What is the coefficient of x^2y^3 in the expansion of (2x+y)^5

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Answer 1

Answer:

Answer:

Step-by-step explanation:

A P E X

Answer 2

Answer: We figure out the coefficient of x^2y^3 by figuring out the coefficients in both (x+y)^4 and (x+2y)^4.

Using the binomial theorem, the coefficient of x^2y^3 on the first expansion is

(4 choose 3)x^2y^3=6x^2y^3,

and the coefficient of x^2y^3 on the second expansion is

(4 choose 3)x^2(2y)^3=6x^2(4y^2)=24x^2y^3.

Thus, the coefficient in the sum of these two expansions is 6+24=30.

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Which measurement is most accurate to describe the amount of water a teaspoon could hold?5 mL
3 L
25 mL
0.3 L

Answers

5 mL. 1 (US)teaspoon = 4.92892 mL

Answer:

5ml

hope that helps

Step-by-step explanation:

Translate the variable expression into a word phrase. k + 8

A.
the sum of a number and eight

B.
the product of a number and eight

C.
the quotient of a number and eight

D.
the difference of a number and eight

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A you are adding 8 and an unknown number

A catering service offers 12 appetizers, 9 main courses, and 7 desserts. A banquet chairperson is to select 8 appetizers, 8 main courses, and 6 desserts for a banquet. In how many ways can this be done?

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$12-appetizers, \ 9- main\ courses, \ 7\ desserts\n \n selection:\ 8\ appetizers,\ 8\ main\ courses, 6\ desserts\n\na=the\ number\ of\ selection\ of\ appetizers:\n \n{12 \choose 8}= (12!)/(8!\cdot (12-8)!) = (12\cdot11\cdot10\cdot9\cdot8!)/(8!\cdot4\cdot3\cdot2) =11\cdot5\cdot9=495\n \nc=the\ number\ of\ selection\ of\ main\ courses:\n \n{9 \choose 8}= (9!)/(8!\cdot (9-8)!) = (9\cdot8!)/(8!\cdot 1) =9$

$d=the\ number\ of\ selection\ of\ desserts:\n \n{7 \choose 6}= (7!)/(6!\cdot (7-6)!) = (7\cdot6!)/(6!\cdot 1) =7\n \nthe\ number\ of\ selection\ sets\ the\ banquet:\n \na\cdot c\cdot d=495\cdot9\cdot7=31185$

[(12! / (8!*4!) ]* [9! / (8!*1!) ] * [ 7!/ (6!*1!)] = ( 12 * 11 * 10 * 9 / 4 * 3 * 2 * 1) * 9 * 7 = 45 * 11 * 9 * 7 = 31185 ways

What is the median of this data set? 23,37,49,15,82

Answers

Answer:37

Step-by-step explanation:

Answer:37

Step-by-step explanation: rearrange so it becomes 15, 23,37, 49,82 middle is then 37

Solve 5(g-2)+g = 6(g-4)

Answers

$5(g-2)+g = 6(g-4)$
$5g-10+g = 6g-24$
$6g-10 = 6g-24$
$6g-6g=-24+10$
$0=-14$
$0 \neq -14$

5(g-2)+g = 6(g-4)
5g-10+g = 6g-24
6g-10=6g-24
contradiction

In a queueing system, customers arrive once every 3 minutes (standard deviation=4) and services take 2 minutes (standard deviation =6.3) ( Do not round intermediate calculations . Round your answer to three decimal places) What is the average number of customers in the system? customers

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Final answer:

In a queueing system with customer arrivals every 3 minutes and service times of 2 minutes, the average number of customers in the system is calculated to be approximately 0.667

Explanation:

To calculatethe average number of customers in the system, we can use Little's Law, which states that the average number of customers in a stable queueing system is equal to the average arrival rate multiplied by the average time spent in the system.

First, we need to calculate the average arrival rate. Since customers arrive once every 3 minutes, the arrival rate is 1 customer per 3 minutes or 1/3 customers per second.

The total service time is 2 minutes, and the standard deviation is 6.3. Therefore, the average service time is 2 minutes.

Using Little's Law, we multiply the average arrival rate (1/3 customers per minute) by the average service time (2 minutes) to obtain the average number of customers in the system.

Average number of customers in the queue = (1/3) × 2 = 2/3 ≈ 0.667

What is the coefficient of x^2y^3 in the expansion of (2x+y)^5

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Final answer:

Explanation:

Read more about standard deviaton at: