Jorge’s printer can print 24 pages in 15 minutes (1/4 per hour). How many pages can it print in 3/4 hour? In 1 hour?

Zero extraneous solutions does the equation have (2m)/(2m+3)-(2m)/(2m-3) = 1.

What is Quadratic Equation?

ax^2 + bx + c = 0 is a quadratic equation, which is a second-order polynomial equation in a single variable a ≠0. It has at least one solution because it is a second-order polynomial equation, which is guaranteed by the algebraic fundamental theorem. The answer might be simple or complicated.

Given that;

[tex]\frac{2m}{2m+3}-\frac{2m}{2m-3} = 1[/tex]

⇒ [tex]\frac{2m(2m-3)-2m(2m+3)}{(2m+3)(2m-1)}=1[/tex]

⇒ [tex]\frac{4m^2-6m-4m^2-6m}{(4m^2-9)}=1[/tex]

⇒ [tex]\frac{-12m}{4m^2-9}=1\\[/tex]

⇒ [tex]-12m = 4m^2-9[/tex]

4m^2 +12m - 9 = 0(1)

The formula for calculating the roots of the quadratic equation ax^2 + bx + c can be utilized because (1) is a quadratic equation.

[tex]\frac{-b\pm \sqrt{b^2-4ac} }{2a}[/tex]

Variable m is in equation (1), where a = 4, b = 12, and c = -9.

The roots are calculated as:

[tex]\frac{-12\pm \sqrt{12^2-4\times 4\times (-9)} }{2\times 4}[/tex]

[tex]\frac{-12\pm \sqrt{2\times 144} }{8}[/tex]

[tex]\frac{-12\pm 12\sqrt{2} }{8}[/tex]

[tex]\frac{-3}{2} \pm \frac{3}{2}\sqrt{2}[/tex]

[tex]\frac{-3}{2} - \frac{3}{2}\sqrt{2} \ and \ \frac{-3}{2} + \frac{3}{2}\sqrt{2}[/tex]

Subsitituting [tex]\frac{-3}{2} - \frac{3}{2}\sqrt{2}[/tex]  in equation (1);

[tex]9+18+18\sqrt{2}-18-18\sqrt{2} -9 = 0[/tex]

0 = 0

The root -3/2 - 3([tex]\sqrt{2}[/tex])/2 is therefore not an auxiliary solution.

Now substituting [tex]\ \frac{-3}{2} + \frac{3}{2}\sqrt{2}[/tex] in equation (1);

[tex]9+18+18\sqrt{2}-18-18\sqrt{2} -9 = 0[/tex]

0 = 0

Therefore, the root -3/2 + 3([tex]\sqrt{2}[/tex])/2 IS NOT AN ADDITIONAL SOLUTION.

The above problem can be solved using either of the two roots.

There is no superfluous solution to the equation (2m)/(2m+3)-(2m)/(2m-3) = 1 as a result.

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If each student scored the same on the midterm and final, the equation of the least-squares regression line is [tex]\hat{y}=x[/tex].

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions.

For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

So, Gary Smith of Pomona College reviewed the test results of all 346 students who took his statistics course over a ten-year period.

Take into account that both the midterm and final tests were rated out of 100.

Let the midterm score (x) and the final score (y) be the same.

The data for the explanatory variable x and the response variable y will be the same if each student receives the same grade on the midterm and final.

The linear model will predict that the two variables are equal if the data for the two variables are the same, and as a result, the linear model will assume that the expected y-variable is equal to the predicted x-variable.

Thus, the following is how the least-square regression line appears:

[tex]\hat{y}=x[/tex]

Therefore, if each student scored the same on the midterm and final, the equation of the least-squares regression line is [tex]\hat{y}=x[/tex].

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The rate of increase of the surface area of a spherical balloon is 8π square feet when r is 1 ft, 64π square feet when r is 8 ft, 72π square feet when r is 9ft and 16π square feet when r is 2 ft.

According to the question,

We have the following information:

A spherical balloon is being inflated. We need to find the rate of increase of the surface area of a spherical balloon with respect to r.

Surface area = [tex]4\pi r^{2}[/tex]

Differentiating with respect to r:

ds/dr = 8πr

Now, we will put all the values of r in this formula.

(a) r = 1 ft

Rate of increase = 8π*1

Rate of increase = 8π square feet

(b) Radius = 8 ft

Rate of increase = 8π*8

Rate of increase of area = 64π square feet

(c) Radius = 9 ft

Rate of increase of area = 8π*9

Rate of increase of area = 72π square feet

(d) Radius = 2 ft

Rate of increase of surface area = 8π*2

Rate of increase = 16π square feet

Hence, the rate of increase of the surface area of a spherical balloon is 8π square feet when r is 1 ft, 64π square feet when r is 8 ft, 72π square feet when r is 9ft and 16π square feet when r is 2 ft.

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To determine the accuracy of a "population parameter," a "sample statistic" is used to create a confidence interval.

Although they are connected, confidence level and confidence interval are not the same thing.

Thus, to evaluate the accuracy of a "population parameter," a "sample statistic" is used to create a confidence interval.

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To be a relation to a function there must be single output for single input thus tables (1) and (3) represent the function.

A certain kind of relationship called a function binds inputs to essentially one output.

A function can be regarded as a computer, which is helpful.

The machine will only accept specified inputs, described as the function's domain, and will potentially produce one output for each input.

In a function for every single input (x), there must be one output(y).

In the given second table,

For x = 0 → y =2 and y = 1 thus it will not be a function.

In the fourth table,

For x = 2 → y =2 and y = 6 thus it will not be a function.

Hence "To be a relation to a function there must be single output for single input thus tables (1) and (3) represent the function".

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Below is the stem-and-leaf plot to represent the ages of the top 30 highest-paid CEOs.

What is the stem-and-leaf plot?

A stem-and-leaf display, also known as a stem-and-leaf plot, is a device used to visualize the shape of a distribution by presenting quantitative data in a graphical format, similar to a histogram. They developed from the work of Arthur Bowley in the early 1900s and are useful tools in exploratory data analysis.

Stem Leaf

4          8 9

5          0 0 0 1 2 5 5 5 6 7 7 8 9 9

6          0 0 0 1 2 2 2 3 3 4 4 4 7

7          4

Hence, this is the stem-and-leaf plot to represent the ages of the top 30 highest-paid CEOs.

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Answer: public static void randomize(RegularPolygon r){

  int side = (int)((20-10) * Math.random()) + 10;

  int length = (int)((12-5)  * Math.random()) + 5;

  // assuming the regularpolygon class has setSide and setLength methods.

  r.set.Side(side);

  r.setLength(length);

The randomize method is used to access and change the state of the RegularPolygon class attributes sides and length. The method accepts the class as an argument and assigns a random number of sides and length to the polygon object.

Step-by-step explanation:

The correct option is option (a). Using Binomial Probability distribution,

the probability of getting a sum of 7 in at least 3 of the 10 rolls is 0.225..

We have given that,

probability of getting a sum of 7 on rolling of two dice once (p) = 6/36

so, 1 - p = 1 - 6/36 = 30/36 = 5/6

Using Binomial Probability distribution,

where "X" is random variable

the probability of getting a sum of 7 in at least 3 of the 10 rolls is

P( X ≥3 ) = 1 - P(X< 3)

= 1 - [ P(X= 0) + P(X= 1) + P(X= 2) ]

= 1 - [ 10C0 (1/6)0 (5/6)10 + 10C2 (1/6)1(5/6)9 + 10C3(1/6)3 (5/6)7

= 1- [ 0.1615 + 0.3230112 + 0.290710 ]

= 1 - [ 0.775522]

= 0.22475 ~0.225

Hence, the required probability is 0.225

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Answer:

6

Step-by-step explanation:

45-45-90 tri so x=6

3sqrt2^2=18

18+18=36

sqrt36=6

The SAS standard for similarity of triangles states that triangles are similar if two sides of one triangle are proportional to two sides of another triangle and their included angles are congruent.

Statement : The statement can be expressed as follows:

If two triangles ABC and DEF are such that

∠A=∠D and AC /DF =AB/DE

then △ABC∼△DEF

Proof :

Given: △ABC and △DEF are such that

AC /DF =AB/DE and ∠A=∠D

To Prove : △ABC∼△DEF

Construction : Draw a line PQ such that DP= AB , DQ= AC

In △ABC and △DPQ

AB = DP ( by construction)

DQ= AC ( by construction)

∠A=∠D (given)

=> △ABC ≅△DPQ (by SSA congruence property)

AB/DE = AC/DF (given )

=> DP/DE = DQ/DF ( using AB = DP ; DQ= AC)

=> PQ||EF (by converse of B.P.T)

Now , ∠P =∠E and ∠Q =∠F ( by corresponding angles)

△DEF ≅ △DPQ (Using AAS congruence )

=> △ABC ∼△DEF ( because two congrunt triangles are always similar )

Hence proved .

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The visibility rate for the only dominant phenotype is 100%. There is no phenotypic ratio since there is no second phenotype. The ratio that would be used to represent this outcome is 4:0 phenotypic ratio.

In the given question we have to explain about a 4:0 phenotypic ratio.

The visibility rate for the only dominant phenotype is 100%. There is no phenotypic ratio since there is no second phenotype. The ratio that would be used to represent this outcome is 4:0. However, the genotypic ratio considers probable allele combinations rather than the observable trait (phenotype).

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The vertex angle is defined as the angle opposite the base. It can be calculated by formula, 180° - 2B = A where, B=base angle and A=vertex angle.

The two sides of an isosceles triangle are congruent, which means they are the same length. The third side of an isosceles triangle is larger than the other two and is known as the base.

Every triangle has three angles that add up to a total of 180°. The base angles are the two angles located along the base of isosceles triangles. In isosceles triangles, the base angles are always congruent, or equal.

The vertex angle is defined as the angle opposite the base. The vertex angle is always greater than the sum of the two base angles. The vertex angle is always calculated by subtracting the base angles from 180°, using the general formula: 180° - 2B = A, where B represents the base angle and A represents the vertex angle.

Thus, vertex angle is defined as the angle opposite the base.

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The answer to the question probability of randomly selected person has a blood pressure of 182.6 mmHg is 0.0088.

What is standard deviation?

A measure of a group of values' variance or dispersion in statistics is called the standard deviation. When the standard deviation is low, the values are more likely to fall within a narrow range, also known as the expected value, whereas when the standard deviation is high, the values tend to be closer to the mean.

The lowercase Greek letter sigma, which stands for the population standard deviation, or the Latin letter s, which stands for the sample standard deviation, are most frequently used in mathematical equations and texts to represent standard deviation. Standard deviation is also sometimes referred to as SD.

The mean blood pressure for people in china is 128 mmHg.

The standard deviation of 23 mmHg.

For blood pressure of 182.6 mmHg

=p(x> 182.6)

=p(z> 182.6-128/23)

=p(z> 2.37)

=0.0088

Hence the probability of a randomly selected person has a blood pressure of 182.6 mmHg is 0.0088.

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Answer:

factors : 1, 3, 5 and 15

Step-by-step explanation:

1 x 15 = 15

5 x 3 = 15

so those are the only factors of 15

it is negative or positive depending upon the sign of the coefficients associated with the variable x

How do you define leading coefficient?

In a polynomial function, the leading term is the term containing the highest power of x. The coefficient of the leading term is called the leading coefficient.

it is negative or positive depending upon the sign of the coefficients associated with the variable x

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From the following four observations among the given hypothesis with significance level is 0.05 the null hypothesis is not true.

Null  hypothesis is all means are equal and in alternative at least there is a difference in one mean.

As given in the question,

Significant level is equal to 0.05

a. Null hypothesis : Null hypothesis is the one where there is no significant difference between the means of all the treatment groups.

Where as alternative hypothesis is the one which represents that there is significant difference between the means of all the treatment groups.

Therefore, from the following four observations among the given hypothesis with significance level is 0.05 the null hypothesis is not true.

Null  hypothesis is all means are equal and in alternative at least there is a difference in one mean.

The complete question is:

The following is sample information. Test the hypothesis that the treatment means are equal. Use the .05 significance level.

Treatment 1:     8,    6,    10,    9

Treatment 2:    3,    2,     4,     3

Treatment 3:     3,    4,     5,    4

a. State the null and alternative hypothesis

b. What is the decision rule?

c. Compute the SST,SSE and SS total

d. Compute an ANOVA table

e. State decision regarding null hypothesis

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The probability of exactly one car and exactly one bus during a cycle is 0.030.

What is probability?

Probability is that the branch of arithmetic regarding numerical descriptions of however possible an incident is to occur, or however possible it's that a proposition is true. The chance of an incident could be a range between 0 and 1.

Main body:

A) The joint pmf of X and Y is computed as,

p(x,y)=P(X=x and Y=y)

Such that,  p(x,y)≥0  and  ∑ p(x,y)=1.

The probabilities that there is exactly one car and exactly one bus during a cycle is denoted by

P (X =1,Y =1) = p(1,1).

From the given joint probability table, p(1,1)=0.030.

Therefore, the probability that there is exactly one car and exactly one bus during a cycle is 0.030.

Hence probability of exactly one car and exactly one bus during a cycle is 0.030.

B) Required to find the probability that there is at most one car and at most one bus during a cycle,

P(X ≤ 1 and Y ≤1 ), and is computed as follows:

P(X ≤ 1 and Y ≤1)=p(0,0)+p(0,1)+p(1,0)+p(1,1)

From the given joint probability table,

P(X ≤ 1 and Y≤1)=0.025+0.015+0.050+0.030=0.120

Therefore, the probability that there is at most one car and at most one bus during a cycle is 0.120.

