Determine whether each statement is true or false.

1. In figure A,
2. In figure B,
3. In figure B, m
4. In figure C,

About 0.03% of the class would be expected to score less than 50 points, while around 1.1% of the class would be expected to score more than 90 points. Approximately 78.1% of the class would be expected to score between 60 and 80 points. The third quartile of the test score is 80.72. The 90th quantile of the test score is 83.97.

To find the proportion of the class expected to score less than 50 points, we need to standardize the score using the z-score formula

z = (x - μ) / σ

where x is the score, μ is the mean, and σ is the standard deviation. Plugging in the values, we get

z = (50 - 74) / 7 = -3.43

Using a calculator, we can find that the proportion of the class expected to score less than 50 points is approximately 0.0003 or 0.03%.

To find the proportion of the class expected to score more than 90 points, we again need to standardize the score

z = (90 - 74) / 7 = 2.29

Using a standard normal distribution table or a calculator, we can find that the proportion of the class expected to score more than 90 points is approximately 0.011 or 1.1%.

To find the proportion of the class expected to score between 60 and 80 points, we need to standardize both scores

z1 = (60 - 74) / 7 = -2.00

z2 = (80 - 74) / 7 = 0.86

Using a calculator, we can find the proportion between these two z-scores. Specifically, we need to find the area to the right of z1 and the area to the left of z2, and subtract the two values:

P(60 < x < 80) = P(z1 < z < z2) = P(z < 0.86) - P(z < -2.00)

≈ 0.803 - 0.022

≈ 0.781 or 78.1%

The third quartile is the value that separates the top 25% of the scores from the bottom 75%. We can find this value using the z-score formula

z = invNorm(0.75) ≈ 0.6745

where invNorm is the inverse normal cumulative distribution function. Solving for the corresponding score x, we get

z = (x - μ) / σ

0.6745 = (x - 74) / 7

x ≈ 80.72

Therefore, the third quartile of the test score is approximately 80.72.

The 90th quantile is the value that separates the top 10% of the scores from the bottom 90%. We can find this value using the inverse normal cumulative distribution function

z = invNorm(0.90) ≈ 1.2816

Solving for the corresponding score x, we get

z = (x - μ) / σ

1.2816 = (x - 74) / 7

x ≈ 83.97

Therefore, the 90th quantile of the test score is approximately 83.97.

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The solution is, the selection can be made in 593775ways

Combination has to do with selection of r objects from a total number of n objects and this can be done in nCr ways. Generally,

nCr = n!/(n-r)!r!

Since the math teacher has to select 6 students from a class of 30, this can be done in 30C6 number of ways to have;

30C6 = 30!/(30-6)!6!

30C6 = 30!/24!6!

30C6 = 30×29×28×27×26×25×24!/24!×6×5×4×3×2

30C6 = 30×29×28×27×26×25/6×5×4×3×2

30C6 = 427,518,000/720

30C6 = 593775ways

This means, the selection can be made in 593775ways.

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Mary's monthly take-home pay after National Insurance and pension contributions would be approximately 29,294.17.

To calculate Mary's National Insurance contribution, we can multiply her salary by the monthly rate of 12.5%:

National Insurance = 34833.33 * 0.125 = 4354.16625 per month

To calculate Mary's pension contribution, we can multiply her salary by the monthly rate of 3.4%:

Pension contribution = 34833.33 * 0.034 = 1184.9982 per month

Therefore, Mary's total monthly deductions for National Insurance and pension contributions would be:

Total deductions = National Insurance + Pension contribution

Total deductions = 4354.16625 + 1184.9982

Total deductions = 5539.16445

So Mary's monthly take-home pay after these deductions would be:

Take-home pay = Salary - Total deductions

Take-home pay = 34833.33 - 5539.16445

Take-home pay = 29294.16555

Therefore, Mary's monthly take-home pay after National Insurance and pension contributions would be approximately 29,294.17.

