Find the general solution to the equation:
x dy/dx = 3(y+x^2) = Sin x / x

The UCR (Uniform Crime Reporting) is B. not a truly reliable measure.

The UCR is a program established by the FBI in 1930 to collect and analyze crime statistics from law enforcement agencies across the United States. Although it provides useful data and insights into crime trends, it is not without its limitations. One significant issue with the UCR is that it relies on voluntary reporting from law enforcement agencies, meaning that some areas may not provide complete or accurate data. This can lead to an underrepresentation of certain crimes or inconsistencies in reporting across jurisdictions.

Another limitation is that the UCR only includes reported crimes, excluding any unreported criminal activity. This means that the data does not necessarily provide a comprehensive picture of all crimes occurring in a given area. Additionally, the UCR uses a hierarchy rule, meaning that if multiple crimes are committed during a single incident, only the most severe crime is counted. This can result in an undercounting of less severe but still significant crimes.

In summary, although the UCR provides valuable information on crime trends and patterns, it is not a truly reliable measure due to its reliance on voluntary reporting, exclusion of unreported crimes, and hierarchy rule. Therefore, the correct option is B.

The question was incomplete, Find the full content below:

it is fair to say that the ucr is: group of answer choices

A. A mutually exclusive measure

B. Not a truly reliable measure

C. An exhaustive measure

D. All of the above

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The conditional probability of passing the second test, given that the student passed the first test, is approximately 0.857 or 85.7%.

The random variable X represents the outcome of the first test, where it takes on a value of 1 if the student passes and 0 if the student fails.

Similarly, the random variable Y represents the outcome of the second test, taking on a value of 1 if the student passes and 0 if the student fails. Given that the joint probability of passing both tests is 0.6, we can interpret this as the probability of X=1 and Y=1.

The marginal probability of failing the first test is 0.3, which can be represented as P(X=0). To find the conditional probability of passing the second test, given that the student passed the first test, we use the formula \(P(Y=1 | X=1) = P(X=1 and Y=1) / P(X=1).\)

Since we know that \(P(X=1 and Y=1) = 0.6, and P(X=1) = 1 - P(X=0) = 1 - 0.3 = 0.7\), we can substitute these values into the formula:
\(P(Y=1 | X=1) = 0.6 / 0.7\)

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The conditional probability of passing the second test, given that the student passed the first test, is approximately 0.8571 or 85.71%.

The conditional probability of passing the second test, given that the student passed the first test, can be calculated using the formula for conditional probability:

P(Y=1 | X=1) = P(X=1 and Y=1) / P(X=1)

We are given that the joint probability of passing both tests is 0.6, which means P(X=1 and Y=1) = 0.6.

To find P(X=1), we need to use the marginal probability of failing the first test, which is given as 0.3. Since the marginal probability of passing the first test is the complement of failing the first test (i.e., 1 - 0.3 = 0.7), we can say P(X=1) = 0.7.

Now we can substitute these values into the conditional probability formula:

P(Y=1 | X=1) = 0.6 / 0.7

Simplifying this expression, we have:

P(Y=1 | X=1) = 0.8571

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Answer:

88 cm^2

Step-by-step explanation:

one rectangle = perimeter of 28 and times 4 equals 112 but you have to subtract 24 the perimeter of the square  and get your answer

Answer:

81

Step-by-step explanation:

First we go with exponents, 2x2=4 and 5x2=25. Now we go with what's inside the parentheses so, 4 (Originally 2x2) plus 4 plus 6, which equals 14. Now we multiply 4 and 14, which equals 56. Then we add 56 and 25 which equals 81.

A small freezer costs $100,000 in cash and $139,360 by hire purchase.

Hire purchase refers to a payment system by which the purchaser of an item makes regular installment payments, which include finance charges.

Retailers require a downpayment or initial deposit to offer customers hire purchases.

The cash price of a small freezer = $100,000

Hire purchase costs:

Deposit (downpayment) = $62,560

Installment period = 24 months

Installment amount = $3,200

Total installment payments = $76,800 ($3,200 x 24)

The total cost under hire purchase = $139,360 ($62,560 + $76,800)

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It can be brought on hire purchase by depositing $62,560 and 24 monthly installments of $3,200.

