the 24th percentile for the standard normal distribution is -0.65.

e) 10th percentile:

The area to the left of the z-score is 0.10.

The corresponding z-score is -1.28.

Hence, the 10th percentile for the standard normal distribution is -1.28.

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Answer:

Point-Slope Form: y - 1 = -1/2(x - 4) or Standard Form: y = -1/2x + 3

Step-by-step explanation:

For a line to be perpendicular, you take the negative inverse of the slope of 2x - y = 4. To do this, rearrange the y to one side and you get y = 2x - 4. The slope of the line is 2. So, taking the negative inverse would be -1/m (with m being slope of the the equation given in the problem. This would give you -1/2.

Using point slope formula, y - y1 = m(x - x1), you can plug in the point given, (4,1) and the slope you found to get y - 1 = -1/2(x - 4). For standard form, isolating the y gets you y = -1/2x + 3.

You can check your answer by using Desmos by putting in the line 2x - y = 4, the point (4,1), and the equation you got as your answer. You will see that the equation is perpendicular to 2x - y = 4 and passes through point (4,1). Your equation of the line is y - 1 = -1/2(x - 4) or y = -1/2x + 3

Answer:

She will draw 120 times for a red marble

Step-by-step explanation:

Answer:

Step-by-step explanation:

9m = 7m + 4

9m - 7m = 4

2m = 4

m = 2

----------------------------------

check

9 x 2 = 7 x 2 + 4

18 = 18

this answer is good

n + 6 = 2n - 1

n + 7 = 2n

7 = n

-----------------------------------

7 + 6 = 2 x 7 - 1

13 = 13

this answer is good

Answer:15 percent

Step-by-step explanation:

The work required to pump all the water out of the rectangular swimming pool over the top is approximately 2,323,200 ft-lb.

We have,

To find the work required to pump all the water out of the rectangular swimming pool, we can use the concept of work as the force multiplied by the distance.

First, let's calculate the weight of the water in the pool.

The weight of an object is given by the formula:

Weight = mass x gravitational acceleration

Since the density of water is given as 1 lb/ft³, we need to find the volume of water in the pool.

The volume of the pool is given by the formula:

Volume = length x width x depth

Volume = 50 ft x 30 ft x 6 ft = 9000 ft³

Now, let's calculate the weight of the water:

Weight = density x volume x gravitational acceleration

Weight = 1 lb/ft³ x 9000 ft³ x 32.2 ft/s² ≈ 290,400 lb

To pump all the water out over the top, we need to raise it to the height of the pool, which is 8 ft.

The work required to pump the water out is given by the formula:

Work = weight x height

Work = 290,400 lb x 8 ft = 2,323,200 ft-lb

Therefore,

The work required to pump all the water out of the rectangular swimming pool over the top is approximately 2,323,200 ft-lb.

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Answer:

"9 more than A" is a verbal expression.

In summary, to find the null spaces of the matrices given in exercises 9 and 10, use the Gauss-Jordan elimination method and refer to the Remarks that follow example 3 in section 4.2 of the text. This will give the dimension of the null space and the number of free variables.
In exercises 9 and 10, the null space of the given matrices can be found by solving the homogeneous linear system of equations. In order to do this, use the Gauss-Jordan elimination method. Refer to example 3 in section 4.2 of the text for a detailed explanation. Afterwards, use the Remarks that follow the example to determine the dimension of the null space and the number of free variables.

The null space of a matrix is the set of all vectors that produce a zero vector when the matrix is multiplied by the vector. Therefore, to find the null space of a matrix, the homogeneous linear system of equations needs to be solved. The Gauss-Jordan elimination method involves adding multiples of one row to another to get a row with all zeroes. After this is done for all the rows, the equations can be solved for the free variables. The number of free variables will determine the dimension of the null space. Refer to example 3 in section 4.2 of the text for more details.

The Remarks that follow the example are important when determining the dimension of the null space and the number of free variables. In the Remarks, it is mentioned that the number of free variables is equal to the number of columns with a zero row. Therefore, after using the Gauss-Jordan elimination method to get the row with all zeroes, the number of columns with a zero row can be counted. This will give the dimension of the null space and the number of free variables.

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Answer:

operaciones vectoriales, Extensión de las leyes del álgebra elemental a los vectores. Incluyen suma, resta y tres tipos de multiplicación. La suma de dos vectores es un tercer vector, representado como la diagonal del paralelogramo construido con los dos vectores originales como lados.

Answer:

operaciones vectoriales, Extensión de las leyes del álgebra elemental a los vectores. Incluyen suma, resta y tres tipos de multiplicación. La suma de dos vectores es un tercer vector, representado como la diagonal del paralelogramo construido con los dos vectores originales como lados.

Step-by-step explanation:

The monthly payment required to pay off a loan of $140,000 at 7% interest would be $776.89 is the correct statement(A).

The statement given is describing a function that relates the monthly payment R of a 25-year variable-rate mortgage loan to the loan amount A and the current interest rate i.

The given values are R = $776.89 and A = $140,000, with an interest rate of 7%. This means that the monthly payment required to pay off a loan of $140,000 at 7% interest would be $776.89.

However, the other statements are incorrect interpretations. For instance, the statement "For a loan of $140,000 at 7.7689% interest, 700 monthly payments would be required to pay off the loan" is incorrect.

This is because the number of payments required to pay off a loan depends not only on the loan amount and interest rate, but also on the term of the loan.

Similarly, the statement "For a loan of $140,000 at 7% interest, 776.89 monthly payments would be required to pay off the loan" is also incorrect, as the number of payments required would be determined by the term of the loan.

Finally, the statement "For a loan of $140,000 at 7.7689% interest, the monthly payment is $700" is also incorrect. This is because, for the given loan amount and interest rate, the monthly payment required would be $776.89, as calculated above.

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The measure of ∠J in ΔJKL is approximately 57.5 degrees.

The measure of ∠J in ΔJKL can be found using the trigonometric function tangent, which is defined as the ratio of the opposite side to the adjacent side.

The straight line that "just touches" the plane curve at a given point is called the tangent line in geometry. It was defined by Leibniz as the line that passes through two infinitely close points on the curve.

tan(∠J) = JK/KL

tan(∠J) = 7.3/4.7

∠J = arctan(7.3/4.7)

∠J = 57.5 degrees (rounded to the nearest tenth of a degree)

Therefore, the measure of ∠J in ΔJKL is approximately 57.5 degrees.

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16h^(10/2) *remove the root sign

16h^5 *simplify the exponent

Answer: 16h^5

Step-by-step explanation: im correct

Answer:

436g

Step-by-step explanation:

1kg=1000g

3kg=3000g

3000+52=3052

3052÷7=436

Answer:

X

Step-by-step explanation:

We first must check the total amount of breakfast. Y happens to have 130 instead of 125. Now, we see that W and Z have a majority on strawberries with oatmeal, which is not what we are looking for. The last answer we have is X, where there is a majority of oatmeal + blueberries and there is a total of 125 breakfasts.

Hope this helps!

The missing amounts for Walco Corporation and Gunther Enterprises assuming  all changes in stockholders equity are due to changes in retained earnings are
(a) Walco Corporation Total Stockholders' Equity =  $54,000
(b) Walco Corporation Total Assets = $182,000
(c) Walco Corporation Dividends = $47,100
(d) Gunther Enterprises Total Liabilities = $140,000
(e) Gunther Enterprises Total Stockholders' Equity = $91,500
(f) Gunther Enterprises Total Revenues =  $135,100

A balance sheet is a financial statement that reports a company's assets, liabilities, and stockholder equity on a specific date. Assets are resources a company owns that have monetary value, liabilities are obligations that must be paid in the future, and stockholder equity is the difference between a company's assets and liabilities. To calculate the missing amounts, you need to subtract the beginning of year figures from the end of year figures.

a) Total liabilities + Total stockholders' equity = Total assets

Total liabilities + $54,000 = $100,000

Total liabilities = $46,000

(b) Total assets = Total liabilities + Total stockholders' equity

Total assets = $128,000 + $54,000

Total assets = $182,000

(c) Changes during year in retained earnings = Total revenues - Total expenses - Dividends

Changes during year in retained earnings = $219,000 - $167,000 - $4,900

Changes during year in retained earnings = $47,100

The missing values for Gunther Enterprises:

(d) Total liabilities + Total stockholders' equity = Total assets

$67,500 + $(e) = $159,000

$(e) = $91,500

(f) Changes during year in retained earnings = Total revenues - Total expenses - Dividends

Changes during year in retained earnings = $(f) - $79,000 - $4,900

Changes during year in retained earnings = $(f) - $83,900

Using the balance sheet equation, we can find the missing values:

(d) Total liabilities = Total assets - Total stockholders' equity

Total liabilities = $159,000 - $67,500

Total liabilities = $91,500

(e) Total stockholders' equity = Total assets - Total liabilities

Total stockholders' equity = $190,000 - $50,000

Total stockholders' equity = $140,000

(f) Changes during year in retained earnings = Total revenues - Total expenses - Dividends

Changes during year in retained earnings = $219,000 - $79,000 - $4,900

Changes during year in retained earnings = $135,100

Therefore, the missing amounts are:

(a) Walco Corporation Total Stockholders' Equity =  $54,000
(b) Walco Corporation Total Assets = $182,000
(c) Walco Corporation Dividends = $47,100
(d) Gunther Enterprises Total Liabilities = $140,000
(e) Gunther Enterprises Total Stockholders' Equity = $91,500
(f) Gunther Enterprises Total Revenues =  $135,100

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The approximate area of the surface formed by revolving the polar equation over the given interval about the polar axis is 67.59 square units.

To solve the question, we can use the integration capabilities of a graphing utility to approximate to two decimal places the area of the surface formed by revolving the polar equation over the given interval about the polar axis. Polar curve is a type of curve that is made up of points that represent polar coordinates (r, θ) instead of Cartesian coordinates.

A polar curve can be represented in parametric form, but it is often more convenient to use the polar equation for a curve. According to the question, r = 7 cos(20), [0, Phi/4] is the polar equation and we need to find the approximate area of the surface formed by revolving the polar equation over the given interval about the polar axis.

To solve the problem, follow these steps: Convert the polar equation to a rectangular equation. The polar equation r = 7 cos(20) is converted to a rectangular equation using the following formulas: x = r cos θ, y = r sin θx = 7 cos (20°) cos θ, y = 7 cos (20°) sin θx = 7 cos (θ - 20°) cos 20°, y = 7 cos (θ - 20°) sin 20°

Sketch the curve in the plane. We can sketch the curve of r = 7 cos(20) by plotting the points (r, θ) and then drawing the curve through these points. Use the polar equation to set up the integral for the volume of the solid of revolution.

The volume of the solid of revolution is given by the formula: V = ∫a b πf2(x) dx where f(x) = r, a = 0, and b = Φ/4.We can find the volume of the solid of revolution using the polar equation: r = 7 cos(20) => r2 = 49 cos2(20) => x2 + y2 = 49 cos2(20)Thus, f(x) = √(49 cos2(20) - x2) = 7 cos(20°) sin(θ - 20°)

So, V = ∫a b πf2(x) dx = ∫0 Φ/4 π(7 cos(20°) sin(θ - 20°))2 dθStep 4: Use a graphing utility to evaluate the integral to two decimal places. Using a graphing utility to evaluate the integral, we get V ≈ 67.59.

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Answer:

x = 4

Step-by-step explanation:

Alternative interior angles means these angles are equal in magnitude and sign

[tex]{ \tt{(20x + 10) = (10x + 50)}} \\ \\ { \tt{20x - 10x = 50 - 10}} \\ \\ { \tt{10x = 40}} \\ \\ { \tt{x = 4}}[/tex]

Answer:

To find the equation of the line passing through the points (5,-12) and (0,-2), we first need to find the slope of the line:

slope = (change in y) / (change in x)

slope = (-2 - (-12)) / (0 - 5)

slope = 10 / (-5)

slope = -2

Now that we have the slope, we can use the point-slope form of the line equation to find the equation of the line:

y - y1 = m(x - x1)

where m is the slope, and (x1, y1) is one of the given points on the line.