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[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\dotfill & \stackrel{ 4540+1328.54 }{\$ 5868.54}\\ P=\textit{original amount deposited}\dotfill &\$4540\\ r=rate\to r\%\to \frac{r}{100}\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{per year, thus once} \end{array}\dotfill &1\\ t=years\dotfill &10 \end{cases}[/tex]

[tex]5868.54 = 4540\left(1+\frac{\frac{r}{100}}{1}\right)^{1\cdot 10} \implies \cfrac{5868.54}{4540}=\left( 1+\cfrac{r}{100} \right)^{10} \\\\\\ \cfrac{5868.54}{4540}=\left( \cfrac{100+r}{100} \right)^{10}\implies \sqrt[10]{\cfrac{5868.54}{4540}}=\cfrac{100+r}{100} \\\\\\ 100\sqrt[10]{\cfrac{5868.54}{4540}}=100+r\implies 100\sqrt[10]{\cfrac{5868.54}{4540}}-100=r\implies \stackrel{ \% }{2.6}\approx r[/tex]

Revenue is decreasing at a rate of $5,576.58 per month.

What is revenue?

Revenue is the multiplication of the quantity of items sold and the cost at that they are sold.

The mathematical form of revenue is R(p) = z(p) × p where z(p) is the number of items sold at price p

Here given that the equation z = 30000/√(4p+1).

Now, we can use the chain rule to find the rate of change of revenue with respect to time t, given that the price is increasing at a rate of $3 per month. The chain rule tells us that: dR/dt = (dR/dp) × (dp/dt)

We want to find dR/dt when p = $210. We know that dp/dt = $3 per month, so we just need to find dR/dp at p = $210. We can do this by differentiating the expression for R(p) with respect to p:

dR/dp = dz/dp × p + z(p) where dz/dp is the derivative of z with respect to p. We can find this using the quotient rule:

[tex] \frac{dz}{dp} = \frac{-15000}{(4p+1)^{(3/2)}}[/tex]

Putting it all together, we have:

[tex] \frac{dR}{dp} = \frac{-15000p}{(4p+1)^{(3/2) }}+ \frac{30000}{√(4p+1)}[/tex]

When p = $210, we have:

dR/dp = -1858.86

And when dp/dt = $3, we have:

dp/dt = 3

So, by the chain rule:

dR/dt = (dR/dp) × (dp/dt) = (-1858.86) × 3 = -5576.58

Therefore, the rate of change of revenue when the company is selling widgets at 210 each and increasing the price by 3 per month is approximately -5,576.58 per month. This means that revenue is decreasing at a rate of 5,576.58 per month under these conditions.

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The domain and the range of the equation y = 7ˣ - 4 are (a) Domain: All real numbers Range: y>-4

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

y = 7ˣ - 4

The above equation is an exponential function

The rule of an exponential function is that

The domain is the set of all real numbers

This means that the input value can take all real values

However, the range is always greater than the constant term

In this case, it is -4

So, the range is y > -4

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Answer: To find the selling price of the house, we can use the formula for the present value of an annuity:

PV = A * ((1 - (1 + r)^-n) / r)

Where:

PV = Present Value

A = Annuity payment per period

r = Interest rate per period

n = Total number of periods

In this case, the annuity payment is $525 per month, the interest rate is 7.8% per year compounded monthly (which is equivalent to a monthly interest rate of 7.8% / 12 = 0.65%), and the total number of periods is 30 years * 12 months/year = 360 months.

Using these values, we can calculate the present value of the annuity:

PV = 525 * ((1 - (1 + 0.0065)^-360) / 0.0065)

PV = 525 * 162.577

PV = $85,192.25

So the selling price of the house was $85,192.25 + $25,000 down payment = $110,192.25.

To calculate the total interest paid over 30 years, we can subtract the total payments from the selling price:

Total payments = $525/month * 360 months = $189,000

Total interest paid = $189,000 - $110,192.25 = $78,807.75

Therefore, the friends will pay $78,807.75 in interest over 30 years.

