Mathematics: 7/12 1/2 5/12 1/3 what is the next fraction in this sequence

7/12 1/2 5/12 1/3 what is the next fraction in, №13709739, 19.04.2022 12:25

Mathematics

1. find the digit that makes 3,71_ divisible by 9. a. 3 b. 7 c. 1 d. 5 2.list all the factors of the number 30. a. 1, 2, 3, 5, 6, 10, 15, 30 b. 2, 3, 4, 10, 20, 30, 40 c. 1, 2, 4, 5, 10, 15, 30 d. 1, 2, 4, 5, 8, 10, 20, 40 3. find the prime factorization of the number 168. a. 24 x 3 x 7 b. 23 x 3 x 7 c. 24 x 33 x 13 d. 23 x 33 x 7 4. find the gcf of the numbers 140 and 180. a. 20 b. 90 c. 30 d. 10 5. the weights of 3 bags containing footballs are 15 oz, 30 oz, and 60 oz. the greatest common factor of 15, 30, and 60 gives the weight of each ball

Step-by-step answer

P Answered by PhD

64

QUESTION 1

We want to find the digit that should fill the blank space to make

3,71-

divisible by 9.

If a number is divisible by 9 then the sum of the digits should be a multiple of 9.

The sum of the given digits is,

3 + 7 + 1 = 11

Since

11 + 7 = 18

which is a multiple of 9.

This means that

3,717

is divisible by 9.

The correct answer is B

QUESTION 2

The factors of the number 30 are all the numbers that divides 30 exactly without a remainder.

These numbers are ;

1,2,3,5,6,10,15,30

The correct answer is A.

QUESTION 3.

We want to find the prime factorization of the number 168.

The prime numbers that are factors of 168 are

$2,3 \: and \: 7$

We can write 168 as the product of these three prime numbers to obtain,

$168={2}^{3}\times 3\times7$

We can also use the factor tree as shown in the attachment to write the prime factorization of 168 as

$168 ={2}^{3}\times 3\times7$

The correct answer is B.

QUESTION 4.

We want to find the greatest common factor of

$140\:\:and\:\:180$

We need to express each of these numbers as a product of prime factors.

The prime factorization of 140 is

$140={2}^{2}\times 5\times7.$

The prime factorization of 180 is

$180={2}^{2} \times{3}^{2}\times5.$

The greatest common factor is the product of the least degree of each common factor.

$GCF={2}^{2}\times5$

GCF=20

The correct answer is A.

QUESTION 5.

We want to find the greatest common factor of

$15,30\: and\:60.$

We need to first find the prime factorization of each number.

The prime factorization of 15 is

$15=3\times5.$

The prime factorization of 30 is

$30=2\times 3\times 5.$

The prime factorization of 60 is

$60={2}^{2}\times3 \times5$

The greatest common factor of these three numbers is the product of the factors with the least degree that is common to them.

$GCF=3 \times5$

GCF=15

The correct answer is C.

QUESTION 6

We want to determine which of the given fractions is equivalent to

$\frac{3}{8}.$

We must therefore simplify each option,

$A.\: \: \frac{15}{32}=\frac{15}{32}$

$B.\:\:\frac{12}{32}=\frac{4\times 3}{4\times8}=\frac{3}{8}$

$C.\:\:\:\:\frac{12}{24}=\frac{12\times1}{12\times 2}=\frac{1}{2}$

$D.\:\:\frac{9}{32}=\frac{9}{32}$

The simplification shows that

$\frac{12}{32}\equiv \frac{3}{8}$

The correct answer is B.

QUESTION 7.

We want to express

$\frac{10}{22}$

in the simplest form.

We just have to cancel out common factors as follows.

$\frac{10}{22}=\frac{2\times5}{2 \times11}$

This simplifies to,

$\frac{10}{22}=\frac{5}{11}$

The correct answer is C.

QUESTION 8.

We were given that Justin visited of the states.

The question requires that we express as a fraction of 50.

This will give us

$\frac{25}{50}=\frac{25\times1}{25\times2}$

We must cancel out the common factors to have our fraction in the simplest form.

$\frac{25}{50}=\frac{1}{2}$

The correct answer is C.

QUESTION 9.

We want to write

$2\frac{5}{8}$

as an improper fraction.

We need to multiply the 2 by the denominator which is 8 and add the product to 5 and then express the result over 8.

This gives us,

$2 \frac{5}{8}=\frac{2\times8+5}{8}$

this implies that,

$2\frac{5}{8}=\frac{16+5}{8}$

$2\frac{5}{8}=\frac{21}{8}$

Sarah needed

$\frac{21}{8}\:\:yards$

The correct answer is D.

QUESTION 10

See attachment

QUESTION 11

We wan to write

$3\: and\:\:\frac{7}{8}$

as an improper fraction.

This implies that,

$3+\frac{7}{8}=3\frac{7}{8}$

To write this as a mixed number, we have,

$3\frac{7}{8}=\frac{3\times8+7}{8}$

This implies that,

$3\frac{7}{8}=\frac{24+7}{8}$

This gives

$3\frac{7}{8}=\frac{31}{8}$

The correct answer is B.

QUESTION 12

We want to find the LCM of and using prime factorization.

The prime factorization of 30 is $30=2\times 3\times 5$

The prime factorization of 46 is $40=2\times 23$ .

The LCM is the product of the common factors with the highest degrees. This gives us,

$LCM=2\times \times3 5\times 23$

LCM=690

The correct answer is D.

QUESTION 13

We want to find the least common multiple of 3,6 and 7.

The prime factorization of is .

The prime factorization of 6 is $6=2\times 3$ .

The prime factorization of 7 is .

The LCM is the product of the common factors with the highest degrees. This gives us,

$LCM=2\times3 \times7$

LCM=42 .

The LCM is 42, therefore 42 days will pass before all three bikes will at the park on the same day again.

The correct answer is B.

See attachment for continuation.

1. find the digit that makes 3,71_ divisible by 9. a. 3 b. 7 c. 1 d. 5 2.list all the factors of the

Mathematics

1. find the digit that makes 3,71_ divisible by 9. a. 3 b. 7 c. 1 d. 5 2.list all the factors of the number 30. a. 1, 2, 3, 5, 6, 10, 15, 30 b. 2, 3, 4, 10, 20, 30, 40 c. 1, 2, 4, 5, 10, 15, 30 d. 1, 2, 4, 5, 8, 10, 20, 40 3. find the prime factorization of the number 168. a. 24 x 3 x 7 b. 23 x 3 x 7 c. 24 x 33 x 13 d. 23 x 33 x 7 4. find the gcf of the numbers 140 and 180. a. 20 b. 90 c. 30 d. 10 5. the weights of 3 bags containing footballs are 15 oz, 30 oz, and 60 oz. the greatest common factor of 15, 30, and 60 gives the weight of each ball

Step-by-step answer

P Answered by PhD

64

QUESTION 1

We want to find the digit that should fill the blank space to make

3,71-

divisible by 9.

If a number is divisible by 9 then the sum of the digits should be a multiple of 9.

The sum of the given digits is,

3 + 7 + 1 = 11

Since

11 + 7 = 18

which is a multiple of 9.

This means that

3,717

is divisible by 9.

The correct answer is B

QUESTION 2

The factors of the number 30 are all the numbers that divides 30 exactly without a remainder.

These numbers are ;

1,2,3,5,6,10,15,30

The correct answer is A.

QUESTION 3.

We want to find the prime factorization of the number 168.

The prime numbers that are factors of 168 are

$2,3 \: and \: 7$

We can write 168 as the product of these three prime numbers to obtain,

$168={2}^{3}\times 3\times7$

We can also use the factor tree as shown in the attachment to write the prime factorization of 168 as

$168 ={2}^{3}\times 3\times7$

The correct answer is B.

QUESTION 4.

We want to find the greatest common factor of

$140\:\:and\:\:180$

We need to express each of these numbers as a product of prime factors.

The prime factorization of 140 is

$140={2}^{2}\times 5\times7.$

The prime factorization of 180 is

$180={2}^{2} \times{3}^{2}\times5.$

The greatest common factor is the product of the least degree of each common factor.

$GCF={2}^{2}\times5$

GCF=20

The correct answer is A.

QUESTION 5.

We want to find the greatest common factor of

$15,30\: and\:60.$

We need to first find the prime factorization of each number.