Let's use the point (5,-12):

y - (-12) = -2(x - 5)

y + 12 = -2x + 10

y = -2x - 2

Therefore, the equation of the line passing through the points (5,-12) and (0,-2) is y = -2x - 2.

The inverse of the function g(x) is g⁻¹(x) = 0.5 + √(1.25 - x) and the value for x for which f(g(x)) = g(f(x))​ is 1

Given that

f(x) = 3 - 2x

Rewrite as

g(x) = -x² + x + 1

Express as vertex form

g(x) = -(x - 0.5)² + 1.25

Express as equation and swap x & y

x = -(y - 0.5)² + 1.25

Make y the subject

y = 0.5 + √(1.25 - x)

So, the inverse is

g⁻¹(x) = 0.5 + √(1.25 - x)

Here, we have

f(g(x)) = g(f(x))​

This means that

f(g(x)) = 3 - 2(-x² + x + 1)

g(f(x)) = -(3 - 2x)² + (3 - 2x) + 1

Using a graphing tool, we have

f(g(x)) = g(f(x))​ when x = 1

Hence, the value of x is 1

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Complete question

f(x) = 3 - 2x and g(x) = x - x² + 1 where x is an element of f have set of numbers

Find the inverse of G and the value for x for which f(g(x)) = g(f(x))​.

The given third-order linear equation is (t - 2t^2)y' - 4y'' = -2t with y(3) = -2, y'(3) = 2, y''(3) = -3.

We can write this equation as a system of first-order linear equations with initial values by introducing three new variables x_1, x_2, and x_3 such that:

x_1 = y

x_2 = y'

x_3 = y''

with initial values x_1(3) = -2, x_2(3) = 2, x_3(3) = -3.

The resulting system of equations is:

x_1' = x_2

x_2' = x_3

x_3' = (2t^2 - t)x_2 - 4x_3 + 2t

This system can be solved numerically for the unknown functions x_1, x_2, and x_3 with the initial conditions given.

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Answer:

Step-by-step explanation:

i think you have to times it

The shortest interval that contains 95% of the debt values is $9,492.02 to $20,507.98

Given that a credit risk study found that an individual with good credit score has an average debt of $15,000 and the debt of an individual with good credit score is normally distributed with standard deviation $3,000.

Then the 95% confidence interval can be calculated as follows:

Upper limit: µ + Zσ

Lower limit: µ - Zσ

Where

The z-score corresponding to a 95% confidence interval can be found using the standard normal distribution table.

The area to the left of the z-score is 0.4750 and the area to the right is also 0.4750.

The z-score corresponding to 0.4750 can be found using the standard normal distribution table as follows:z = 1.96Therefore

Upper limit: µ + Zσ= $15,000 + 1.96($3,000) = $20,880

Lower limit: µ - Zσ= $15,000 - 1.96($3,000) = $9,120.02

The shortest interval that contains 95% of the debt values is $9,492.02 to $20,507.98.

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Cindy and tom, working together, can rake the yard in 8 hours. Working alone, Tom takes twice as long as Cindy, it takes Cindy to rake the yard 2 hours

To find the time it takes Cindy to rake the yard alone, let's use the following steps:Let x be the time taken by Cindy to rake the yard alone . Then the time taken by Tom to rake the yard alone will be 2xIt is given that Cindy and Tom can rake the yard in 8 hours when they work together.

Using the formula for working together, we get:[tex]\[\frac{1}{x} + \frac{1}{2x} = \frac{1}{8}\][/tex] Multiplying the equation by the least common multiple of the denominators, we get:[tex]\[16 + 8 = 2x\][/tex] Simplifying, we get:[tex]\[2x = 24\][/tex]Dividing both sides by 2, we get:[tex]\[x = 12\][/tex]Therefore, it takes Cindy 12 hours to rake the yard alone.

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