Step-by-step explanation:

Answer:

orange

Step-by-step explanation:

If the bag contained an equal amount of each color of bead, we would expect each color to have 1/4 or 25% of the total number of beads, which is 165. Therefore, the theoretical probability of selecting a bead of each color would be 25%.

To determine which color has the experimental probability closest to the theoretical probability, we can compare the experimental probability of selecting a bead of each color to the theoretical probability of 25%. We can use the following formula to calculate the experimental probability:

experimental probability = number of times color is selected / total number of selections

The results are:

Red: 10/165 = 0.061 or 6.1%

Brown: 15/165 = 0.091 or 9.1%

Orange: 17/165 = 0.103 or 10.3%

Yellow: 13/165 = 0.079 or 7.9%

To find the color with the experimental probability closest to the theoretical probability of 25%, we can calculate the difference between the experimental probability and the theoretical probability for each color:

Red: 25% - 6.1% = 18.9%

Brown: 25% - 9.1% = 15.9%

Orange: 25% - 10.3% = 14.7%

Yellow: 25% - 7.9% = 17.1%

Based on these calculations, the color with the experimental probability closest to the theoretical probability is orange, with a difference of 14.7%. Therefore, orange is the color for which the experimental probability is closest to the theoretical probability of selecting a bead of each color.

Using a calculator or computer program, we find that there are two real solutions, approximately x = -1.1503 and x = 1.1503

How to solve the question?

To sketch a graph of the function f(x) = (x²-1)²/ x, we first need to analyze its behavior using the first and second derivatives.

The first derivative of f(x) is given by f'(x) = (3x⁴ - 2x - 1)/x². To find the critical points, we need to set f'(x) = 0 and solve for x:

3x⁴- 2x - 1 = 0

This equation cannot be solved analytically, but we can use numerical methods to approximate the solutions. Using a calculator or computer program, we find that there are two real solutions, approximately x = -1.1503 and x = 1.1503.

To determine the behavior of f(x) around these critical points, we need to look at the second derivative of f(x), which is given by f''(x) = 6x^4 + 2/x³. Evaluating this expression at the critical points, we find that f''(-1.1503) < 0 and f''(1.1503) > 0, which means that the first critical point is a local maximum and the second critical point is a local minimum.

Now we can sketch the graph of f(x) by plotting the critical points (-1.1503, f(-1.1503)) and (1.1503, f(1.1503)), and connecting them with a smooth curve that passes through the origin (since f(0) = 0). Since f(x) is defined for all x except x = 0 (where it has a vertical asymptote), we can extend the graph to include all real numbers except 0.

The graph of f(x) should look like a "W" shape, with two local extrema and a vertical asymptote at x = 0. The exact shape and position of the curve will depend on the scale and axis limits of the graph, but the overall behavior should be consistent with the analysis of the first and second derivatives.

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This is difficult to estimate exactly without knowing more details about the investment fund and returns, but we can make some reasonable assumptions and calculations:

* Let's assume the fund generates an average annual return of 6% over 40 years. This is a modest but achievable return for a balanced stock/bond fund.

* At a 6% annual return, that amounts to a 0.06 annual return on the money invested.

* Let's also assume an average annual inflation rate of 3% over 40 years. So the returns need to beat inflation by at least 3% to generate real growth.

* $15,000 invested today at 6% annual return for 40 years:

1) $15,000 * (1 + 0.06)^40 = $263,174

2) Inflation adjustment (at 3% for 40 years): $263,174 * (1 - 0.03^40) = $79,378

* So after 40 years, the initial $15,000 investment could be worth around $79,378 in today's dollars.

* As a very rough estimate, if inflation averages out and the nominal returns are decent but not too high, the $15,000 could grow to $100,000 to $200,000 in 40 years. A lot will depend on how the specific fund performs versus the broader market and economy.

* The future value will also depend on whether any money is withdrawn or added over the 40 years. I have assumed the full $15,000 is invested for the entire 40 years.

The possible polynomial function with the given properties is:

f(x) = -1/5(x2 - 10x + 16)

Now, Based on the given properties, a possible polynomial function would be:

⇒ f (x) = a(x + 2)(x - 4)

To satisfy the second-degree requirement, we need to have an x² term in the function.

By factoring the function above as shown, we can see that it has two roots: x = -2 and x = 4.

Therefore, we can say that this function has zeros at x = -2 and x = 4.

To determine the value of the coefficient "a", we can use the information that the function goes to -∞ as x → -∞.

This means that the leading coefficient of the function must be negative.

Since, we have a(x + 2)(x - 4), and the x² term has a coefficient of a, we can see that a must be negative.

To further simplify the function and reduce all fractions to lowest terms, we can distribute the negative sign and multiply out the factors:

f(x) = a(x + 2)(x - 4)

     = a(x² - 2x - 8x + 16)

     = a(x² - 10x + 16)

Therefore, The possible polynomial function with the given properties is:

f(x) = -1/5(x2 - 10x + 16)

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Answer:

1384.7

Step-by-step explanation:

42/2     21^2x3.14=1384.74

Hope this Helps :)

The decrease in price is approximately 21.4% of the price in 2008.

A share cost $56 in 2008 and $44 in 2016, respectively. The price has dropped because:

56 - 44 = 12

The drop must be divided by the 2008 price in order to be expressed as a percentage of that price, which must then be multiplied by 100:

(12/56) x 100 ≈ 21.4%

As a result, the price is down around 21.4% from what it was in 2008.

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The values in the left column are 2:5 the values in the right column, and the last value in the left column is retained if another row is added would be 55 and the last value in the right column would be 22, making option A the only correct choice.

Based on the given information, the ratio of the values in the left column to the values in the right column is 2:5. This means that for every 2 in the left column, there are 5 in the right column.

The last value in the left column of the multiplication chart would be 55, and the last value in the right column would be 22. This information can be used to eliminate options B and D, as they provide different values for the last entries in the columns.

Therefore, the correct answer is either A or C. However, we can also see that option C contradicts the given information about the last values in the columns. Thus, the only option that is consistent with all of the given information is A.

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The function f(n) = 2n – 2 represents the nth term of the sequence 0, 2, 4, 6, 8.

What is sequence?

In mathematics, a sequence is an ordered list of numbers, usually written in a specific pattern. Each number in the sequence is called a term, and the position of a term in the sequence is called its index or subscript.

A function f(n) that represents the nth term of the sequence given above can be written as follows:

f(n) = 2n – 2

This function can be explained as follows:

The function f(n) represents the nth term of the given sequence. The first term of the sequence is 0, which is equal to f(1). The second term of the sequence is 2, which is equal to f(2). This pattern can be seen throughout the sequence, as each subsequent term is two more than the preceding one. Thus, the general form of the function can be written as f(n) = 2n – 2, where n represents the nth term of the sequence.

For example, when n = 5, the function f(n) = 2n – 2 = 10. This is equal to the fifth term of the sequence, 8.

Therefore, the function f(n) = 2n – 2 represents the nth term of the sequence 0, 2, 4, 6, 8.

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P + 4P is most equivalent to 5P.

To obtain this result, we can use the distributive property of multiplication over addition, which states that:

a(b + c) = ab + ac

Using this property, we can rewrite P + 4P as:

= P + 4P

= P + (4 x P)

= 1P + (4P)

= (1+4)P

= 5P

Therefore, P + 4P is equivalent to 5P.

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Step-by-step explanation:

First, we need to determine the total revenue from docking 100 boats:

$850 per boat x 100 boats = $85,000

Next, we need to determine the total cost of operating the boathouse:

$2200 (fixed cost) + $550 for each of the 100 boats = $77,200

Finally, we can calculate the monthly profit:

Revenue - Cost = $85,000 - $77,200 = $7,800

Therefore, the answer is option C: $27,800.

Answer:

23.33

Step-by-step explanation:

The function f such that f'(x) = x² - 9 and f(0) = 7 is given by, f(x) = x³/3 - 9x + 7.