Answer:

5.59 times per second.

Step-by-step explanation:

Direct variation is in the form:

\(y=kx\)

Where k is the constant of variation.

Inverse variation is in the form:

\(\displaystyle y=\frac{k}{x}\)

In the given problem, the frequency of a vibrating guitar string varies inversely  as its length. In other words, using f for frequency and l for length:

\(\displaystyle f=\frac{k}{\ell}\)

We can solve for the constant of variation. We know that the frequency f is 4.3 when the length is 0.65 meters long. Thus:

\(\displaystyle 4.3=\frac{k}{0.65}\)

Solve for k:

\(k=4.3(0.65)=2.795\)

So, our equation becomes:

\(\displaystyle f=\frac{2.795}{\ell}\)

Then when the length is 0.5 meters, the frequency will be:

\(\displaystyle f=\frac{2.795}{.5}=5.59\text{ times per second.}\)

Answer:

24/43

Step-by-step explanation:

2 feet = 24 inches

The answer is 24/43 or 24:43. I can't be simplified.

So, the area of the composite figure is 96.57 square centimeters.

In geometry, area refers to the measure of the size of a two-dimensional surface or region. It is typically expressed in square units, such as square meters, square feet, or square centimeters.

To find the area of a shape, you need to measure the length and width of the shape and then multiply those measurements together. The formula for calculating the area of a rectangle, for example, is length x width. The formula for calculating the area of a circle is pi x radius squared, where pi is a mathematical constant, and the radius is the distance from the center of the circle to its edge.

by the question.

sure, I can help you with that!

To find the area of the composite figure, we need to find the area of each individual shape and then add them up.

First, let's find the area of the sector of the circle. We know that the radius of the circle is 6 cm, and the central angle of the sector is 82% of a full circle. Since a full circle has 360 degrees, we can find the central angle of the sector by multiplying 360 by 0.82:

\(Central angle of sector = 360 x 0.82 = 295.2 degrees\)

The area of the sector can be found using the formula:

Area of sector = (central angle/360) x π x radius^2

Substituting the values, we know:

\(Area of sector = (295.2/360) x 3.14 x 6^2 = 56.57 cm^2\)

Next, let's find the area of the triangle. We know that the base of the triangle is 8 cm, and the height is 10 cm. We can use the formula for the area of a triangle:

\(Area of triangle = 1/2 x base x height\)

Substituting the values, we know:

\(Area of triangle = 1/2 x 8 x 10 = 40 cm^2\)

Now, we can add the areas of the sector and the triangle to find the total area of the composite figure:

Total area = area of sector + area of triangle

\(Total area = 56.57 + 40 = 96.57 cm^2\)

Rounding this to the nearest hundredth, we get:

\(Total area =96.57 cm^2\)

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's' and 't' represent free parameters that can take on any real values.

In the given system of equations:

x1 - x2 + 4x3 = -4

6x1 - 5x2 + 7x3 = -5

3x1 - 39x3 = 45

To solve this system, we can use the method of Gaussian elimination or matrix operations. Let's use Gaussian elimination:

Step 1: Write the augmented matrix for the system:

[1 -1 4 | -4]

[6 -5 7 | -5]

[3 0 -39 | 45]

Step 2: Perform row operations to transform the matrix into row-echelon form:

R2 = R2 - 6R1

R3 = R3 - 3R1

The updated matrix becomes:

[1 -1 4 | -4]

[0 1 -17 | 19]

[0 3 -51 | 57]

Step 3: Perform additional row operations to further simplify the matrix:

R3 = R3 - 3R2

The updated matrix becomes:

[1 -1 4 | -4]

[0 1 -17 | 19]

[0 0 0 | 0]

Step 4: Write the system of equations corresponding to the row-echelon form:

x1 - x2 + 4x3 = -4

x2 - 17x3 = 19

0 = 0

Step 5: Express the variables in terms of a parameter:

x1 = s

x2 = 19 + 17s

x3 = t

where s and t are parameters.

