It takes 5 people 4 hours to clean a hall. How long will it take 8 people to clean the same hall at the same rate?

The distance from the point (15,-21) to the line is 5.39 units.

The equation of a line in point-slope form is:

y - y1 = m(x - x1) (x - x1)

where (x1, y1) is a point on the line and m is the slope of the line. When we are unsure of the y-intercept but are aware of the line's slope and a point on the line, we can utilise this form of the equation.

To calculate the equation of a line using the point-slope method, we must first determine the slope of the line using the following formula:

m = (y2 - y1)/(x2 - x1) (x2 - x1)

where the two points on the line are (x1, y1) and (x2, y2). We may enter the slope, along with one of the line's points, into the point-slope form to obtain the equation of the line.

Given that, the line has the following values f(4)=-8 and f(8)=-18.

The coordinates of the line are (4, -8) and (8, -18)

Thus, the slope of the line is:

m = y2 - y1/ x2 - x1

m = -18 + 8 / 8 - 4

m = -10/4 = -5/2

Now the slope intercept form is given as:

y - y1 = m (x - x1)

Substitute the values:

y + 8 = -5/2(x - 4)

2y + 16 = -5x + 20

2y = -5x + 20 - 16

2y = -5x + 4

The distance from the line to point is given as:

Distance = |ax + by + c| / √(a² + b²)

Substituting the values:

Distance = |-5(15) + -2(-21) + 4| √(-5² + -2²)

Distance = |-29|/ 5.38

Distance = 5.39

Hence, the distance from the point (15,-21) to the line is 5.39 units.

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Probability of the number being part of A∩B= 2/9

The Venn diagram, a style of diagram that illustrates the logical connection between sets, was created by John Venn in the 1880s. The examples are used to illustrate fundamental set connections and introduce basic set theory in the fields of probability, logic, statistics, linguistics, and computer science.

A Venn diagram is a type of visual representation that uses circles to show the relationships between various items or constrained groups of objects. Circles that coincide and those that intersect have certain properties in common. Venn diagrams are helpful for visually illustrating the relationship and differences between two ideas.

The probability of an occurrence is a figure used to indicate the likelihood that the event will occur. It is expressed as a figure between 0 and 1, or between 0% and 100%, when expressed as a percentage. The likelihood that the occurrence will occur increases with the probability.

In this question,

A∩B= 4,9

Probability of the number being part of A∩B= 2/9

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Answer:

The answer is 4

Step-by-step explanation:

yeeeeeeeee

Answer:

4

Step-by-step explanation:

25% of 16

Change the percent to decimal form.

.25 * 16

4

Answer:

0, 4, 16, 36, 64

Step-by-step explanation:

Divide the area by 10 , then the format for graphing would be (0,0) , (40, 4) , (160, 16) and so on.

All answers are listed below:

The area of the parallelogram (A), in square feet, is equal to the product of the base (b) and the height (h), both in feet. By applying the rigid transformation of dilation on each side, we have the following formula:

[tex]A = k^2 \times b \times h[/tex]   (1)

Where k is the scale factor.

And we can derive a scale factor by comparing two areas:

[tex]k=\sqrt{\frac{A}{A_o} }[/tex]   (2)

Where  is the original area, in square feet.

If we know that [tex]A_o=10 \ ft^2[/tex], then the scales factors are shown below:

For A = 0 ft², the scale factor is 0.

For A = 40 ft², the scale factor is 2.

For A = 160 ft², the scale factor is 4.

For A = 360 ft², the scale factor is 6.

For A = 640 ft², the scale factor is 8.

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P(0 received correctly) = P(0 sent) × P(0 received correctly | 0 sent)= [tex](2/3) × 0.8= 0.5333[/tex] (rounded to 1 decimal place)Thus, the probability that a 0 is received is 0.5333 (rounded to 1 decimal place).

