The minimum point of a quadratic curve is (7,-4).
Write down the equation of the curve in the form y = (x + a)² + b, where
a and b are numbers.
What are the values of a and b?

if a decimal number is divisible by 3 if and only if the sum of its digits is divisible by three is evident and proved below.

Let n be a decimal number.

Assume n is divisible by 3.

lets consider n in terms of its digits as

n = d_1 * 10^(m-1) + d_2 * 10^(m-2) + ... + d_m * 10^0

where m is the number of digits in n and d_1, d_2, ..., d_m are its digits.

Substituting n = 3k into the above equation, we get

3k = d_1 * 10^(m-1) + d_2 * 10^(m-2) + ... + d_m * 10^0

Subtracting 3k from both sides of the equation, we get

0 = d_1 * 10^(m-1) + d_2 * 10^(m-2) + ... + d_m * 10^0 - 3k

Adding 3k to both sides of the equation, we get

3k = d_1 * 10^(m-1) + d

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Therefore , Mrs. Garcia needs 280 grams of gluten-free flour.

Equations are classified by identity equations or conditional equations. There is an identity for each possible value of the variables. A conditional equation can only have a certain set of variable values. Equation is represented by equals ("="), which divides two expressions.

Here,

Mrs. Garcia  needs 70% of the flour to be almond flour

Thus ,

70% of 400 is

=> 70/100*400 =  280

Therefore , Mrs. Garcia needs 280 grams of gluten-free flour.

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The radius of convergence is a-R a+R = 6+12 =18 and 6-12 = -6 for the |6x 12/<78 and diverges if |6x 12| 78.

The set of actual numbers x wherein the collection converges is the c program language period of convergence. If there exists a actual wide variety R such that the collection converges for |x−a|R, then R is the radius of convergence.

The radius of convergence is 1/2 of of the duration of the c program language period of convergence. If the radius of convergence is R then the c program languageperiod of convergence will consist of the open c program languageperiod: (a − R, a + R). To discover the radius of convergence, R, you operate the Ratio Test.

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Answer:

82 degrees

Step-by-step explanation:

due to the resemblance of 90 degrees

The expression P(A + B) = P(A) + P(B) - P(AB) is proved.

Proved is shown below.

A set is a collection of items where there are operations such as:

Union of sets, the intersection of sets, complements of sets.

We have,

Consider A = {1, 2, 3, 4, 5}

B = {2, 3, 4, 6, 7}

P (A + B) = P (A U B)

P (AB) = P (A ∩ B) (Common values}

P (AB) = {2, 3, 4}

P (A + B ) = {1, 2, 3, 4, 5, 6, 7}

Now,

P(A + B) = P(A) + P(B) - P(AB)

{1, 2, 3, 4, 5, 6, 7} = {1, 2, 3, 4, 5} + {2, 3, 4, 6, 7} - {2, 3, 4}

{1, 2, 3, 4, 5, 6, 7} = {1, 2, 2, 3, 3, 4, 4,5, 6, 7} - {2, 3, 4}

{1, 2, 3, 4, 5, 6, 7} = {1, 2, 3, 4, 5, 6, 7}

Thus,

P{A + B) = P(A) + P(B) - P(AB) proved.

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Of the following, a sequence which is not a geometric sequence is 3, 6, 9, ... (Option A)

A geometric sequence refers to a sequence in which each term is determined by multiplying the preceding term by the same value which is called the common ratio (r). Hence, the common ratio determined by dividing a term by preceding term is constant in a geometric sequence.

In the given options,

A) r = 6/3 ≠ 9/6

B) r = 9/3 = 27/9 = 3

C) r = 8/4 = 16/8 = 2

D) r = -7/7 =7/-7 = -7/7 = -1

As the common ratio r is constant for option B, C and D, they are geometric sequences. The ratio between consecutive terms is not the same for option A, it is not a geometric sequence.

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The average value of the given function on the given interval is = 7/2 and 6.25 respectively

What is Average?

The middle number, which is obtained by dividing the sum of all the numbers by the variety of numbers, is the average value in a set of numbers. To calculate the average of a set of data, add up all the values and divide the result by the total number of values.