The prime factorization of 15 is

$15=3\times5.$

The prime factorization of 30 is

$30=2\times 3\times 5.$

The prime factorization of 60 is

$60={2}^{2}\times3 \times5$

The greatest common factor of these three numbers is the product of the factors with the least degree that is common to them.

$GCF=3 \times5$

GCF=15

The correct answer is C.

QUESTION 6

We want to determine which of the given fractions is equivalent to

$\frac{3}{8}.$

We must therefore simplify each option,

$A.\: \: \frac{15}{32}=\frac{15}{32}$

$B.\:\:\frac{12}{32}=\frac{4\times 3}{4\times8}=\frac{3}{8}$

$C.\:\:\:\:\frac{12}{24}=\frac{12\times1}{12\times 2}=\frac{1}{2}$

$D.\:\:\frac{9}{32}=\frac{9}{32}$

The simplification shows that

$\frac{12}{32}\equiv \frac{3}{8}$

The correct answer is B.

QUESTION 7.

We want to express

$\frac{10}{22}$

in the simplest form.

We just have to cancel out common factors as follows.

$\frac{10}{22}=\frac{2\times5}{2 \times11}$

This simplifies to,

$\frac{10}{22}=\frac{5}{11}$

The correct answer is C.

QUESTION 8.

We were given that Justin visited of the states.

The question requires that we express as a fraction of 50.

This will give us

$\frac{25}{50}=\frac{25\times1}{25\times2}$

We must cancel out the common factors to have our fraction in the simplest form.

$\frac{25}{50}=\frac{1}{2}$

The correct answer is C.

QUESTION 9.

We want to write

$2\frac{5}{8}$

as an improper fraction.

We need to multiply the 2 by the denominator which is 8 and add the product to 5 and then express the result over 8.

This gives us,

$2 \frac{5}{8}=\frac{2\times8+5}{8}$

this implies that,

$2\frac{5}{8}=\frac{16+5}{8}$

$2\frac{5}{8}=\frac{21}{8}$

Sarah needed

$\frac{21}{8}\:\:yards$

The correct answer is D.

QUESTION 10

See attachment

QUESTION 11

We wan to write

$3\: and\:\:\frac{7}{8}$

as an improper fraction.

This implies that,

$3+\frac{7}{8}=3\frac{7}{8}$

To write this as a mixed number, we have,

$3\frac{7}{8}=\frac{3\times8+7}{8}$

This implies that,

$3\frac{7}{8}=\frac{24+7}{8}$

This gives

$3\frac{7}{8}=\frac{31}{8}$

The correct answer is B.

QUESTION 12

We want to find the LCM of and using prime factorization.

The prime factorization of 30 is $30=2\times 3\times 5$

The prime factorization of 46 is $40=2\times 23$ .

The LCM is the product of the common factors with the highest degrees. This gives us,

$LCM=2\times \times3 5\times 23$

LCM=690

The correct answer is D.

QUESTION 13

We want to find the least common multiple of 3,6 and 7.

The prime factorization of is .

The prime factorization of 6 is $6=2\times 3$ .

The prime factorization of 7 is .

The LCM is the product of the common factors with the highest degrees. This gives us,

$LCM=2\times3 \times7$

LCM=42 .

The LCM is 42, therefore 42 days will pass before all three bikes will at the park on the same day again.

The correct answer is B.

See attachment for continuation.

Mathematics

1.what’s the least common multiple (lcm) for each group of numbers? a. 6 and 15 b. 4 and 11 c. 6, 9, and 12 d. 8, 10, and 20 2.what’s the least common denominator (lcd) for each group of fractions? a. 1⁄6 and 7⁄8 b. 3⁄4 and 7⁄10 c. 7⁄12, 3⁄8 and 11⁄36 d. 8⁄15, 11⁄30 and 3⁄5 3.insert the “equal” sign or the “not equal” sign ( = or ≠) to make each statement true. a. 18/36 1/2 b. 13/15 7/10 c. 3/5 5/9 d. 3/8 10/16 4.on a hot summer day, john drank 5⁄11 of a quart of iced tea; gary drank 7⁄10 of a quart; and carter drank 3⁄5 of a quart. which man was

Step-by-step answer

P Answered by PhD

7

c. 27⁄90

d. 63⁄77

e. 24⁄32

f. 73⁄365

7.What is the next fraction in each of the following patterns?

a. 1⁄40, 4⁄40, 9⁄40, 16⁄40, 25⁄40 . . .?

b. 3⁄101, 4⁄101, 7⁄101, 11⁄101, 18⁄101, 29⁄101. . .?

c. 5⁄1, 10⁄2, 9⁄2, 18⁄4, 17⁄8, 34⁄32, 33⁄256. . .?