0.5333

A space probe near Neptune communicates with Earth using bit strings. Suppose that in its transmissions it sends a 1 one-third of the time and a 0 two-thirds of the time. When a 0 is sent, the probability that it is received correctly is 0.8 and the probability that it is received incorrectly (as a 1) is 0.2. When a 1 is sent the probability that it is received correctly is 0.8 and the probability that it is received incorrectly (as a 0) is 0.2.The probability that a 0 is received correctly is given in the problem as 0.8, and the probability that a 0 is sent is 2/3. Therefore, the probability that a 0 is received correctly

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Model: S(t) = 5000 + 3000t. With a starting value of 5000 subscribers in 1970 and a steady rise of 3000 subscribers each year, this model predicts a linear increase in the number of subscribers through time.

With a starting value of 5000 subscribers in 1970 and a steady rise of 3000 subscribers each year, this model predicts a linear increase in the number of subscribers through time. Simply enter the value of t into the equation to get the number of subscribers after t years. For example, if you want to know the number of subscribers in 1990, which is 20 years after 1970, you would enter in t=20 into the equation and obtain S(20) = 5000 + 3000(20) = 65000. As a result, our model predicts that there would be 65,000 members in 1990. It's crucial to note that this is a simplified model and may not adequately reflect the genuine behaviour of subscriber growth over time.

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The area of the isosceles trapezoid is 37.25 unit².

An isοsceles trapezοid is a trapezοid with cοngruent base angles and cοngruent nοn-parallel sides. A trapezοid is a quadrilateral with οnly οne side parallel.

An isοsceles trapezοid can be defined as a trapezοid whοse nοn-parallel sides and base angles have the same measure. That is, if the twο οppοsite sides (bases) οf a trapezοid are parallel and the twο nοn-parallel sides are οf equal length, it is an isοsceles trapezοid. See the diagram belοw.

Area of trapezium = 1/2(h)(a + b)

where h =  height

a =  smaller base = 10

b = larger base = 15

Now to find height, we see a triangle at the end of trapezium, draw the imaginary altitude

Now, the base = 5/2     ⇒(15 - 10= 5)/2

= 2.5

Using trigonometry ratio

tan(θ) = Height/ Base

tan(40°) = Height/ 2.5

0.8391 = Height/ 2.5

Height = 2.5/ 0.8391

Height ≈ 2.98

Now, The area = 1/2(2.98)(10 + 15)

= 1/2(2.98)(10 + 15)

= 37.25 unit²

Thus, The area of the isosceles trapezoid is 37.25 unit².

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The correct answer is option (C).

Sine (sin), cosine (cos), tangent (tan), cosecant (csc), secant (sec), and cotangent are the six functions (cot).

The equation t = Q - P, where Q and P are the specified locations, can be used to determine the components of the vector t. Therefore:

t = (–18, 2) – (–13, 11) = (–18 + 13, 2 – 11) = (–5, –9) (–5, –9)

The vector's magnitude is given by:

|t| = √(–5)^2 + (–9)^2 = √106 ≈ 10.296

The formula = tan1 (y/x), where x and y are the vector's components, can be used to determine the direction of the vector t. The direction must be expressed in terms of sine and cosine functions because we are required to represent the vector in trigonometric form.

θ = tan⁻¹ (–9/–5) ≈ 60.945°

In trigonometric form, the vector t is thus represented as follows:

t = [t|cos|i] + [t|sin|j]

We get the following by altering the values of |t| and:

t = 10.296 cos I + 10.296 sin j of angle 60.945

As a result, the following is the proper trigonometric representation of the vector t:

t = 10.296 cos I + 10.296 sin j of angle 60.945

Thus, alternative is the right response (C).

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Check the picture below.

To summarize, the 95% confidence interval for the proportion of vaccinated preschool children in Camperdown is [tex]0.5040 ≤ μ ≤ 0.6960[/tex], indicating that we can be 95% confident that the true proportion of vaccinated preschool children in Camperdown lies between 50.4% and 69.6%.

A 95% confidence interval for the proportion of preschool children in Camperdown who have been vaccinated is [tex].5040 ≤ μ ≤ .6960.[/tex] This indicates that we can be 95% confident that the true proportion of vaccinated preschool children in Camperdown lies between 50.4% and 69.6%.

To calculate this interval, we first need to calculate the sample proportion of vaccinated preschool children. To do this, we divide the number of vaccinated children (60) by the total number of children in the sample (100). This yields a sample proportion of 0.6.