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Using the solution of Algebraic expression,

we get that total 28 games won by sports team.

We have given that,

let a sports team lost be x games .

then, total number of games won by sports team

= 2x

total number of games played by sports team

= 42

i.e , 2x + x = 42

=> 3x = 42

=> x = 42/3

=> x = 14

so, number of games lost by sports team is 14

but we have to calculate the total number of games won by spots team .

using the value of x , we get 2x = 2×14

=> 28 games

Hence, total 28 games out of 42 games are won by sports team.

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The Cox-Ross-Rubinstein (CRR) model is a mathematical model used in finance to evaluate the potential future value of an asset or portfolio. The model is based on the concept of a binomial tree.

A binomial tree is a mathematical model used in finance to estimate the probable future value of an asset or portfolio. The notion of a binomial, a mathematical expression with two potential outcomes, forms the foundation of the model. In a binomial tree, the future value of the asset is defined by two potential outcomes at each time step: a "upper" element and a down factor. The underlying variables that affect the asset, such as interest rates and market circumstances, dictate the up and down components. Reflecting This enables investors to assess the advantages and dangers of a possible investment and come to wise judgments.

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Percentage by mass in sample will be 67.8%.

We know that volume of NaOH dispensed is 24.68 ml.

And mass of the NaOH is 39.997 g/mol.

Also mass of acid is 58.94 g/mol.

We have to find percentage by mass in sample.

To calculate the mass percent of an element in a compound, we divide the mass of the element in 1 mole of the compound by the compound's molar mass and multiply the result by 100.

Therefore

Mass percent = (mass of chemical / total mass of compound) × 100

                       = (mass of NaOH/ mass of acid) × 100

                       = (39.997/58.94) × 100

                       = 0.678 × 100

Mass percent = 67.8

Hence percentage by mass in sample is 67.8%

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The expected value of winnings is 0.

The expected value will be calculated by taking the sum of winning and loosing = E(x) = ΣxP(x), where X is the outcome and P is the probability of that outcome.

The probability of winning = X P(x)

The probability of winning = 1 × 0.5

The probability of winning = 0.5

The probability of loosing = -1 × 0.5 (-1 because it will be the loss)

The probability of loosing = -0.5

Calculating their sum = 0.5 + (-0.5)

Expected value = 0.5 - 0.5

Expected value = 0

Hence, the expected value is 0.

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On average number of customers arrives at a grocery shop per minute is equal to 1.2 customers per minute.

As given in the question,

Following a Poisson distribution:

Number of customers arrives at grocery store

= Average rate of 70 per hours

Conversion hours to minutes

1 hour = 60 minutes

λ = average rate of 70 per hours

  = average rate of 70 per 60 minutes

  = average rate of ( 7 / 6 ) per minute

 = average rate of 1.1666...per minute

= average rate of 1.2 per minute

Therefore,  on average 1.2 number of customers arrives per minute.

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Answer:

just count 3 digit and round it off then the answer would be 34000

A 90% confidence interval will be 82.5% < p < 84.9%

What is the confidence interval in statistics?

A confidence interval is the mean of your estimate plus and minus its variation. Within a certain level of confidence, this is the range of values you expect your estimate to fall between if you redo your test. In statistics, confidence is another word for probability.

We have to find a 90% confidence interval estimate of adults who used at least one prescription medication.

Here, the sample proportion [tex]\hat {p} = 0.837[/tex]

We know that for true population proportion confidence interval is given by

[tex]C.I.= \left( \hat{p}-z_{c}\sqrt{\frac{\hat{p}(1-\hat{p})}{n}} , \hat{p}+z_{c}\sqrt{\frac{\hat{p}(1-\hat{p})}{n}}\right)[/tex]

For 90% confidence interval [tex]z_c[/tex] = 1.645 from normal table

[tex]C.I.= \left( 0.837-1.645\sqrt{\frac{0.837(1-0.837)}{3072}} , 0.837+1.645\sqrt{\frac{0.837(1-0.837)}{3072}}\right)[/tex]

[tex]C.I.= \left( 0.837-1.645\sqrt{\frac{0.837(0.163)}{3072}} , 0.837+1.645\sqrt{\frac{0.837(0.163)}{3072}}\right)[/tex]

[tex]C.I.= \left(0.837-1.645\times 0.007 , 0.837+1.645\times 0.007 \right)[/tex]

[tex]C.I.= \left(0.837-0.012 , 0.837+0.012\right)[/tex]

[tex]C.I.= \left(0.825 , 0.849\right)[/tex]

Converting our confidence interval into percentages by multiplying it by 100 we get (82.5%, and 84.9%).

