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shusha [124]
3 years ago
13

There is money to send four of nine city council members to a conference in Honolulu. All want to go, so they decide to choose t

he members to go to the conference by a random process. How many different combinations of four council members can be selected from the nine who want to go to the conference
Mathematics
1 answer:
FrozenT [24]3 years ago
7 0

Answer:

126

Step-by-step explanation:

There are 9 city council members.

We have to choose 4 of them.

We have to use the combination as :

$^9C_4$

where, 9 is the population size

4 is the sample size.

Therefore, the total number of possible samples without replacement is given as :

$^9C_4=\frac{9!}{4!(9-4)!}$

      $=\frac{9!}{5! \ 4!}$

     $=\frac{9 \times 8 \times 7 \times 6}{4 \times 3 \times 2 \times 1}$

    = 126

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A rectangle's width is twice as long as its length. If the perimeter is 36 in., what is the length?
Bumek [7]
Okay here: 

Let L be the length and W the width of the rectangle. 

1. w=2•L
2. 2L+2W=36

Substitute eq. 1 into eq. 2, 

2L+2•(2•L)=36

2L+4L=36

6L=36

L=9

Not done yet, then from eq. 1, 
 
W=2•L
W=2•9
W=18 <------- Your answer. :)
6 0
3 years ago
Fourth Quarter
Nina [5.8K]

Answer:

A.

Step-by-step explanation:

playing in the garden

7 0
3 years ago
A farmer has 520 feet of fencing to construct a rectangular pen up against the straight side of a barn, using the barn for one s
Setler [38]

Answer:

310\text{ feet and }210\text{ feet}

Step-by-step explanation:

GIVEN: A farmer has 520 \text{ feet} of fencing to construct a rectangular pen up against the straight side of a barn, using the barn for one side of the pen. The length of the barn is 310 \text{ feet}.

TO FIND: Determine the dimensions of the rectangle of maximum area that can be enclosed under these conditions.

SOLUTION:

Let the length of rectangle be x and y

perimeter of rectangular pen =2(x+y)=520\text{ feet}

                                                x+y=260

                                               y=260-x

area of rectangular pen =\text{length}\times\text{width}

                                       =xy

putting value of y

=x(260-x)

=260x-x^2

to maximize \frac{d \text{(area)}}{dx}=0

260-2x=0

x=130\text{ feet}

y=390\text{ feet}

but the dimensions must be lesser or equal to than that of barn.

therefore maximum length rectangular pen =310\text{ feet}

                              width of rectangular pen =210\text{ feet}

Maximum area of rectangular pen =310\times210=65100\text{ feet}^2

Hence maximum area of rectangular pen is 65100\text{ feet}^2 and dimensions are 310\text{ feet and }210\text{ feet}

5 0
3 years ago
tres hermanos danvueltas circuito en bicicleta. el mayor tarda 18 en dar Una vuelta el del medio 24 minutos yel menos 36 minutos
hodyreva [135]
Tienes que hallar el mínimo común múltiplo de las 3 cantidades.

18= 2×3²
24= 2³×3
36= 2²×3²

mcm(18,24,36) = 2³×3²=8×9= 72

Eso quier decir que si partieron a la misma hora se encontraran  de nuevo en el punto de partida 72 minutos después de la salida.

Las vueltas que habrán realizado será el resultado de dividir 72 entre el tiempo que tardan en dar una vuelta

<span>Mayor: </span>  = 4

<span>Mediano: </span>  = 3

<span>Pequeño: </span>  =  2

Soluciónes:

se vuelven a encontrar a los 72 min de la salida
<span>El mayor dió 4 vueltas, el mediano 3 y el pequeño 2</span>
6 0
3 years ago
Need help with this one, please only serious people answer or I’ll report your answer
frutty [35]
Vertical shift is -2. Horizontal shift is 1. Check the box that says reflect over x-axis. Horizontal shrink should be 4. Then to check if it looks right go to Desmos.com and in the graphing calculator put in y=-4(x-1)^2-2 and see if it looks like the one you did in your work
3 0
3 years ago
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