(a) f(x) = x2 – 8x + 10

f = 1/b-a [tex]\int\limits^b_a {f(n)} \, dx[/tex]

f = 1/5-2 [tex]\int\limits^5_2 {x^{2} -8x+10} \, dx[/tex]

Here, a=2

b=5

f(x) =x2 – 8x + 10

f = 1/3 (x³/3 - 8x²/2+10x)5/2

f = -25/9 -20/9

f = -45/9

= -5

Mean Value Theorem

If f(x) = continous on (a, b)

If f(x) = differentiable on (a, b)

Then f(c) = f(b) -f(a)/b-a

were c∈ (a,b)

Here, f(c) = f(-5)-f(2)/5-2

f(c) = -5+2/3

f(c) = -1 ......................(1)

Here, f(x) = x²-8x+10

f(c) = c²-8c+10

f(x) = 2c-8...................(2)

equating 1&2

2c -8 = -1

2c = -1 +8

c = 7/2

c∈ (2,5)

(b) f(x) = Vx on [1, 16]

f = [tex]\sqrt{x}[/tex] on (1 ,16)

f= 1/b-a [tex]\int\limits^b_a {f(n)} \, dx[/tex]

f = 1/16-1 [tex]\int\limits^6_1 {\sqrt{x} } \, dx[/tex]

f = ( 2x (3/2)/45)₁¹⁶

f = 128/45-2/45

f = 126/45

= 14/5

Mean Value Theorem

f(x) = [tex]\sqrt{x}[/tex]

f(c) =[tex]\sqrt{c}[/tex]

f(c) = 1/2[tex]\sqrt{c}[/tex]....................(1)

we know that

f(c) = f(b)-f(a)/b-a

f(c) = f(16)-f(1)/16-1

f(c) = [tex]\sqrt{16}[/tex] -[tex]\sqrt{1}[/tex]/15

f(c) = 4-1/15

= 3/15.....................(2)

Equating (1) and (2)

1/2[tex]\sqrt{c}[/tex] = 3/15

2[tex]\sqrt{c}[/tex] = 15/3

2[tex]\sqrt{c}[/tex] = 5

[tex]\sqrt{c}[/tex] = 5/2

c = (5/2)²

=25/4

c≅ 6.25

6.25 = (1 ,16)

The average value of the given function on the given interval is = 7/2 and 6.25 respectively

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The set of independent variables of a function called the domain of the function.

Domain is the set of values for which the given function is defined.

The set of all possible values of the dependent variable called the range.

The range of a function refers to all the possible values y could be. The formula to find the range of a function is y = f(x). In a relation, it is only a function if every x value corresponds to only one y value.

The set of all possible values for the function called the the domain of the function.

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It's true, any irrational number squared will result in a rational number

A real number that can NOT be made by dividing two integers (an integer has no fractional part).

"Irrational" means "no ratio", so it isn't a rational number. We aren't saying it's crazy!

Its decimal also goes on forever without repeating.

A counterpart problem in measurement would be to find the length of the diagonal of a square whose side is one unit long; there is no subdivision of the unit length that will divide evenly into the length of the diagonal. (See Sidebar: Incommensurables.) It thus became necessary, early in the history of mathematics, to extend the concept of number to include irrational numbers. Irrational numbers such as π can be expressed as an infinite decimal expansion with no regularly repeating digit or group of digits. Together the irrational and rational numbers form the real numbers.

Irrational numbers are those that cannot be expressed as a fraction of integers.

 If we square the irrational numbers then it becomes rational numbers as it can be shown as ratio of integers.

[tex]\sqrt{3}[/tex]  is a irrational number but by squaring it [tex](\sqrt{3 )^{2}[/tex] is a rational number

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It should be close to 7m at around 5pm. In fact, this is the time of day when the water rises the fastest, so perhaps 8m

The interval between successive peaks in the sinusoidal signal graph, or period, is only the number of seconds needed for one cycle of the sinusoid.

Depending on the values of angular frequency (), discrete-time sinusoidal sequences may or may not be periodic. A discrete-time sinusoidal signal must have an angular frequency () that is a multiple of 2 to be considered periodic.

It takes roughly 6 hours from low tide to high tide, or 12 hours for the entire tide cycle. Since low tide was at 2 a.m., low tide will be at around 2 p.m. as well. Three hours later, or at around 5 p.m., the water should be at the average level, which should be at (12.4+1.2)/2=6.8 m. Therefore, it should be close to 7m around 5:45. Actually, this is when the water rises the fastest, so it's probably close to 8m. Your 5.5m is obviously too low, regardless of where it is.

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The factored form of the equation x² + 3x - 10 is  (x - 2)(x + 5)  .

In the question ,

it is given that ,

the equation is x² + 3x - 10 , we have to express it in factor form ,

So , rewriting the equation by using the split the middle term method .