8.In each pair, tell if the fractions are equal by using cross multiplication.

a. 5⁄30 and 1⁄6

b. 4⁄12 and 21⁄60

c. 17⁄34 and 41⁄82

d. 6⁄9 and 25⁄36

1.

a. 30

b. 44

c. 36

d. 40

2.

a. 24

b. 20

c. 4

d. 5

3.

a. =

b. not =

c. not =

d. not =

4. Gary

5.

a. 5/6

b. 5/12

c. 19/45

d. 13/14

e. 7/11

f. 1/2

6.

a. 2/3

b. 8/9

c. 3/10

d. 9/11

e. 3/4

f. 1/5

7.

a. 36/40

b.

c.

8.

a. yes

b. no

c. no

d. no

9. no

10. yes

11.

a. 40

b. 48

c. 77

d. 48

12. 4,620

Step-by-step explanation:

Mathematics

What’s the least common multiple (LCM) for each group of numbers? a. 6 and 15 b. 4 and 11 c. 6, 9, and 12 d. 8, 10, and 20 What’s the least common denominator (LCD) for each group of fractions? a. 1⁄6 and 7⁄8 b. 3⁄4 and 7⁄10 c. 7⁄12, 3⁄8, and 11⁄36 d. 8⁄15, 11⁄30, and 3⁄5 Insert the “equal” sign or the “not equal” sign (= or ≠) to make each statement true. a. 18/36 1/2 b. 13/15 7/10 c. 3/5 5/9 d. 3/8 10/16 On a hot summer day, John drank 5⁄11 of a quart of iced tea; Gary drank 7⁄10 of a quart; and Carter drank 3⁄5 of a quart. Which man was the

Step-by-step answer

P Answered by Master

A, C, =, $\neq \\$ , $\neq$ , $\neq$ , A,

Step-by-step explanation:

Mathematics

1.what’s the least common multiple (lcm) for each group of numbers? a. 6 and 15 b. 4 and 11 c. 6, 9, and 12 d. 8, 10, and 20 2.what’s the least common denominator (lcd) for each group of fractions? a. 1⁄6 and 7⁄8 b. 3⁄4 and 7⁄10 c. 7⁄12, 3⁄8 and 11⁄36 d. 8⁄15, 11⁄30 and 3⁄5 3.insert the “equal” sign or the “not equal” sign ( = or ≠) to make each statement true. a. 18/36 1/2 b. 13/15 7/10 c. 3/5 5/9 d. 3/8 10/16 4.on a hot summer day, john drank 5⁄11 of a quart of iced tea; gary drank 7⁄10 of a quart; and carter drank 3⁄5 of a quart. which man was

Step-by-step answer

P Answered by PhD

7

c. 27⁄90

d. 63⁄77

e. 24⁄32

f. 73⁄365

7.What is the next fraction in each of the following patterns?

a. 1⁄40, 4⁄40, 9⁄40, 16⁄40, 25⁄40 . . .?

b. 3⁄101, 4⁄101, 7⁄101, 11⁄101, 18⁄101, 29⁄101. . .?

c. 5⁄1, 10⁄2, 9⁄2, 18⁄4, 17⁄8, 34⁄32, 33⁄256. . .?

8.In each pair, tell if the fractions are equal by using cross multiplication.

a. 5⁄30 and 1⁄6

b. 4⁄12 and 21⁄60

c. 17⁄34 and 41⁄82

d. 6⁄9 and 25⁄36

1.

a. 30

b. 44

c. 36

d. 40

2.

a. 24

b. 20

c. 4

d. 5

3.

a. =

b. not =

c. not =

d. not =

4. Gary

5.

a. 5/6

b. 5/12

c. 19/45

d. 13/14

e. 7/11

f. 1/2

6.

a. 2/3

b. 8/9

c. 3/10

d. 9/11

e. 3/4

f. 1/5

7.

a. 36/40

b.

c.

8.

a. yes

b. no

c. no

d. no

9. no

10. yes

11.

a. 40

b. 48

c. 77

d. 48

12. 4,620

Step-by-step explanation:

Mathematics

(07.02 mc) what is the value of y in the equation 2(2y − 12) = 0? (5 points) 4 6 7 8 4. (07.03 lc) how many solutions does the equation 6z − 3z − 7 = −2 + 3 have? (5 points) two none infinitely many one 5. (07.03 lc) the steps below show the incomplete solution to find the value of y for the equation 4y − 2y − 4 = −1 + 13: step 1: 4y − 2y − 4 = −1 + 13 step 2: 4y − 2y − 4 = 12 step 3: 2y − 4 = 12 which of these is most likely the next step? (5 points) 2y = 3 2y = 8 2y = 16 2y = 18 6. (07.03 mc) what is the value of z in the equation 2(4z − 3 −

Step-by-step answer

P Answered by Specialist

14

Y=6 In this equation you also use combine like terms .

Mathematics

(07.02 mc) what is the value of y in the equation 2(2y − 12) = 0? (5 points) 4 6 7 8 4. (07.03 lc) how many solutions does the equation 6z − 3z − 7 = −2 + 3 have? (5 points) two none infinitely many one 5. (07.03 lc) the steps below show the incomplete solution to find the value of y for the equation 4y − 2y − 4 = −1 + 13: step 1: 4y − 2y − 4 = −1 + 13 step 2: 4y − 2y − 4 = 12 step 3: 2y − 4 = 12 which of these is most likely the next step? (5 points) 2y = 3 2y = 8 2y = 16 2y = 18 6. (07.03 mc) what is the value of z in the equation 2(4z − 3 −

Step-by-step answer

P Answered by Specialist

14

Y=6 In this equation you also use combine like terms .

Mathematics

EXAMPLE 2 Find a formula for the general term of the sequence 3 5 , − 4 25 , 5 125 , − 6 625 , 7 3125 , assuming that the pattern of the first few terms continues. SOLUTION We are given that a1 = 3 5 a2 = − 4 25 a3 = 5 125 a4 = − 6 625 a5 = 7 3125 . Notice that the numerators of these fractions start with 3 and increase by 1 Correct: Your answer is correct. whenever we go to the next term. The second term has numerator 4, the third term has numerator 5; in general, the nth term will have numerator Incorrect: Your answer is incorrect. . The denominators

Step-by-step answer

P Answered by PhD

The given terms can be written in the generalized format as

$\rm a_n=\dfrac{(2n+1)(-1)^{n+1}}{5^n}$ and this can be done by observing the given terms.

Given :

General Terms --

$\rm a_1 = \dfrac{3}{5}$ $\rm a_2 = -\dfrac{4}{25}$ $\rm a_3 = \dfrac{5}{125}$ $\rm a_4 = -\dfrac{6}{625}$ $\rm a_5 = \dfrac{7}{3125}$

The term $\rm a_2$ can be written as:

$\rm a_2 = \dfrac{4}{5^2}$

The term $\rm a_3$ can be written as:

$\rm a_3 =\dfrac{5}{5^3}$

The term $\rm a_4$ can be written as:

$\rm a_4 =\dfrac{6}{5^4}$

The term $\rm a_5$ can be written as:

$\rm a_5 =\dfrac{7}{5^5}$

So, the above terms can be written in the generalized format as:

$\rm a_n=\dfrac{(2n+1)(-1)^{n+1}}{5^n}$

For more information, refer to the link given below:

link

Mathematics

90 p Step 1: Calculating with rational numbers in real-world contexts In the first event, the eighth graders are running a baton relay race with three other classmates. The team’s top speed for each leg is 56.81 seconds, 59.22 seconds, 57.39 seconds, and 60.11 seconds. Use the information to predict the team’s best time for the race. (2 points) If the team’s best time for the race is less than 4 minutes, then the eighth graders earn 40 points. If not, the seventh graders earn 40 points. Which grade should be awarded 40 points? Each leg of the race

Step-by-step answer

P Answered by Master

5

1 - The sum of best times for the legs is 56.81 +59.22 +57.39 +60.11 = 233.53 seconds (3.89 minutes). Without additional information about the effects of training or the normal variation in times, this is the best prediction we can make.

