A city architect is designing a parking garage at city hall. the garage layout is in the shape of a rectangle. the width of the
garage is x + 15, where x is measured in feet. the length of the garage is 49 feet less than 2 times the width. the square
footage (area) that the parking garage covers should be 162 more than 27 times the garage's perimeter. find the length an
width of the parking garage that fits these requirements.
part a

J in 55min

J in 45min ( bigger hose)

Alternative method

The trick is to convert the numbers you are given to numbers that you can add together.

You have minutes per pool. You can’t work with that. But if you take the reciprocal of each you get pools per minute.

So if the first hose fills 1/55 = 0.01818 pools per minute and the second one fills 1/45 = 0.0222 pools per minute, then both of them will fill 0.1818 + 0.0222 = 0.04040 pools per minute. If we take the reciprocal of that we end up with 1/0.04040 = 24.75 minutes per pool.

The statement "Any u linearly independent vectors from Py will definitely form a basis for the vector space P4" is false.

To understand why this statement is false, we need to first understand what a basis is. A basis for a vector space is a set of vectors that are linearly independent and span the entire vector space. In other words, any vector in the vector space can be expressed as a linear combination of the basis vectors, and no basis vector can be expressed as a linear combination of the other basis vectors.

Now let's consider the vector space P4, which consists of all polynomials of degree 4 or less. Suppose we have a set of u linearly independent vectors from Py, where Py is a subset of P4. It is possible that these vectors do not span the entire vector space P4. In other words, there may be some polynomials in P4 that cannot be expressed as a linear combination of the u vectors. If this is the case, then the u vectors do not form a basis for P4.

To illustrate this, consider the following example. Let Py = {1, x, x^2} be a subset of P4. We can see that these three vectors are linearly independent, since there is no non-zero linear combination of them that equals the zero polynomial. However, they do not span the entire vector space P4, since there are polynomials of degree 3 or less that cannot be expressed as a linear combination of 1, x, and x^2. For example, the polynomial p(x) = x^3 cannot be expressed as a linear combination of 1, x, and x^2. Therefore, 1, x, and x^2 do not form a basis for P4.

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Answer:

y = -5/3x + 4

Step-by-step explanation:

slope = -5/3

-1 = -5/3(3) + b

-1 = -5 + b

4 = b

y = -5/3x + 4

Answer:

\(y=-\frac{5}{3}x+4\)

Step-by-step explanation:

To write down a line that is perpendicular to one line, make sure that their slopes give a product of -1:

\(\frac{3}{5}*m_2 =-1\\m_2=-\frac{5}{3}\)

Write down an equation in the point-slope form and replace everything in and simplify:

\(y_2-y_1=m(x_2-x_1)\\y-(-1)=-\frac{5}{3} (x-3)\\y+1=-\frac{5}{3}x+5\\y=-\frac{5}{3}x+4\\\)

Based on the given data, there is not significant evidence at the 5% level to prove that Sweatin to the Oldies is better than Tae Bo in terms of weight loss.

To determine if there is a significant difference between the two programs, we can conduct a hypothesis test using the two-proportion z-test. The null hypothesis (H0) would be that there is no difference in the proportion of weight loss between Sweatin to the Oldies and Tae Bo, while the alternative hypothesis (Ha) would be that there is a significant difference.

Using the given data, we can calculate the sample proportions for weight loss in each program:

- Sweatin to the Oldies: 1280/2340 ≈ 0.547

- Tae Bo: 1180/2006 ≈ 0.588

We can then calculate the test statistic and compare it to the critical value at the 5% level of significance. If the test statistic falls in the critical region, we reject the null hypothesis and conclude that there is a significant difference. Otherwise, if the test statistic falls outside the critical region, we fail to reject the null hypothesis.

However, the critical values for the two-proportion z-test depend on the specific test being conducted (one-tailed or two-tailed) and the desired level of significance. Without this information, we cannot provide a conclusive answer.

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Answer:

\(3b(a^{3} - 18)\)

Step-by-step explanation:

\(3a^{2}b-54b\)  => \(3b(a^{3} - 18)\)

Answer:

Step-by-step explanation:

\(\Large \boldsymbol{} 3a^3\underline b-54\underline b=b(3a^3-54)=\boxed{3b(a^3-18)}\)

Answer:

1) The slope-intercept and standard forms are \(y = -5\cdot x + 1\) and \(5\cdot x +y = 1\), respectively.

2) The slope-intercept form of the line is \(y = \frac{5}{2}\cdot x -\frac{9}{2}\). The standard form of the line is \(-5\cdot x +2\cdot y = -9\).

3) The slope-intercept form of the line is \(y = \frac{5}{2}\cdot x + 5\). The standard form of the line is \(-5\cdot x +2\cdot y = 10\).

4) The slope-intercept and standard forms of the family of lines are \(y = \frac{2}{7}\cdot x -\frac{c}{7}\) and \(2\cdot x -7\cdot y = c\), \(\forall \,c \in \mathbb{R}\), respectively.

5) The slope-intercept form of the line is \(y = 2\cdot x-7\). The standard form of the line is \(-2\cdot x +y = -7\).

Step-by-step explanation:

From Analytical Geometry we know that the slope-intercept form of the line is represented by:

\(y = m\cdot x + b\) (1)

Where:

\(x\) - Independent variable, dimensionless.

\(m\) - Slope, dimensionless.

\(b\) - y-Intercept, dimensionless.

\(y\) - Dependent variable, dimensionless.

In addition, the standard form of the line is represented by the following model:

\(a\cdot x + b \cdot y = c\) (2)

Where \(a\), \(b\) are constant coefficients, dimensionless.

Now we process to resolve each problem:

1) If we know that  \(m = -5\) and \(b = 1\), then we know that the slope-intercept form of the line is:

\(y = -5\cdot x + 1\) (3)

And the standard form is found after some algebraic handling:

\(5\cdot x +y = 1\) (4)

The slope-intercept and standard forms are \(y = -5\cdot x + 1\) and \(5\cdot x +y = 1\), respectively.

2) From Geometry we know that a line can be formed by two distinct points on a plane. If we know that \((x_{1},y_{1})=(1,-2)\) and \((x_{2},y_{2}) = (3,3)\), then we construct the following system of linear equations:

\(m+b= -2\) (5)

\(3\cdot m +b = 3\) (6)

The solution of the system is:

\(m = \frac{5}{2}\), \(b = -\frac{9}{2}\)

The slope-intercept form of the line is \(y = \frac{5}{2}\cdot x -\frac{9}{2}\).

And the standard form is found after some algebraic handling:

\(-\frac{5}{2}\cdot x +y = -\frac{9}{2}\)

\(-5\cdot x +2\cdot y = -9\) (7)

The standard form of the line is \(-5\cdot x +2\cdot y = -9\).

3) From Geometry we know that a line can be formed by two distinct points on a plane. If we know that \((x_{1},y_{1})=(-2,0)\) and \((x_{2},y_{2}) = (0,5)\), then we construct the following system of linear equations:

\(-2\cdot m +b = 0\) (8)

\(b = 5\) (9)

The solution of the system is:

\(m =\frac{5}{2}\), \(b = 5\)

The slope-intercept form of the line is \(y = \frac{5}{2}\cdot x + 5\).

And the standard form is found after some algebraic handling:

\(-\frac{5}{2}\cdot x+y =5\)

\(-5\cdot x +2\cdot y = 10\) (10)

The standard form of the line is \(-5\cdot x +2\cdot y = 10\).

4) If we know that \(a = 2\) and \(b = -7\), then the standard form of the family of lines is:

\(2\cdot x -7\cdot y = c\), \(\forall \,c \in \mathbb{R}\)

And the standard form is found after some algebraic handling:

\(-7\cdot y = -2\cdot x +c\)

\(y = \frac{2}{7}\cdot x -\frac{c}{7}\), \(\forall \,c\in\mathbb{R}\) (11)

The slope-intercept and standard forms of the family of lines are \(y = \frac{2}{7}\cdot x -\frac{c}{7}\) and \(2\cdot x -7\cdot y = c\), \(\forall \,c \in \mathbb{R}\), respectively.

5) If we know that \((x,y) = (3,-1)\) and \(m = 2\), then the y-intercept of the line is:

\(3\cdot 2 + b = -1\)

\(b = -7\)

Then, the slope-intercept form of the line is \(y = 2\cdot x-7\).

And the standard form is found after some algebraic handling:

\(-2\cdot x +y = -7\) (12)

The standard form of the line is \(-2\cdot x +y = -7\).

London is currently on British Summer Time (BST), which is 1 hour ahead of Greenwich Mean Time (GMT).

The time in London is determined by the British Summer Time (BST) which is 1 hour ahead of Greenwich Mean Time (GMT) during the summer months when Daylight Saving Time is in effect.

BST starts at 1:00 am GMT on the last Sunday of March and ends at 1:00 am GMT on the last Sunday of October. At other times of the year, London is on Greenwich Mean Time (GMT).

However, it's important to note that the United Kingdom has announced it will not be returning to GMT from BST from 2021, therefore London will remain on British Summer Time year-round.

During the months when BST is in effect, London is 4 hours and 30 minutes ahead of Indian Standard Time (IST).

It's also important to note that the time in London may change depending on the political decisions and if there are any changes in the time zone, it's always better to check the current time on reliable sources such as official websites or local news.

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The values x such that (6, x, −11) and (5, x, x) are orthogonal is 6,5.

The orthogonal vectors have dot product to be zero. Thus, the formula to be used is -

a . b = a1b1 + a2b2 + a3b3, where a1, a2 and a3 are components a vector and b1, b2 and be are components of b vector.

Keep the values in formula -

a . b = 6(5) + x² + (-11)x

a . b = 30 + x² - 11x = 0

So, x² - 11x + 30 = 0

x(x - 6) - 5(x - 6) = 0

(x - 6) (x - 5) = 0

So, the value of x is 6,5.

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Answer:

Should be the first one. You have $5 flat fee and an additional 10 cents per text. Then you have a $10 flat fee and an additional 5 cents per text. so the first equation would be 0.1x + 5 and the second one would be 0.05x + 10

The value of the given expression will be 4.

Expression in maths is defined as the relation of numbers variables and functions by using mathematical signs like addition, subtraction, multiplication and division.

Given that the expression is 2⁴ / ( 3.2 x 0.8 0 + 1.44 ). SOlve the expression as below,

E = 2⁴ / ( 3.2 x 0.8 ) + 1.44 )

Solve the denominator by mathematical operation.

E = 16 / ( 2.56 + 1.44 )

Divide the numerator by denominator,

E = 16 / 4

E = 4

Therefore, the solution of the expression is 4.

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a) The selling price of the skis is $79.80.

b) The final price is 140% of the original price.

c) The percent increase from the original price to the final price is 40%.

a) Calculation of selling price:

Markup rate is 40%

Original cost = $57

Selling price = (100% + Markup percentage) × Original cost

Selling price = (100% + 40%) × $57

Selling price = 1.4 × $57

Selling price = $79.80

b) Calculation of percentage of the original price that is the final price

Percentage of original price that is the final price = (Final price / Original price) × 100%

Percentage of original price that is the final price = ($79.80 / $57) × 100%

Percentage of original price that is the final price = 140%

c) Calculation of the percentage increase

Percentage increase = (Final value − Initial value) / Initial value × 100%

Percentage increase = ($79.80 − $57) / $57 × 100%

Percentage increase = $22.80 / $57 × 100%

Percentage increase = 40%

Therefore, The store charges $79.80 for the skis. The final price is 140% of the original price and the percent increase from the original price to the final price is 40%.

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Answer:

92

Step-by-step explanation:

If the 4 consecutive even integers have a sum of 380, then the average value is 380/4.

380/4 = 95

There must be 2 integers less than 95 and 2 grater than 95.