Next, we need to calculate the standard error of the proportion, which is calculated by taking the square root of (sample proportion * (1 - sample proportion) / sample size). Plugging in our values yields a standard error of 0.0435.

We then use the standard error to calculate the 95% confidence interval, which is equal to (sample proportion +/- (1.96 * standard error)). Plugging in our values yields an interval of 0.5040 ≤ μ ≤ 0.6960. This indicates that we can be 95% confident that the true proportion of vaccinated preschool children in Camperdown lies between 50.4% and 69.6%.

To summarize, the 95% confidence interval for the proportion of vaccinated preschool children in Camperdown is 0.5040 ≤ μ ≤ 0.6960, indicating that we can be 95% confident that the true proportion of vaccinated preschool children in Camperdown lies between 50.4% and 69.6%.

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Hence, AA"B"Ccoordinates "'s in green are: A" (0, 0), B" (-4, -5), and C" (1, -4).

An illustration of data or mathematical functions is a graph. It is a method for presenting numerical data in a way that is simple to comprehend and interpret. A set of axes, one for each variable being represented, and one or more plots or lines that reflect the data or function being graphed are the main components of a graph. There are many distinct graph kinds, each of which is appropriate for displaying various sorts of data, including line graphs, bar graphs, scatter plots, and pie charts.

given

The axes cannot be identified because they are not specified in the query.

The blue ABC bar graph is as follows:

Using the equation (x, y) (y, -x), rotate AABC 90 degrees clockwise by applying the following transformation to each point:

A(-3, 0) → A' (0, 3) (0, 3)

B(-2, 4) → B' (-4, -2) (-4, -2)

C(1, -1) → C' (1, -1) (1, -1)

The red A'B'C' coordinates are as follows: A' (0, 3), B' (-4, -2), and C' (1, -1).

We take the y-coordinate of each point and subtract 3 to translate AA'B'C' three units down:

A' (0, 3) → A" (0, 0) (0, 0)

B' (-4, -2) → B" (-4, -5) (-4, -5)

C' (1, -1) → C" (1, -4) (1, -4)

Hence, AA"B"Ccoordinates "'s in green are: A" (0, 0), B" (-4, -5), and C" (1, -4).

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The complete question is:-  

1. Label the axes.

2. Graph: A(-3, 0) B(-2, 4) C(1,-1) Draw ABC in blue.

3. Rotate AABC 90° clockwise to

create ▲A'B'C' in red. List the coordinates below:

Formula: (x, y) → (y, -x)

A(-3, 0) A' ()

B(-2, 4)→ B' ()

C(1, -1) C' ()

4. Translate AA'B'C' three units down to create ▲A"B"C" in green. What are the coordinates of AA"B"C"?

Answer:153

Step-by-step explanation:

The integration of the given function using substitution and matching it with the Taylor series is equal to 4/3.

Step 1: Find the Taylor series of the given function f(x).

f(x) = e^(x^2)cos(x)

Therefore, we can say that the Taylor series of the given function is: f(x) = 1 + x^2 + (1/2)x^4 + (1/6)x^6 + (1/24)x^8 + ...

Step 2: Substitute the required value of x into the Taylor series. Let us substitute x = 1 into the Taylor series we got above.

f(1) = 1 + 1^2 + (1/2)1^4 + (1/6)1^6 + (1/24)1^8 + ...

f(1) = 1 + 1 + (1/2) + (1/6) + (1/24) + ...

Step 3: Simplify the expression to get the answer. We can simplify the above expression by using the formula for the sum of an infinite geometric series. The formula is given as follows:

Sum of infinite geometric series = a / (1 - r), where a is the first term and r is the common ratio. Here, a = 1 and r = 1/4. Sum of the series = a / (1 - r) = 1 / (1 - 1/4) = 4/3.

Therefore, we can say that the integration of the given function using substitution and matching it with the Taylor series is equal to 4/3.

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Twice a number decreased by four is less than 8 is x< 6.

2x - 4 < 8

2x < 8 + 4

2x < 12

x < 12 / 2

x < 6

Inequality refers to the unequal distribution of resources, opportunities, and outcomes among individuals or groups in a society. It can manifest in various forms, including economic inequality, social inequality, gender inequality, and racial inequality. Economic inequality refers to the unequal distribution of wealth and income, where some individuals or groups have access to more resources and opportunities than others.