Given that the differentiated function is,

f'(x) = x² - 9

We have to do integration the function in order to get the initial function that is f(x).

f(x) = ∫(x² - 9).dx = ∫x².dx - ∫9.dx = x³/3 - 9x + c, where c is an integration constant.

f(x) = x³/3 - 9x + c

Again it is given that f(0) = 7.

f(0) = 7

0³/3 - 9*0 + c = 7

c = 7

Hence the function is, f(x) = x³/3 - 9x + 7.

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The half-life of the substance is approximately 3.18 time units (where the unit depends on what t is measured in).

An equation is a mathematical statement that indicates the equality of two expressions. It consists of two sides separated by an equal sign, and it expresses a relationship between the values of the expressions on either side of the equal sign. Equations can be used to describe various mathematical relationships, such as the properties of shapes, the behavior of physical systems, or the patterns of numbers.

The given equation is:

[tex]Q = 72(0.5)t/32.5[/tex]

where Q is the quantity of the substance remaining after time t.

To find the half-life of the substance, we need to find the value of t for which Q is half of its initial quantity.

Initially, let's assume that the quantity of the substance is Q₀. Then we have:

Q₀ = 72

Now, we need to find the value of t for which Q = Q₀/2.

Substituting Q = Q₀/2 in the given equation, we get:

Q₀/2 = 72(0.5)t/32.5

Simplifying this equation, we get:

[tex]2^(t/h) = 32.5/72[/tex]

where h is the half-life of the substance.

Taking the logarithm of both sides, we get:

t/h = log₂(32.5/72)

Solving for h, we get:

h = t/log₂(32.5/72)

We don't have a specific value of t given in the question, but we can calculate the half-life using any value of t. For example, if we take t = 1, then we get:

h = 1/log₂(32.5/72) ≈ 3.18

Therefore, the half-life of the substance is approximately 3.18 time units (where the unit depends on what t is measured in).

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The half-life of the substance is approximately 3.18 time units (where the unit depends on what t is measured in).

What is equation?

An equation is a mathematical statement that indicates the equality of two expressions. It consists of two sides separated by an equal sign, and it expresses a relationship between the values of the expressions on either side of the equal sign.

The given equation is:

Q = 72(0.5)t/32.5

where Q is the quantity of the substance remaining after time t.

To find the half-life of the substance, we need to find the value of t for which Q is half of its initial quantity.

Initially, let's assume that the quantity of the substance is Q₀. Then we have:

Q₀ = 72

Now, we need to find the value of t for which Q = Q₀/2.

Substituting Q = Q₀/2 in the given equation, we get:

Q₀/2 = 72(0.5)t/32.5

Simplifying this equation, we get:

[tex]2^{(t/h)}=32.5/72[/tex]

where h is the half-life of the substance.

Taking the logarithm of both sides, we get:

t/h = log₂(32.5/72)

Solving for h, we get:

h = t/log₂(32.5/72)

We don't have a specific value of t given in the question, but we can calculate the half-life using any value of t. For example, if we take t = 1, then we get:

h = 1/log₂(32.5/72) ≈ 3.18

Therefore, the half-life of the substance is approximately 3.18 time units (where the unit depends on what t is measured in).

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Answer:

Okay

Step-by-step explanation:

this is sort of personal to the person asking, but here’s mine

( I don’t own car so doing the second one)

I can provide you with information about the minimum coverage requirements for car insurance in Florida.

In Florida, the minimum required car insurance coverage is:

$10,000 in Personal Injury Protection (PIP) coverage

$10,000 in Property Damage Liability (PDL) coverage

PIP coverage pays for medical expenses, lost wages, and other related expenses if you or your passengers are injured in a car accident, regardless of who is at fault. PDL coverage pays for damage you may cause to another person's property, such as their car or a fence.