Therefore, the solution to the system is:

[x1] = [s]

[x2] = [19 + 17s]

[x3] = [t]

In the provided solution format:

[x1] = [s] []

[x2] = [19 + 17s] + s []

[x3] = [t] [__]

Here, 's' and 't' represent free parameters that can take on any real values.

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Answer: No slope

Step-by-step explanation: The line is going straight down.

To find the red area, we need to determine the area of the quarter circle and subtract it from the area of the square.

The area of the quarter circle can be calculated using the formula for the area of a circle, considering that it is a quarter of the full circle. The radius of the quarter circle is given as 1, so its area is (1/4) * π * (1^2) = π/4.

The area of the square is found by squaring its side length, which is given as 2. Therefore, the area of the square is 2^2 = 4.

To find the red area, we subtract the area of the quarter circle from the area of the square: 4 - (π/4). This simplifies to (16 - π)/4, which is the final value for the red area.

In summary, the red area, when the side length of the square is 2 and the radius of the quarter circle is 1, is given by (16 - π)/4.

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Working 32 hours a week will fetch you $818

From the question, the given parameters are:

Number of hours = 160

Earnings in a month = $4090

Start by calculating the unit rate

This is calculated using the following unit rate formula

So, we have

Unit rate = Earnings in a month/Number of hours

Substitute the known values in the above equation

So, we have

Unit rate =  4090/160

Evaluate the quotient

Unit rate =  25.5625

For 32 hours, the total earnings is

Total = Unit rate x Number of houts

So, we have

Total = 25.5625 x 32

Evaluate

Total = 818

Hence, you will earn $818 weekly

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Answer:

see explanation

Step-by-step explanation:

In math, when a number is squared, it means it has been multiplied by itself. For instance, two squared equals two times two, or four.

In this same case x^2---> x * x

x times x ---> x^2

The cylindrical shell is subjected to an internal pressure of 70MPa. The shell's inner radius is 10 cm, and the outer radius is 16 cm. The maximum and minimum hoop stresses in the cylindrical shell are determined below.

For an element of thickness dr at a distance r from the center, the hoop stress is given by equation i:

σθ = pdθ...[i]Where, p is the internal pressure.

The thickness of the shell is drThe circumference of the shell is 2πr.

Therefore, the force acting on the element is given by:F = σθ(2πrdr)....[ii]

Let σmax be the maximum stress in the shell. The stress at radius r = a, which is at the maximum stress, is given by:σmax = pa/b....[iii]

Here a = radius of the shell, and b = thickness of the shell.

According to equation [i], the hoop stress at radius r = a is given by:σmax = pa/b....[iii].

Substitute the given values:σmax = 70 × 10^6 × (16 - 10)/(2 × 10) = 56 × 10^6 Pa.

The minimum hoop stress in the shell occurs at the inner surface of the shell. Let σmin be the minimum stress in the shell.σmin = pi/b....[iv].

According to equation [i], the hoop stress at radius r = b is given by:σmin = pi/b....[iv]Substitute the given values:

σmin = 70 × 10^6 × 10/(2 × 10) = 35 × 10^6 Pa.

Therefore, the maximum hoop stress in the shell is 56 × 10^6 Pa and the minimum hoop stress is 35 × 10^6 Pa.

A thick cylindrical shell with an inner radius of 10 cm and an outer radius of 16 cm is subjected to an internal pressure of 70MPa. Maximum and minimum hoop stresses in the cylindrical shell can be determined using equations and the given data. σθ = pdθ is the formula for hoop stress in the cylindrical shell.

This formula calculates the hoop stress for an element of thickness dr at a distance r from the center.

For the cylindrical shell in question, the force acting on the element is F = σθ(2πrdr).

Let σmax be the maximum stress in the shell. According to equation [iii], the stress at the radius r = a, which is the maximum stress, is σmax = pa/b.σmax is calculated by substituting the given values.

The maximum hoop stress in the shell is 56 × 10^6 Pa according to this equation.

Similarly, σmin = pi/b is the formula for minimum hoop stress in the shell, which occurs at the inner surface of the shell.

