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arlik [135]
2 years ago
10

Four members from a ​"55"person committee are to be selected randomly to serve as​ chairperson, vice-chairperson,​ secretary, an

d treasurer. The first person selected is the​ chairperson; the​ second, the​ vice-chairperson; the​ third, the​ secretary; and the​ fourth, the treasurer. How many different leadership structures are​ possible?
Mathematics
1 answer:
liq [111]2 years ago
3 0

Answer:

8,185,320 different leadership structures

Step-by-step explanation:

Since the order at which the members of the committee are chosen matters, this is a permutation of 4 out 55 people and it is given by:

n=\frac{55!}{(55-4)!}=55*54*53*52 \\\\n=8,185,320

8,185,320 different leadership structures are​ possible.

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A restaurant sells about 330 sandwiches each day at a price of $6 each $.25 decrease in price. 15 more sandwiches are sold per d
zmey [24]

Answer:

restaurant should charge $(6-0.25) = $5.75per sandwich to maximize daily revenue.

the revenue is $1983.75

Step-by-step explanation:

to calculate current revenue= $6 x 330 = $1980

suppose x as the number of times the price to be dropped by $0.25

then find new price.. i.e

new price= $(6-0.25x)

and, new sell=330 +15x sandwiches

therefore, the new revenue would be= (6-0.25x)(330 +15x)

in order to maximize the current revenue, simplify the above equation and make it complete square using x

(6-0.25x)(330 +15x)

=1980-82.5x +90x -3.75x^{2}

=1980 + 7.5x -3.75x^{2}

=1980-3.75 (-2x+x^{2}) ----> taking out common

now, to make a complete square lets add and subtract 1 inside the parentheses

=1980-3.75(-1+1-2x+x^{2})

=1980 +3.75 -3.75(x^{2} -2x +1)

=1983.75 -3.75 (x-1)^{2}---->(1)

as (x-1)^{2} is positive always, minimize the other term in order to maximize the total revenue.

so the minimum possible value of (x-1)^{2} = 0

therefore, x=1

putting x in eq(1) the revenure becomes,

$(1983.75-0)=> $1983.75

therefore, restaurant should charge $(6-0.25) = $5.75per sandwich to maximize daily revenue.

the revenue is $1983.75

3 0
3 years ago
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kiruha [24]
The statement is false.
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The answers are 5 x (80 x 7) and 80 fives plus 7 fives
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2 years ago
Nathaniel has $2 worth of dimes and quarters. He has 6 more dimes than quarters. By following the steps below, determine the num
Aleksandr-060686 [28]

Answer:

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Step-by-step explanation:

  • Number of dimes = d, each d = 10 c
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<u>Equations according the given:</u>

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<u>Solve for q by substitution:</u>

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<u>Find the value of d:</u>

  • d = 4 + 6 = 10

Nathaniel has 10 dimes and 4 quarters

8 0
3 years ago
You are graphing Rectangle ABCDABCDA, B, C, D in the coordinate plane. The following are three of the vertices of the rectangle:
emmainna [20.7K]

Answer:

Rectangle ABCDABCDA, B, C, D is graphed in the coordinate plane. vertices of the rectangle: A(-1, -6),A(−1,−6),A, left parenthesis, minus, 1, comma, minus, 24+2 ps y+4 sr y+5 qR 2x + 3 pq 2y+2.

Step-by-step explanation:

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