The 4 integers are: 92, 94, 96, 98

Sum: 92 + 94 + 96 + 98 = 380

Answer: 92

The 4 consecutive even integers are 92,94,96 and 98 whose sum is 380.

Sequence is an enumerated collection of objects in which repetitions are allowed and order matters.

The  4 consecutive even integers has a sum of 380.

x+2+x+4+x+6+x+8=380

Add the like terms

4x+20=380

Subtract 20 on both sides

4x=380-20

4x=360

Divide both sides by 4

x=90

So the four consecutive integers are

x+2=90+2=92

x+4=90+4=94

x+6=90+6=96

x+8=90+8=98

Hence, the 4 consecutive even integers are 92,94,96 and 98 whose sum is 380.

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Answer:

option b is the correct answer

Answer:

20l 10w or it could be the other way around

The greatest area of water she can enclose is 2500 m².

A rectangle is a 2-dimensional quadrilateral with four right angles.

Perimeter of a rectangle = 2 x (length + width)

Area of a rectangle = length x width

In order to determine the greatest area of water the lifeguard can enclose, we have t determine the sum of the dimensions.

200m = 2( l + b)

l + b = 200m / 2

l + b = 100m

The second step is to determine the pair of dimensions that add up to 100.

90 x 10 = 900

80 x 20 = 1600

70 x 30 = 2100

60 x 40 = 2400

50 x 50  = 2500

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y

=

3

(

x

+

3

2

)

2

−

27

4

Use the vertex form,

y

=

a

(

x

−

h

)

2

+

k

, to determine the values of

a

,

h

, and

k

.

a

=

3

h

=

−

3

2

k

=

−

27

4

Find the vertex

(

h

,

k

)

.

(

−

3

2

,

−

27

4

)

The statement is not true for spherical geometry. Because the sum of the angles in a triangle in spherical geometry is not equal to 180 degrees.

"Information available from the question"

In the question:

In Euclidean geometry the sum of the angles in a triangle equals 180 degrees.

We have to identify that this is true for spherical geometry also;

Now, According to the question:

In a Euclidean space, the sum of angles of a triangle equals the straight angle (180 degrees, π radians, two right angles, or a half-turn). A triangle has three angles, one at each vertex, bounded by a pair of adjacent sides.

The sum of the angles of a spherical triangle is not equal to 180°. A sphere is a curved surface, but locally the laws of the flat (planar) Euclidean geometry are good approximations. In a small triangle on the face of the earth, the sum of the angles is only slightly more than 180 degrees.

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Write the mixed fraction on the right side as a proper fraction.

The given equation becomes

The value of x is 9.

Answer:

-21y+7

Step-by-step explanation:

-7(3y-1) = 3y(-7) -1(-7) = -21y+7

Answer:

-21y + 7

Step-by-step explanation:

Just times - 7 with 3y then - 7 times with - 1

The conclusion of the symbolised argument is that N implies (O and P). This can be proven using conditional proof and the eighteen rules of inference, or using the rule of conjunctive simplification.

The symbolic argument's conclusion is that N implies (O and P). This can be demonstrated using conditional proof and the eighteen inference rules.

Proof:

1. N ⊃ O (Premise)

2. N ⊃ P (Premise)

3. N (Assumption)

4. O (1,3 Modus Ponens)

5. P (2,3 Modus Ponens)

6. O•P (4,5 Conjunction)

7. N ⊃ (O•P) (3-6 Conditional Proof)

8. N ⊃ (O•P) (2,7 Disjunctive Syllogism)

This leads us to the conclusion that N implies (O and P).

Without the use of conditional proof, the identical result can be reached. The conjunctive simplification rule can be used to do this.

Proof:

1. N ⊃ O (Premise)

2. N ⊃ P (Premise)

3. N (Assumption)

4. O (1,3 Modus Ponens)

5. P (2,3 Modus Ponens)

6. O•P (4,5 Conjunction)

7. N ⊃ (O•P) (Conjunctive Simplification)

Therefore, we have derived the conclusion that N implies (O and P).