The minimum hoop stress is obtained by substituting the given values into equation [iv].

The minimum hoop stress in the shell is 35 × 10^6 Pa.As a result, the maximum and minimum hoop stresses in the cylindrical shell are 56 × 10^6 Pa and 35 × 10^6 Pa, respectively.

Thus, the maximum hoop stress in the shell is 56 × 10^6 Pa and the minimum hoop stress is 35 × 10^6 Pa. These results are obtained using equations and given data.

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Answer:

13 \(\frac{1}{3}\)

Step-by-step explanation:

\(20+.1x=.4\left(40+x\right)\)

x=40/3 = 13 \(\frac{1}{3}\)

Answer:

P(x) = (\(\frac{2}{5}\))x(x + 3)(x - 1)²

Step-by-step explanation:

Given - The polynomial of degree 4, P(x) has a root of multiplicity 2 at x=1 and roots of multiplicity 1 at x=0 and x=-3. It goes through the point (5,256)

To find - Formula for P(x) ?

Proof -

Given that,

P(x) has a root of multiplicity 2 at x=1

So,

(x - 1)² is a factor.

Now,

Given that, there is roots of multiplicity 1 at x=0 and x=-3

So,

(x - 0) and ( x - (-3) are also factor

So,

P(x) can be written as

P(x) = Ax(x + 3)(x - 1)²           .........(1)

where A is a constant.

Now,

Given that, It goes through the point (5,256)

⇒At x = 5, P(x) = 256

So,

Put the values of x and P(x) in equation (1), we get

P(x) = Ax(x + 3)(x - 1)²

⇒256 = A(5)(5 + 3)(5 - 1)²

⇒256 = 5A(8)(4)²

⇒256 = 40A(16)

⇒256 = 640 A

⇒A = \(\frac{256}{640}\) = \(\frac{2}{5}\)

∴ we get

P(x) = (\(\frac{2}{5}\))x(x + 3)(x - 1)²

Answer:690

Step-by-step explanation:

690

Answer:  $3,261.

Step-by-step explanation:

The answer is $3,261. Jayden would have more money in his account than Camden because his account pays a higher interest rate and is compounded continuously, which allows more frequent compounding of interest. This means that Jayden's account accumulates more interest than Camden's account over time.

Answer:

33.33%

Step-by-step explanation:

The percentage was a decrease.

Let the percent be x.

60 × (1 - x%) = 40

60 × (1 - x/100) = 40

1 - x/100 = 40/60

-x/100 = 40/60 - 1

-x/100 = -1/3

x/100 = 1/3

x = 1/3 × 100

x = 33.33333

Answer:

Step-by-step explanation:

For the 2 triangles to be ≅by HL we need the hypothenuse and pair of legs to be congruent.

We know for sure that we have a pair of legs ≅

the legs MP≅MP by reflexive propriety ( is congruent with itself)

But we do not know from the picture that the hypothenuses are ≅

in ΔLMP the  hypothenuse is LM

inΔNMP the hypothenuse is NM

So unless is given that LM si congruent to MN the Δs are not ≅ by HL theorem

Answer:

Expected value of drawing a card in this game on the first turn = 6

Step-by-step explanation:

Given - Consider a game in which players draw playing cards one at a time from a standard 52-card deck. If a player draws a face card (a jack, a queen, or a king), the player is awarded 16 points. Any other card drawn earns the player 3 points.

To find -  What is the expected value of drawing a card in this game on the first turn?

Formula used -

Expected value, E[x] = ∑ x p(x)

where p(x) is the probability

Proof -

Total cards in a standard deck = 52

Total face cards = 12 (a jack, a queen, or a king)

Other cards = 40

Now,

Probability of getting a face card = \(\frac{12}{52}\)

Probability of getting a other card = \(\frac{40}{52}\)

So,

Expected value, E[x] = ∑ x p(x)

                                  = (16)(\(\frac{12}{52}\)) + (3)(\(\frac{40}{52}\))

                                  = \(\frac{192}{52} + \frac{120}{52}\)

                                  = \(\frac{312}{52}\)

                                  = 6

∴ we get

Expected value of drawing a card in this game on the first turn = 6

So,

The correct option is - B. 6 points

Patel needs about 1/6 cups of orange juice to reach his estimate.