Social inequality refers to the unequal distribution of social status and power, which can lead to marginalized groups being excluded from certain societal benefits. Gender and racial inequality refer to the unequal treatment and opportunities that certain genders or races face in society. Inequality can have negative consequences on individuals and society, including lower levels of social trust, reduced economic growth, and increased social tensions.

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Complete Question: -

Twice a number decreased by four is less than 8 is equation or inequality

We can calculate that sin 30 degrees is equal to the opposite side divided by the hypotenuse, which is x√3/(2x) = √3/2. Therefore, sin 30 degrees is equal to √3/2 in this case.

A 30-60-90 triangle is a type of right triangle where the angles measure 30, 60, and 90 degrees. Its side lengths are in a fixed ratio of 1 : √3 : 2, with the shortest side opposite the 30-degree angle having length x, the side opposite the 60-degree angle having length √3x, and the hypotenuse having length 2x. To find sin 30 degrees, we use the sine function, which is the ratio of the opposite side to the hypotenuse. Thus, sin 30 degrees is equal to x divided by 2x, or 1/2. Therefore, in this specific case where the side lengths are in the ratio 1 : 3 : 2, sin 30 degrees is equal to 1/2.

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The expression shows the height, in meters, of the sail is 2(sin 40°) (option A)

One way to approach this problem is to use the sine function.

We know that sin(40 degrees) is equal to the length of the side opposite angle 40 degrees divided by the length of the hypotenuse. In other words, sin(40 degrees) = b/c.

We want to find the length of the segment that drops from the top of the sail to side a, which we will call h.

This segment is the side adjacent to angle 40 degrees, so we can use the cosine function to relate it to the length of side b. Specifically, cos(40 degrees) = h/b. Solving for h, we get

h = 2 x sin(40 degrees) = 2(sin 40°)

Hence the option (A) is correct.

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Answer:

I got 162?

Step-by-step explanation:

I broke down each individual shape (7 rectangles and 2 triangles) and used each shapes surface area formula.

triangle surface area formula is 1/2*b*h, and there are 2 of the same triangles of the exact same size and 7 rectangles. 3 are same size rectangles, 2 are same size rectangles and the other 2 are different sized rectangles. Then add altogether.

Answer:

its 3

Step-by-step explanation:

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The integers 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 have been written on a chalkboard by Dayna. She then erased the integers from 1 through 6, as well as their multiplicative inverse $\mod{13}$.

We can find the multiplicative inverse of an integer { a modulo 13 } by using the extended Euclidean algorithm.The integers from 1 to 6 are 1, 2, 3, 4, 5, and 6.The multiplicative inverse of : 1 modulo 13 is 1, 2 modulo 13 is 7,  3 modulo 13 is 9, 4 modulo 13 is 10, 5 modulo 13 is 8, and 6 modulo 13 is 11.The only integer that Dayna does not erase is 12.

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Answer:

Step-by-step explanation:

.

The test statistic based on the number of students who preferred to get out early equals 3.65.

A test statistic is a numerical summary of the sample data that is employed to determine the strength of the evidence for a hypothesis. It is a quantitative measure that compares the observed data to the hypothesis. The t-value, Z-score, F-value, and chi-squared value are examples of common test statistics. In statistical hypothesis testing, a test statistic is used to make decisions about whether or not to reject the null hypothesis.

Based on the given problem, the number of students who preferred to get out of class early is 80, while the number of students who preferred a 10-minute break is 40. Hence, the number of students who had no preference is 30.

Now, we will find the test statistic based on the number of students who preferred to get out of class early as follows:

Test Statistic = (Observed Value - Expected Value) / Standard Deviation

To find the observed value, we need to calculate the proportion of students who preferred to get out of class early in the sample as follows:

Proportion of students who preferred to get out of class early = 80 / (150-30)= 80 / 120= 0.67

Therefore, the observed value is 0.67.

To find the expected value, we need to assume that there is no difference in students' preferences, and the proportion of students who preferred to get out of class early is the same as the proportion of students who preferred a 10-minute break.