Thus, a 90% confidence interval will be 82.5% < p < 84.9%.

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The degree of freedom for the numerator is 5 and the degree of freedom for the denominator is 114.

Analysis of variance (ANOVA) is a type of statistical test used to determine if there is a statistically significant difference among two or more categorical groups by testing for differences of means using variance. An ANOVA test is used to analyze the differences between group means in a sample.

In this case, the number of groups, k is the number of distinct groups = 6

The total number of samples, N = number of groups x number of samples per each group

Thus, N = 6 x 20 = 120

Degree of freedom (df):

df within = df of numerator = k – 1 = 6 – 1 = 5

df between = df of denominator = N – k = 120 – 6 = 114

Hence, the required degrees of freedom are 5 numerator and 114 denominator.

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Before graphing a given rational function, it is occasionally necessary to simplify it. If, other than at asymptotes, there are any excluded values then graphing the function requires an additional step.

The function y=f(x), where f(x) is a rational expression, is the formula for a rational function.

Drawing the graphs of the rational functions might be challenging. Finding the asymptotes and intercepts is a good place to start when attempting to sketch a graph of a rational function.

The steps in graphing rational functions are as follows:

Find the rational function's asymptotes, if any exist.

Create dotted lines for the asymptotes.

Find the rational function's x-intercept (s) and y-intercept, if any.

For various x values, determine the values of y.

Plot the spots and then create a straight line to connect them and check to see if the graph crosses the vertical asymptotes.

Make sure the function is not a continuous smooth curve at the excluded value if you want to portray an undefined function. Typically referred to as the "hole in the rational function," this excluded value

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A cubic polynomial is a polynomial of degree 3. That is, it is a polynomial with three terms. The relationship between the zeros and the coefficients of a cubic polynomial can be found by using the factoring theorem.

This theorem states that if a polynomial has a factor of (x-a), then a is a zero of the polynomial. In other words, the zeros of a polynomial are the values of x that make the polynomial equal to zero.

To find the zeros of a cubic polynomial, we can use the factoring theorem to factor the polynomial into factors of the form (x-a). For example, if we have the cubic polynomial x³+ax²+bx+c, we can factor it as (x-a)(x²+px+q), where a, p, and q are constants. We can then use the factoring theorem to find the values of a, p, and q that make the polynomial equal to zero.

The coefficients of a cubic polynomial are the values of a, p, and q in the factored form of the polynomial. In other words, the coefficients of a cubic polynomial are the values that determine the zeros of the polynomial.

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The midpoint of the midsegment of Trapezoid is   E(2m, 2n) and F (2(q+p), 2n).

According to the question,

The vertices of the trapezoid are A(4m , 4n) , B(4q , 4n) , C(4p , 0) and D(0,0).

Let mid-point of midsegment of Trapezoid be E and F

Using section formula

E (x- coordinate)= 1*4m + 0 /2

E (x- coordinate)=2m

E (Y- coordinate)= 4n/2

E  (Y- coordinate)=2n

So, the coordinates of E (2m, 2n)

similarly,

F (x- coordinate)= (1*4q + 1*4p)/2

F (x- coordinate)=2(p + q)

F (Y- coordinate)= 4n/2

F(Y- coordinate)=2n

So, the coordinates of F (2(q +p), 2n)

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Answer:

Is there a diagram or picture??

Step-by-step explanation:

The required cubic polynomial is

f(x) = [tex]-2x^3-2x^2-28x+48[/tex]

What is a polynomial?

An algebraic expression of the form [tex]a_0 + a_1x+ .... + a_nx^n[/tex] ([tex]a_0 \neq 0[/tex]) is called a polynomial of degree n.

The zeroes of the cubic polynomial are -4, 2, 3

Let the cubic polynomial is

f(x) = a(x - (-4))(x - 2)(x - 3)

f(x) = a(x + 4)(x - 2)(x - 3)

If x = -5, f(x) = 112

112 = a(-5 + 4) (-5 - 2)(-5 - 3)

112 = -56a

a = [tex]-\frac{112}{56}[/tex]

a = -2

f(x) = -2(x+ 4)(x - 2)(x - 3)

[tex]f(x) = -2(x+ 4)(x^2 -3x -2x +6)\\f(x) = -2(x + 4)(x^2 - 5x + 6)\\f(x) = -2(x^3 - 5x^2+4x^2+6x - 20x+24)\\f(x) = -2(x^3 - x^2 - 14x +24)\\f(x) = -2x^3 -2x^2 - 28x + 48[/tex]

(x +4)(x - 2)(x - 3)

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