The quantity of orange juice squeezed by Patel from each orange:

1st orange = 4/17 cups

2nd orange = 3/10 cups

3rd orange = 9/20 cups

4th orange = 3/11 cups

5th orange = 7/15 cups

Total cups of orange juice squeezed by Patel is,

4/17 + 3/10 + 9/20 + 3/11 + 7/15

Taking L.C.M. of the denominators i.e., L.C.M. of 17, 10, 20, 11 & 15 = 11220

= ( 2640 + 3366 + 5049 + 3060 + 5236 ) / 11220

= 19351/11220 cups

But, Patel needs 2 cups of juice for his family

∴ The quantity of juice he needs to reach his estimate is,

= 2 - (19351/11220)

= (22440 - 19351) / 11220

= 3089/11220

= 0.2753 cups

Now, we will observe the given options:

1) 1/6 = 0.167 cups

2) 5/6 = 0.833 cups

3) 1 (2/3) = 1.67 cups

4) 1(5/6) = 11/6 = 1.833 cups

Hence, Patel needs about 1/6 cups of orange juice to reach his estimate.

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Answer:

x=-45/11

Step-by-step explanation:

2x/3-3/2=5x/2+6

2x/3=5x/2+7.5

11x/6=7.5

11x=45

x=-45/11

Answer:

80,000

Step-by-step explanation:

1/4(25%)×60,000=20,000

20,000+60,000=80,000

Answer:

x = 52

Step-by-step explanation:

50+(2x +30)+ (2x +20) + X=360

Combine like terms

5x+100 =360

Subtract 100 from each side

5x+100-100 = 360 -100

5x = 260

Divide by 5

5x/5  = 260/5

x = 52

Answer:

x=52

Step-by-step explanation:

50+(2x +30)+ (2x +20) + X=360

First combine like terms

50+30+20=100

2x+2x+x=5x

combine

5x+100=360

subtract 100

5x=260

divide by GCF (5)

x=52

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Mr. Baral has to pay Rs 64000 as an annual income tax at an interest of 10% for his stationary shop.

From the question, we have given that if he is unmarried and his income is between Rs 5,00,001 to Rs 7,00,000, he has to pay an annual interest of 10%.

Given annual income in Rs = 640000.

The annual income tax rate he has to pay at = 10%

So, to find out the income tax from the annual income we have to find out the 10% of 640000.

Income tax = 640000/100 * 10 = 64000

From the above analysis, we can conclude that Mr. Baral has to pay 64000 rs of income tax annually.

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Given question is not having enough information, I am writing the complete question below:

Use it to calculate the income taxes. For an individual Income slab Up to Rs 5,00,000 0% Rs 5,00,001 to Rs 7,00,000 10% Rs 7,00,001 to Rs 10,00,000 20% Rs 10,00,001 to Rs 20,00,000 30% Tax rate For couple Tax rate 0% Income slab Up to Rs 6,00,000 Rs 6,00,001 to Rs 8,00,000 Rs 8,00,001 to Rs 11,00,000 20% Rs 11,00,001 to Rs 20,00,000 30%

a) Mr. Baral has a stationery shop. His annual income is Rs 6,40,000. If he is unmarried, how much income tax should he pay? 10%​

a) The 90% confidence interval for the population mean is approximately (21.52, 23.48).

b) The 95% confidence interval for the population mean is approximately (21.322, 23.678).

c) The 99% confidence interval for the population mean is approximately (20.926, 24.074).

To develop confidence intervals for the population mean, we can use the formula:

Confidence Interval = sample mean ± (critical value * standard error)

where the standard error is equal to the sample standard deviation divided by the square root of the sample size.

a) For a 90% confidence interval, we need to find the critical value corresponding to a confidence level of 90%. The critical value can be obtained from the t-distribution table with (n-1) degrees of freedom. Since the sample size is 56, the degrees of freedom is 56-1 = 55.