Expected value = Proportion of students who preferred to get out of class early * Total number of students= 0.5 * 150= 75

Therefore, the expected value is 75.

To find the standard deviation, we need to use the formula for the standard deviation of a proportion as follows:

Standard Deviation = √[(p*q) / n]

where p is the proportion of students who preferred to get out of class early, q is the proportion of students who preferred a 10-minute break, and n is the total number of students.

Standard Deviation = √[(80/120)*(40/120) / 150]= √(0.1778 / 150)= 0.048

Therefore, the standard deviation is 0.048.

Now, we will substitute the values in the formula for the test statistic as follows:

Test Statistic = (0.67 - 0.5) / 0.048= 3.65

Therefore, the test statistic based on the number of students who preferred to get out early equals 3.65.

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a) The domain of the function is {0,1,2,3,4,...}. The range is also a non-negative integer.

b) The largest decimal digit is 9, thus the domain of the function is all positive integers and the range is {9}.

c) The domain of the function is all bit strings of length n and the range is all integers between -n and n.

d) The domain of the function is all positive integers and the range is also all positive integers.

e) The domain of the function is all bit strings and the range is a non-negative integer.

Domain and range of the function that assigns to each pair of non-negative integers the first integer of the pair.In the given problem, (a) the function that assigns to each pair of non-negative integers the first integer of the pair. The first integer of the pair is always non-negative. Therefore, the domain of the function is {0,1,2,3,4,...}. The range is also a non-negative integer.

Domain and range of the function that assigns to each positive integer its largest decimal digit. In this problem, (b) the function that assigns to each positive integer its largest decimal digit. For all positive integers, the largest decimal digit is 9, thus the domain of the function is all positive integers and the range is {9}.

Domain and range of the function that assigns to a bit string the number of ones minus the number of zeroes in the string.In the problem,  the function that assigns to a bit string the number of ones minus the number of zeroes in the string. The possible bit strings have a length of n. Therefore, the domain of the function is all bit strings of length n and the range is all integers between -n and n.

Domain and range of the function that assigns to each positive integer the largest integer not exceeding the square root of the integer.In the given problem, the function that assigns to each positive integer the largest integer not exceeding the square root of the integer. Let’s say f(n) is the largest integer not exceeding the square root of n, then the domain of the function is all positive integers and the range is also all positive integers.

Domain and range of the function that assigns to a bit string the longest string of ones in the string.In the given problem, the function that assigns to a bit string the longest string of ones in the string. In this case, the domain of the function is all bit strings and the range is a non-negative integer.

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The Simple random sampling method is equivalent to a lottery system in which all the available names are placed in a container, the container is shaken, and the names of the "winners" or participants are then drawn out in an unbiased manner.

What is Simple random sampling?

The Simple random sampling is a sampling technique in which every member of the population has an equal chance of being chosen as a sample. The samples are chosen randomly, without any specific criterion. In this method, the selection of individuals for the sample is done without any specific pattern. This means that each member of the population is equally likely to be selected as a sample.In Simple random sampling, each member of the population is assigned a number, and the samples are selected using a random number generator or drawing names out of a hat. The selected samples are then analyzed to make predictions about the entire population.For example, if a researcher wanted to know the average age of students in a school, they might use Simple random sampling to choose a sample of 50 students. The researcher would assign each student a number and then use a random number generator to select the samples.There are some advantages and disadvantages of Simple random sampling, which are listed below:Advantages of Simple random sampling It is easy to understand and conduct the process.Each member of the population has an equal chance of being selected as a sample.It ensures that the sample is representative of the entire population.Disadvantages of Simple random sampling It can be time-consuming to select the samples.There may be a chance of human error when selecting samples.The sample size may not be large enough to draw meaningful conclusions.

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Answer:

  true

Step-by-step explanation:

You want to know if weight and self-esteem have a negative correlation if an increase in weight causes self-esteem to go down (the slope is negative).

The slope of the line of best fit has the same sign as the correlation coefficient. The magnitude of the correlation coefficient is the ratio of the covariance to the product of the standard deviations of the variables.