Complete Question:

Use conditional proof and the eighteen rules of inference to derive the conclusions of the following symbolized arguments. Having done so, attempt to derive the conclusions without using conditional proof.

1. N ⊃ O

2. N ⊃ P / N ⊃ (O • P)

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The area principle is a fundamental concept in data visualization that states that the size of a graphical element (such as a bar, a pie slice, or a bubble) should be proportional to the quantity it represents.

In other words, the area of the graphical element should accurately reflect the magnitude of the data it is displaying. This principle is particularly important when comparing quantities, as it allows the viewer to quickly and accurately perceive the relative differences between them. For example, if two bars in a bar chart have the same width but different heights, the viewer may be misled into thinking that the two quantities are closer in magnitude than they actually are.

The area principle is often applied in conjunction with other principles of good data visualization, such as using clear and simple designs, avoiding clutter, and choosing appropriate scales and units. The goal is to create visualizations that are not only aesthetically pleasing but also informative and effective in communicating the underlying data.

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Solving a system of equations we can see that each pair of pants costs €82.94 and each coat costs €26.37

Let's define the variables:

x = cost of a pant

y = cost of a coat.

First, we know that:

3x + 2y = 245

And then there are discounts of 20% and 5%, and the cost of one of each is 100.75, then:

0.8x + 0.95y = 100.75

Then we have a system of equations:

3x + 2y = 245

0.8x + 0.95y = 100.75

We can isolate x on the second equation to get:

x = (100.75 - 0.96y)/0.8

x = 125.9 - 1.2y

Replace that in the other equation:

3*(125.9 - 1.2y) + 2y = 245

Solving for y:

3*125.9 - 3*1.2y + 2y = 245

y*(2 - 3*1.2) = 245 - 3*125.9

y = (245 - 3*125.9)/(2 - 3*1.2)

y = 82.94

Then the value of x is:

x = 125.9 - 1.2*82.94

x = 26.37

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Answer:

18 melon

Step-by-step explanation:

Given :

Original stack :

Melon = 45

Grape fruits = 60

Mini version :

Grapefruit = 24

Using grapefruit ; we can obtain the scale factor;

60 : 24 = 2.5 : 1

Hence,

Amount of melon in the mini version is :

45 / 2.5

= 18

Answer:

22

Step-by-step explanation:

You would add 14 and 8.    

22-8=14

Check it on your calculator

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Answer:

x = 22

Step-by-step explanation:

Solving for x means having x alone on the left side as in

x = some number

Since 8 is being subtracted from x on the left side, you need to do the opposite operation of subtracting 8. The opposite operation of subtraction is addition. That means you need to add 8 to the left side to get rid of the subtraction of 8. The rule with equations is that you must do the same operation to both sides of the equation. Therefore, you need to add 8 to both sides of the equation.

x - 8 = 14

Add 8 to both sides.

x - 8 + 8 = 14 + 8

On the left side, -8 + 8 = 0, so you end up with just x.

On the right side, 14 + 8 = 22, so you end up with 22.

x = 22

Answer: x = 22

Storekeepers in electronics companies deal with various types of materials. Five classes of materials include electronic components, raw materials, finished products, packaging materials, and maintenance supplies.

Electronic Components: Storekeepers are responsible for managing a wide range of electronic components such as resistors, capacitors, integrated circuits, connectors, and other discrete components. These components are essential for assembling electronic devices and are typically stored in organized bins or cabinets for easy access.

Raw Materials: Electronics companies require various raw materials for manufacturing processes. Storekeepers handle materials like metals, plastics, circuit boards, cables, and other materials needed for production. These materials are usually stored in designated areas or warehouses and are monitored for inventory levels.

Finished Products: Storekeepers are also responsible for storing and managing finished products. This includes fully assembled electronic devices such as smartphones, computers, televisions, and other consumer electronics. They ensure proper storage, tracking, and distribution of these products to customers or other departments within the company.

Packaging Materials: Packaging plays a crucial role in protecting and shipping electronic products. Storekeepers handle packaging materials such as boxes, bubble wrap, foam inserts, tapes, and labels. They ensure an adequate supply of packaging materials and manage inventory to meet packaging requirements.