It's important to note that these minimum coverage requirements may not be enough to fully protect you in the event of an accident. If you have assets you want to protect, you may want to consider higher coverage limits or additional types of coverage, such as Bodily Injury Liability (BIL) coverage, which can help pay for damages you may cause to another person in an accident.

If you were to regularly drive a vehicle in Florida, you may want to consider higher coverage limits and additional types of coverage to ensure you are adequately protected.

3 standard deviations above the mean is 32.5.

What is standard deviation?

A quantity of how far the data is spread from the mean is called standard deviation. It means that the data is clustered around the mean and a high standard deviation indicates that the data is more spread out. It close to 0 indicates which the data points are near to the mean.While a high or low standard deviation indicates which the data points are above or below the mean respectively.

The value that is 3 standard deviations above the mean of a normally distributed random variable is given by,

mean + 3×standard deviation

Substituting the given values,

24.1 + 3×2.8 = 24.1 + 8.4 = 32.5

Therefore, 3 standard deviations above the mean is 32.5.

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The amount of vegetables that your friend cooks each day is the constant of the proportional relationship.

The equation that defines a direct proportional relationship is given as follows:

y = kx.

In which k is the constant of proportionality.

For this problem, the relationship for the amount of vegetables is given as follows:

Vegetables = Constant x Days.

Hence the daily amount of vegetables is given as follows:

Constant = Vegatables/Days.

The problem is incomplete, hence the general procedure to obtain the amount of vegetables that your friend cooks each day is presented.

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Answer:

Step-by-step explanation:

try adding 18 and 60 the subtracting the answer from 180 :)

Answer:

To simplify 3/27, find the greatest common factor (GCF) of the numerator and denominator and divide both by it123. The GCF of 3 and 27 is 3134. Therefore, 3/27 can be reduced to 1/9 by dividing both 3 and 27 by 312345. This is the simplest form of 3/2715.

Step-by-step explanation:

Answer: We can use the hydrostatic pressure formula to determine the pressure difference PA - PB:

ΔP = ρgh

where ΔP is the pressure difference, ρ is the density of the fluid, g is the acceleration due to gravity, and h is the height difference between the two points.

First, we need to determine the heights of the fluid columns in pipes A and B. Since oil with specific gravity 0.8 is in the upper position of the inverted U, it is higher in pipe B than in pipe A. Let's say that the height of the oil column in pipe B is hB and the height of the oil column in pipe A is hA.

Since mercury with specific gravity 136 is in the bottom of the manometer bends, the height difference between the two points is the height difference between the mercury columns in the two legs of the manometer. Let's say that the height of the mercury column in the left leg is hL and the height of the mercury column in the right leg is hR.

Then, we can write:

hB - hL = hR - hA

Since the pressure at point A is equal to the atmospheric pressure, we can set the pressure at point A to be zero. Then, we have:

PA - PB = ρoilghB - ρoilghA + ρmercuryg(hR - hL)

Substituting the densities and simplifying, we get:

PA - PB = (0.8)(9.81)m(hB - hA) + (136)(9.81)m(hR - hL)

where m is the mass of the fluid column in each pipe.

We don't have enough information to determine the heights of the fluid columns or the mass of the fluid columns, so we cannot calculate the pressure difference PA - PB without further data.

Step-by-step explanation:

The time it will take Pedro to reach investment goal is 104.5 years .

Let the initial amount of  Pedro = P dollars

Amelia starts with twice as much, = 2Pdollars.

Given that Pedro takes 6 times longer than Amelia to reach the investment goal, we can set up the following equation:

6t = t'

where;

Using the compound interest formula for quarterly compounding, to find the time.

A = P (1 + r/n)^(nt)

where;

Plugging in the values, we get:

2P = P (1 + 0.04/4)^(4t)

2 = (1 + 0.04/4)^(4t)

2 = (1 + 0.01))^(4t)

ln(2)= 4t x  ln(1.01)

t = (ln (2) / 4ln(1.01) )

t = 17.42 years

t' = 6t

t' = 6 x 17.42 yrs

t' = 104.5 years = 104 years, 6 months.

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