It is true that the weight and self-esteem have negative correlation.

Using percentages we know that the markup price of the pair of shoes will be $6.3.

In mathematics, a percentage is a number or ratio that is expressed as a fraction of 100.

Although "pct," "pct," and occasionally "pc" are also used as abbreviations, the percent symbol "%" is most usually used to denote it.

A% is a number that has neither dimensions nor a defined unit of measurement.

When expressing a proportionate share of a total, percentages are frequently utilized.

(Similarly, the term "per mille" or the sign "%" can be used to denote a number as a fraction of 1,000.)

So, the market price of the store would be:

= 4.50/100 * 40

= 0.045 * 40

= 1.8

Markup price: 1.8 + 4.5 = $6.3

Therefore, using percentages we know that the markup price of the pair of shoes will be $6.3.

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The weighted mean takes into account the weight of each investment and can provide a more accurate measure of the overall rate of return on the portfolio than the mean or median.

The weighted mean, mean, and median overall rate of return on this investment portfolio can be calculated using the following formulas:

Weighted Mean: Weighted mean = (R1 x W1) + (R2 x W2) + (R3 x W3) + ...

Mean: Mean = (R1 + R2 + R3 + ...) / N

Median: Median = (N + 1) / 2

where R1, R2, etc. are the returns on individual investments, W1, W2, etc. are the weights assigned to each investment, and N is the total number of investments in the portfolio.

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The compounding formula is used to create the quarterly compounding formula. To the nearest cent, the compounded balance is $ [tex]12,832.27.[/tex]

To reflect the quarterly interest computation as the only change, the interest rate is increased by 4*2.

[tex]A = P(1 + r/n)(nt)[/tex]

Assume that we have a $  [tex]10,000[/tex] Initial investment, a 6% yearly interest rate, and a 5-year investment period. We have n = 4 and t = 5 since the interest is compounded every three months.

Plugging in these values, we get:

[tex]A = 10,000(1 + 0.06/4)(4*5)[/tex]

[tex]= 10,000(1.015)^20[/tex]

[tex]= 12,835.72[/tex]

Hence, the final balance is $ [tex]12,835.72[/tex] to the nearest penny.

If the money is compounded continually, we may use the following formula to determine the balance:

[tex]A = Pe(rt)[/tex]

With the identical values as before, we obtain:

[tex]A = 10,000e(0.06 \times5)[/tex]

[tex]= 10,000e(0.3)[/tex]

[tex]= 12,832.27[/tex]

Therefore, So the balance, to the nearest cent, is $ [tex]12,832.27.[/tex]

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Answer:

if it is perpendicular to eacha other I e 0

After calculating, the value of the expression HCF(log²(2^18) + log²(4))(log²(32) + log²(216)) is: 3 log²2 (5 - 3 log 3)

We can start by simplifying the logarithmic expressions inside the parentheses:

log²(2^18) + log²(4) = (18 log 2)^2 + (2 log 2)^2 = 324 log²2 + 4 log²2 = 328 log²2

log²(32) + log²(216) = (5 log 2)^2 + (3 log 6)^2 = 25 log²2 + 27 log²3

Now, we can express the original expression as:

HCF(log²(2^18) + log²(4))(log²(32) + log²(216)) = HCF(328 log²2, 25 log²2 + 27 log²3)

To find the highest common factor of these two terms, we can factor out the common factor of log²2:

HCF(328 log²2, 25 log²2 + 27 log²3) = log²2 HCF(328, 25 + 27 log²3)

Now, we need to find the highest common factor of the two integers 328 and 25 + 27 log²3.

We can factor out 3 from 25 and 27, and then use the difference of squares formula to write:

25 + 27 log²3 = (5 + 3 log 3)(5 - 3 log 3)

So, the highest common factor of 328 and 25 + 27 log²3 is the product of the common factors, which is:

HCF(328, 25 + 27 log²3) = 3(5 - 3 log 3)

Therefore, the value of the expression HCF(log²(2^18) + log²(4))(log²(32) + log²(216)) is:

log²2 HCF(328, 25 + 27 log²3) = log²2 * 3(5 - 3 log 3) = 3 log²2 (5 - 3 log 3)

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