= x² + 3x - 10

= x² + 5x - 2x - 10     , ...because   5x - 2x = 3x

taking  x common from the first two terms ,

we get ,

= x(x + 5) - 2(x + 5) taking (x+5) common from both the terms ,

we get ,

= (x - 2)(x + 5)

Therefore , the factor form is  (x - 2)(x + 5) .

The given question is incomplete , the complete question is

What is the factored form of x² + 3x - 10  ?

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(a) The probability that a 0 is received is 66.7%

(b) By using the Bayes theorem, the probability that a 0 was transmitted, given that a 0 was received is 90%

Probability:

In statistics, probability deals with finding out the likelihood of the occurrence of an event.

Given,

Here the 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 0.6 and the probability that it is received incorrectly (as a 1) is 0.4. 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.

Now, we have to find the probability of the following.

Here the probability that a 0 is received is calculated as,

=> 0.9 of 2/3(0 received when a 0 is sent) and 0.2 of 1/3(0 received when a 1 is sent). So

Now, the probability is

=> p = (0.9 x 2)/3 + (0.2 x 1)/3

=> p = 0.6667

When we convert this into percentage then we get, 66.67% probability that a 0 is received.

Similarly, by using the Bayes theorem, the probability that a 0 was transmitted, given that a 0 was received is calculated as,

Here we know that, Event A: 0 received and Event B: 0 transmitted.

Then 0.6667 = 66.67% probability that a 0 is received, which means that

P(A) = 66.7%

And the zero is transmitted two-thirds of time, which means that

P(B) = 66.7%

Where as if 0 is sent, then the probability that it is received correctly is 0.9, which means that

P(A|B) =0.9

Therefore, the probability is

=> 66.7 x 0.9/66.7

=> 0.9

We know that 0.9 = 90% probability that a 0 was transmitted, given that a 0 was received.

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a)95% confidence interval for the population mean birth weight in these hospitals is (3078.9358,3221.0642).

(b)The P-value is 0.0068.

To test the null hypothesis and the alternative hypothesis, all analysts employ a random population sample. The null hypothesis typically states that two population parameters are identical; for instance, it can claim that the population mean return is equal to zero.

A strategy for determining how reliably one may extrapolate observed results in a study sample to the larger population from is provided by hypothesis testing, a procedure used to assess the strength of the evidence from the sample and give a framework for doing so.

C.I=x-t(alpha/2)xs/sqrt{n}

=3150+_2.01*250/sqrt{50}

=(3078.9358,3221.0642)

b) P value =P(t<-2.83)+P(t>2.83)

use calculator

                 =0.0034+0.0034

                  =0.0068

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The amount of cabbage 12.82 pounds will be to buy for $5.00.

What is Division method?

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

Given that;

The cabbage costs $0.39 per pound.

Now,

Since, The cabbage costs $0.39 per pound.

Hence, The amount of cabbage to buy for $5.00 = 1/0.39 × 5

                                                                            = 12.82 pounds

Thus, The amount of cabbage 12.82 pounds will be to buy for $5.00.

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Therefore , most of the time, a system of linear equations has a single solution, but it is occasionally possible for it to have infinite or no solutions (parallel lines).

A mathematical equation is a formula that uses the equals symbol (=) to connect two expressions and express their equality.  A well-formed formula consisting of two expressions linked by an equals sign is considered to be an equation in English, but the word's cognates in other languages may have slightly different definitions. For instance, an équation is defined as having one or more variables in French. 

There are 3 solutions  to the system of equations

1)single solution

2)infinite solutions

3)no solutions

Therefore , most of the time, a system of linear equations has a single solution, but it is occasionally possible for it to have infinite or no solutions (parallel lines).

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The difference in the mean of the two major automobile manufactures is equal to option c. 2.0.

As given in the questions,

Number of samples selected for each manufactures = 8

For manufacturers A :

Mean of manufacturer A

=(Sum of all the eight data) / ( Number of data)

= ( 32+ 27 + 26 + 26 + 25 + 29 + 31 + 25 ) / 8

= 221 / 8

= 27.625

Mean of manufacturer B

=(Sum of all the eight data) / ( Number of data)

= ( 28 + 22 + 27 + 24 + 24 + 25 + 28 + 27 ) / 8

= 205 / 8

= 25.625

Difference in the mean of manufacturer A and B

= 27.625 - 25.625

= 2.0

Therefore, the difference in the mean of both manufacturer is given by Option C. 2.0.

The complete question is :

Two major automobile manufacturers have produced compact cars with engines of the same size. We are interested in determining whether or not there is a significant difference in the mean MPG (miles per gallon) when testing for the fuel efficiency of these two brands of automobiles. A random sample of eight cars from each manufacturer is selected, and eight drivers are selected to drive each automobile for a specified distance. The following data (in miles per gallon) show the results of the test. Assume the population of differences is normally distributed.