Maintenance Supplies: Electronics companies often require maintenance and repair supplies for their equipment and facilities. Storekeepers handle items like tools, lubricants, cleaning agents, safety equipment, and spare parts. These supplies are necessary to support ongoing maintenance activities and ensure the smooth operation of machinery and infrastructure.

Overall, storekeepers in electronics companies deal with a diverse range of materials, including electronic components, raw materials, finished products, packaging materials, and maintenance supplies. Effective management of these materials is crucial to ensure smooth operations, timely production, and customer satisfaction.

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The set A {a,b,c}  that is neither symmetric nor antisymmetric is option D)  {(a, b), (b, a),(a, c)} on {a,b,c}

We are looking for a relation on the set A that is neither symmetric nor antisymmetric. Here are the given options:
A. the empty set on {a, b, c}
B. {(a, b), (b, a), (a, a), (a, a)} on {a, b, c}
C. {(a, b), (b, a)} on {a, b, c}
D. {(a, b), (b, a), (a, c)} on {a, b, c}

A relation R on set A is symmetric if for all (x, y) in R, (y, x) is also in R. It is antisymmetric if for all (x, y) in R, (y, x) in R implies x = y.

Let's examine each option:

A. The empty set has no elements(null set), so it is both symmetric and antisymmetric, which does not satisfy the required condition.

B. {(a, b), (b, a), (a, a), (a, a)}: Since (a, b) and (b, a) are in the relation, it is symmetric.

However, (a, a) makes it not antisymmetric, as (a, a) does not imply a = b.

Thus, this option is symmetric and does not satisfy the condition.

C. {(a, b), (b, a)}: This relation is symmetric since (a, b) and (b, a) are both in the relation, but it is not antisymmetric. Therefore, this option does not satisfy the condition.

D. {(a, b), (b, a), (a, c)}: This relation is neither symmetric nor antisymmetric. It is not symmetric because (a, c) is in the relation but (c, a) is not.

It is not antisymmetric because (a, b) and (b, a) are both in the relation but a ≠ b. Thus, this option satisfies the required condition.

Hence the relation on the set A that is neither symmetric nor antisymmetric is D. {(a, b), (b, a), (a, c)} on {a, b, c}.

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Answer:3

−

4

=

1

2

Step-by-step explanation: sorry if its wrong

Answer:

option 1

The probability of tossing a head and then rolling a number greater than 5 is 3/16.

To find the probability of tossing a head and then rolling a number greater than 5, we need to calculate the individual probabilities and then multiply them together.

Probability of tossing a head:

Since a fair coin has two equally likely outcomes (head or tail), the probability of tossing a head is 1/2.

Probability of rolling a number greater than 5:

An eight-sided die has eight equally likely outcomes (numbers 1 through 8). Out of these eight outcomes, there are three numbers greater than 5 (6, 7, and 8). Therefore, the probability of rolling a number greater than 5 is 3/8.

To find the probability of both events occurring, we multiply the probabilities:

Probability of tossing a head and rolling a number greater than 5 = Probability of tossing a head × Probability of rolling a number greater than 5

= (1/2) × (3/8)

= 3/16

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The equation that shows the relationship between the variables are T = 0.112N, D = 54A and T = 62.5A

An equation is an expression that shows the relationship between two or more numbers and variables.

Let k represent the constant of proportionality

3) T = kN

28 = 250k

k = 0.112

i) T = 0.112N

ii) T = 0.112(300) = 33.6

iii) 98 = 0.0112N

N = 875

4) D = kA

270 = 5k

k = 54

i) D = 54A

ii) D = 54(4.5) = 243

iii) 324 = 54A

A = 6

5) T = kA

150 = 2.4k

k = 62.5

i) T = 62.5A

ii) T = 62.5(1.8) = 112.5

iii) 3(60) = 62.5A

A = 2.88

The equation that shows the relationship between the variables are T = 0.112N, D = 54A and T = 62.5A

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