2 - Since the team’s best time for the race is less than 4 minutes, the eighth graders earn 40 points.

3- 58.3825 (About 58) Average is found by adding all the data up and dividing by the amount of info there is. In this Case: 233.53 divided by 4 = 58.3825 which is around 58.

4- The seventh graders because the eighth graders got 58 which is more than 50 so the 7th grader would get the points

5- Kate’s best friend jumped 8/21 feet more than Kate did. First to find the difference between two fractions they need a common denominator, 21 works for this. Then the actual fractions need to match the denominator. 7/21 and 15/21 are our new fractions. Then when subtraction you subtract the numerators, the answer to that is 8/21 after simplifying (in this case you cant) you subtract the whole numbers, 6 – 6 = 0 the add the whole and fraction together. Kate’s best friend jumped 8/21 more feet than Kate did.

6- The seventh graders.

7- 42 5/8 + 39 3/5 Find common denominator for the fractions and rewrite them using the common denominator: 5/8 = 25/40 3/5 = 24/40 25/40 + 24/40 = 49/40 = 1 9/40 1 9/40 + 42 + 39 = 82 9/40 feet.

8- 9/40 = 0.225, plus 82 feet = 82.225 feet, this is less than 82.5, so the 8th graders earned the 50 points.

9- The equation would be the total of completed jumps divided by the total number of attempts: (2 +4 + 1) / (3 + 6 +4) = 7/13 = 0.538 average.

10- 0.538 is greater than 1/2 ( 0.50), so the 8th graders earned 50 points.

11- The race is 111.6 m long. 8 hurdles spaced 12.3 m apart means 7 spaces that are 12.3 m in length; 7*12.3 = 86.1

Step-by-step explanation:

Would love brainliest

Mathematics

90 p Step 1: Calculating with rational numbers in real-world contexts In the first event, the eighth graders are running a baton relay race with three other classmates. The team’s top speed for each leg is 56.81 seconds, 59.22 seconds, 57.39 seconds, and 60.11 seconds. Use the information to predict the team’s best time for the race. (2 points) If the team’s best time for the race is less than 4 minutes, then the eighth graders earn 40 points. If not, the seventh graders earn 40 points. Which grade should be awarded 40 points? Each leg of the race

Step-by-step answer

P Answered by Specialist

5

1 - The sum of best times for the legs is 56.81 +59.22 +57.39 +60.11 = 233.53 seconds (3.89 minutes). Without additional information about the effects of training or the normal variation in times, this is the best prediction we can make.

2 - Since the team’s best time for the race is less than 4 minutes, the eighth graders earn 40 points.

3- 58.3825 (About 58) Average is found by adding all the data up and dividing by the amount of info there is. In this Case: 233.53 divided by 4 = 58.3825 which is around 58.

4- The seventh graders because the eighth graders got 58 which is more than 50 so the 7th grader would get the points

5- Kate’s best friend jumped 8/21 feet more than Kate did. First to find the difference between two fractions they need a common denominator, 21 works for this. Then the actual fractions need to match the denominator. 7/21 and 15/21 are our new fractions. Then when subtraction you subtract the numerators, the answer to that is 8/21 after simplifying (in this case you cant) you subtract the whole numbers, 6 – 6 = 0 the add the whole and fraction together. Kate’s best friend jumped 8/21 more feet than Kate did.

6- The seventh graders.

7- 42 5/8 + 39 3/5 Find common denominator for the fractions and rewrite them using the common denominator: 5/8 = 25/40 3/5 = 24/40 25/40 + 24/40 = 49/40 = 1 9/40 1 9/40 + 42 + 39 = 82 9/40 feet.

8- 9/40 = 0.225, plus 82 feet = 82.225 feet, this is less than 82.5, so the 8th graders earned the 50 points.

9- The equation would be the total of completed jumps divided by the total number of attempts: (2 +4 + 1) / (3 + 6 +4) = 7/13 = 0.538 average.

10- 0.538 is greater than 1/2 ( 0.50), so the 8th graders earned 50 points.

11- The race is 111.6 m long. 8 hurdles spaced 12.3 m apart means 7 spaces that are 12.3 m in length; 7*12.3 = 86.1

Step-by-step explanation:

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7/12 1/2 5/12 1/3 what is the next fraction in this sequence

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