From the t-distribution table, the critical value for a 90% confidence interval with 55 degrees of freedom is approximately 1.671.

The standard error can be calculated as:

Standard Error = sample standard deviation / sqrt(sample size)

Standard Error = 4.4 / sqrt(56)

Standard Error ≈ 0.5882

Now we can calculate the confidence interval:

Confidence Interval = 22.5 ± (1.671 * 0.5882)

Confidence Interval = 22.5 ± 0.9816

Confidence Interval ≈ (21.52, 23.48)

b) For a 95% confidence interval, the critical value for 55 degrees of freedom is approximately 2.004 (obtained from the t-distribution table).

Standard Error = 4.4 / sqrt(56) ≈ 0.5882

Confidence Interval = 22.5 ± (2.004 * 0.5882)

Confidence Interval = 22.5 ± 1.178

Confidence Interval ≈ (21.322, 23.678)

c) For a 99% confidence interval, the critical value for 55 degrees of freedom is approximately 2.678 (obtained from the t-distribution table).

Standard Error = 4.4 / sqrt(56) ≈ 0.5882

Confidence Interval = 22.5 ± (2.678 * 0.5882)

Confidence Interval = 22.5 ± 1.574

Confidence Interval ≈ (20.926, 24.074)

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Rounded to the nearest tenth, the angle between the two vectors is approximately 1.8. To find the dot product between two vectors, we multiply their corresponding components and sum the results.

To find the dot product between two vectors, we multiply their corresponding components and sum the results. Let's denote the two vectors as v and w. Given that the components of v are 1 and -5, and the components of w are -5 and 0, the dot product can be calculated as follows:
v · w = (1 * -5) + (-5 * 0) = -5 + 0 = -5
Now, let's find the angle between the two vectors. The dot product can be used to find the angle using the formula:
cos(theta) = (v · w) / (||v|| * ||w||)
Where ||v|| and ||w|| represent the magnitudes (lengths) of the vectors. In this case, both vectors have a magnitude of \(\sqrt(26)\).
Substituting the values into the formula:
cos(theta) = -5 / \((\sqrt(26) * \sqrt(26))\) = -5 / 26
To find the angle theta, we can use the inverse cosine function:
theta = acos(-5 / 26)
Evaluating the expression gives:
theta ≈ 1.810
Rounded to the nearest tenth, the angle between the two vectors is approximately 1.8.

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Let's denote the radius of the cone as 'r' and the height as 'h'.

The formula for the volume of a cone is:

V = (1/3) * π * r^2 * h

And the formula for the circumference of the base of a cone is:

C = 2 * π * r

We know that the volume of the cone is 33π/3, so:

(1/3) * π * r^2 * h = 33π/3

Simplifying this equation, we get:

π * r^2 * h = 99π

r^2 * h = 99

We also know that the circumference of the base of the cone is 6π, so:

2 * π * r = 6π

Simplifying this equation, we get:

r = 3

Now we can substitute this value of 'r' into the equation we obtained earlier:

r^2 * h = 99

3^2 * h = 99

h = 11

Therefore, the height of the cone is 11 units.

The required probability for the given event is given as 0.5.

Probability is the branch of Mathematics that deals with the measurement of the chance of occurrence of a random event.

The probability of any event always lie in the close interval of 0 and 1 [0,1].

Given that,

The probability of a door being locked is 70% = 0.7

Total number of keys is 10.

The number of keys being carried is 2.

Thus, there can be two cases for getting through the door.

Case 1: The door is locked.

The probability to open the door by 1 key is 1/10.

Then, the probability to open the door by 2 keys is 2/10 = 1/5.

Case 2: The door is open.

In this case no keys are needed which means the chance of getting through is the probability of door not being locked which is given as,

1 - 0.7 = 0.3.

Now, the overall probability should consider both the cases as,

P(getting through the door) = P(Door is closed and keys open it)

+ P(The door is open)

= 0.3 + 1/5

= 0.3 + 0.2

= 0.5.

Hence, the probability to get through the door without returning for more keys is 0.5.

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