Driver              Manufacturer A                 Manufacturer B

1                             32                                    28

2                            27                                    22

3                            26                                    27

4                            26                                    24

5                            25                                    24

6                            29                                    25

7                             31                                    28

8                             25                                   27

A) The mean for the differences is __________

a. 0.50               b. 1.5                 c. 2.0              d. 2.5

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As the data says , the null and alternate hypothesis will be H0 :p=0.50 and H1:p ≠ 0.50

Let p stand for the true proportion of odds.

To compare the

null hypothesis H0:P = 0.50

alternative hypothesis H1:p 0.50

Let p represent the sample proportion and n represent the sample size.

here,

p = 14/40

= 0.350

n=40, p₀ = 0.500,

= proportional standard error under null 0.50 * (1 -0.50) /40

= 0.079057

The test statistic is as follows:

z = p - p0 / √ p0  ( 1  - p0) / n )

They follow a typical normal distribution under H0

If P-value 0.05 or |Zobs| > 0, we reject H0 t 0.05 threshold of significance. z0.025

Now,

The test statistic value is -1.897367.

1.959964 is the key value.

P-value = 2*P(Z - 1.897367) + P(|z|>Zobs)

= 2 * 0.028890

= 0.057780≈ 0.0578

Because the p-value is greater than 0.05 and |Zobs|  = 1.959964,

As a result, we fail to reject H0 at the 0.05 threshold of significance.

As a result, the population proportion has decreased.

Null and alternate hypotheses are used in statistical hypothesis testing. The null hypothesis of a test always expects no effect or no association between variables, whereas the alternative hypothesis of a test always predicts no effect or no association between variables.

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Answer:

Step-by-step explanation:

Step 1: The sample proportion is pˆ=1440=0.35, the hypothesized proportion is p0=0.5, and the sample size n=40.

Step 2: The test statistic, rounding to two decimal places, is z=0.35−0.50.5(1−0.5)40−−−−−−−−−−√≈−1.897.

Step 3: Since the test is two-tailed and the test statistic is negative, entering the function =2*Norm.S.Dist(−1.90,1) into Excel returns a p-value, rounding to three decimal places, of 0.058.

Answer:

have her do the number times each number every time so if the number is seven and there is a four on top, add or multiply or subtract 7 by 4

Step-by-step explanation:

The percentage of having a probability of a non-vowel letter is 44%

Probability is the measure of the likelihood that an event will occur in a given set of circumstances. It is a quantifiable measure of the chance of something happening. Probability is expressed as a number between 0 and 1 (or 0% to 100%) where the higher the number, the more likely the event is to occur.

The probability to select a vowel letter is = 15 + 22 + 11 + 6 + 2 = 56%

The probability of selecting any vowel is 56%

In the English alphabet, we have 26 letters and 5 vowel letters.

The probability of not having a vowel letter is calculated as;

26 - 5 = 21

P = 21 / 28

In percentage, we can simply say the probability of having a non-vowel is 100 - 56 = 44

The percentage of having a non-vowel is 44%

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The real zeros in the given equation y = (x-12)³ - 7 will be x =  13.912.

For the real solutions, we know that a real zero is a real number which makes the value of the function zero. By the question, let

y = 0  ..........(1)

Put values of 'y' in equation (1), and we get.

(x-12)³ - 7 = 0         .........(2)
Adding '7' on both sides of equation (2), we get

(x-12)³ = 7
Taking the cube root on sides, the resulting equation will be:

[tex]\sqrt[3]{(x-12)^{3} }[/tex]  =  [tex]\sqrt[3]{7}[/tex]
x - 12 = 1.912
By adding '12' on both sides.
x =  13.912

So the only real zeros for the given equation will be 13.912. Other solutions are imaginary zeros.

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We don't have claim to strength of composite B is smaller than the strength of composite B by at least 2 [N].

From the given data we calculate μ₁s₁ and μ₂s₂ mean and standard deviation of samples A and B respectively.

μ₁ = 464.7, s₁ = 13.42 composite A

μ₂ = 479.49, s₂ = 13.38 composite B

n₁ : n₂ < 30 then we will use t-table.

Null hypothesis  H₀:μ₂-μ₁ ≥ 2

Alternative hypothesis Hₐ : μ₂ - μ₁ < 2

assuming CI 95%

α = 5% = 0.05

and degree of freedom is n₁ + n₂ - 2 = 9 + 9 - 2 = 16

then for the one tail t(c) = 1.746  

now we will compute t(s),

t(s) = (μ₂ - μ₁ - 2)/ sp×√1/n₁ + 1/n₂

sp²= (n₁ - 1) × s₁² + (n₂ - 1) × s₂² / n₁ + n₂ - 2

    = 8 × (13.42)² + 8 × (13.38)²/ 16

     = (8 × 180.1 + 8 × 179) / 16

sp² = 179.55

sp = 13.40

Therefore

t(s) = (479.49 - 464.7 - 2)/ 13.40 ×√1/9+1/9

     = 12.79 / 13.40 × 0.4714

     = 12.79 / 6.32

t(s) = 2.02

t(s) > t(c)

t(s) is rejection region.

Therefore we reject H₀

so we don't have evidence to claim to strength pf composite B is smaller than the strength of composite B at least 2 [N].

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The sample is sufficient to conclude that scores for students using e-books were significantly different from scores for the regular class.

At the null hypothesis, it is tested if the scores are not different from the regular class, that is, if the mean is of 81.7, hence:

[tex]H_0: \mu = 81.7[/tex]

At the alternative hypothesis, it is tested if the scores are different from the regular class, that is, if the mean is different of 81.7, hence:

[tex]H_1: \mu \neq 81.7[/tex]

We have a two-tailed test, as we are testing if the mean is different of a value, with a significance level of 0.05 and 9 - 1 = 8 df, hence the critical value is given as follows:

|t| = 2.306.

Thus the decision rule is given as follows:

The test statistic is given by the equation presented as follows:

[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]

In which:

The parameters for this problem are of:

[tex]\overline{x} = 77.2, \mu = 81.7, s = 5.7, n = 9[/tex]

Hence the test statistic is calculated as follows:

[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]

[tex]t = \frac{77.2 - 81.7}{\frac{5.7}{\sqrt{9}}}[/tex]

t = -2.37.

|t| > 2.306, hence the sample is sufficient to conclude that scores for students using e-books were significantly different from scores for the regular class.

The problem asks if the sample is sufficient to conclude that scores for students using e-books were significantly different from scores for the regular class? Use a two-tailed test with α = .05.

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Answer: 5 i think

because if x^3 = 1/125 then 625 times 1/125 is 5

Answer: x = 56

Step-by-step explanation:

The angle horizontally adjacent from 73 is also equal to 73 due to the triangle being isosceles (the legs are given as equal). Therefore the other angle in that triangle has to be 180 - (73*2) = 34. This angle is a part of the 90 degree angle that is noted in the figure. The other part of that angle must be 90 - 34 = 56. Since this angle is in another isosceles triangle, the angle horizontally adjacent to it must also be 56. x is equal to this angle by definition of vertical angles, so x = 56.

The simplified value of the expression is 23

What is an expression?

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a complete sentence. Any one of the following mathematical operations can be used. A sentence has the following structure: Number/variable, Math Operator, Number/Variable is an expression.

To find the value:

- [ 4 - 3 (-2 + 5)²]

= - [ 4 - 3 (3)²]

= - [ 4 - 3*9]

= - [ 4 - 27]

= - [ -23]

= 23

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The product of the vectors v and w is gotten as; v ⋅ w = 22

We are given the vectors;

r = <8, 8, -6>

v = <3, -8, -3>

w = <-4, -2, -6>

We want to evaluate v.w which is a product of both vectors.

The formula will be;

v.w = (v_x * w_x) + (v_y * w_y) + (v_z * w_z)

Plugging in the values and solving gives;

v.w = (3 * -4) + (-8 * -2) + (-3 * -6)

v.w = -12 + 16 + 18

v.w = 22

We can conclude that the vector expressions has a product of 22

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Answer:

multiplying numerator by denominator, as in number times number equals = A = answer

Step-by-step explanation:

The 500 sample size and 95% confidence level will both tend to increase the width of the confidence interval.

In this question, we have been given  the combinations of sample size and confidence level.

We need to select a combinations of sample size and confidence level that will give the widest interval.

We know that the confidence level is typically set in the range of 99% to 80%. The 95% confidence interval will be wider than the 90% interval and which will be wider than the 80% interval.

As we know increasing the confidence will increase the margin of error which results in a wider interval.

But increasing the sample size decreases the width of confidence intervals, as it decreases the standard error.

This means, for the widest interval we need to select a high confidence interval and small sample size.

Therefore, the sample size = 500 and the confidence interval = 95% will give the widest interval.

Learn more about the confidence interval here:

https://brainly.com/question/22851322

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