a committee consisting of 4 faculty members and 5 students is to be formed. every committee position has the same duties and voting rights. there are 7 faculty members and 13 students eligible to serve on the committee. in how many ways can the committee be formed?

We can conclude that exists 211680 ways.

How many ways can this be done?

We know that the three research department is have 8, 10, and 7 members.

We choose a delegate and an alternate to represent the department.

First case: department have 8 members.

So, for a delegate, we have 8 options, and for a alternate 7, so a total of

[tex]8 \times 7 = 56 \ \text{options}[/tex]

Second case: department have 10 members.

So, for a delegate, we have 10 options, and for a alternate 9, so a total of

[tex]10\times 9 =90 \ \text{options}[/tex]

Third case: department have 7 members.

So, for a delegate, we have 7 options, and for a alternate 6, so a total of

[tex]7\times6 = 42 \ \text{options}[/tex]

Therefore, we get:

[tex]56 \times 90 \times 42 = \bold{211680}[/tex]

Hence, we conclude that exists 211680 ways.

For a similar problem about this, please click the link below:

https://brainly.com/question/30958797

To determine the number of ways to select a delegate and an alternate from each department, we can multiply the number of choices for each department together.

For the first department with 8 members, there are 8 choices for selecting a delegate. After choosing a delegate, there remain 7 members, so there are 7 choices for selecting an alternate. Therefore, there are 8 × 7 = 56 ways to select a delegate and an alternate from the first department.

Similarly, for the second department with 10 members, there are 10 choices for selecting a delegate and 9 choices for selecting an alternate. Hence, there are 10 × 9 = 90 ways to select a delegate and an alternate from the second department.

For the third department with 7 members, there are 7 choices for selecting a delegate and 6 choices for selecting an alternate. Thus, there are 7 × 6 = 42 ways to select a delegate and an alternate from the third department.

To find the total number of ways to select delegates and alternates from all three departments, we multiply the number of choices for each department together:
56 × 90 × 42 = 211,680.

Therefore, there are 211,680 ways to select a delegate and an alternate from each department.

Considering area (A) of garden as 30 square feet:

30 = x(2x+7)

Now we need to expand it:

x(2x+7) = 2x^2 + 7x

2x^2 + 7x = 30

Adding this into an Algebra calculator gives us 5/2 or 2.5

So x = 2.5

To prove this:

2(2.5) + 7 = 12

14 * 2.5 = 30

Since the area is equal to length times width, and you know your area has to be 30, you can plug in your values like this:

(2x+7) x = 30

you can distribute to make this easier

2x^2 + 7x = 30

you can plug this into quadratic formula by setting the equation =0, so:

2x^2 +7x -30 = 0

where 2x^2 = a
7x = b
and -30 = c

you can plug this into your calculator and get an answer of

X = 2.5

Answer:

[tex]13.5 m^{2}[/tex]

Step-by-step explanation:

area = length × width

       = 15m  × 9/10m

       = 15m  ×  0.9m

       = [tex]13.5 m^{2}[/tex]

Answer:

[tex]\Huge \fbox{Area = 13.5 m^{2}$}[/tex]

Step-by-step explanation:

To find the area of the baseboard, we need to multiply the length by the width:

The length of the baseboard is given as 15 metres. The width of the baseboard is given as [tex]\frac{9}{10}[/tex] metre.

To multiply these values, we can convert the width to a decimal by dividing the numerator (9) by the denominator (10):

[tex]\frac{9}{10} = 0.9[/tex]

Now we can multiply the length and width:

[tex]\text{Area = Length $\times$ Width}[/tex][tex]\text{Area = 15 m $\times$ 0.9 m}[/tex][tex]\text{Area = 13.5 m^{2}$}[/tex]

Therefore, the area of the baseboard is 13.5 m².

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The answer I got is somehow 5

Answer:

8

Step-by-step explanation:

area = bh/2

32.4 yd² = 8.1 yd × s / 2

s = 8 yd

Answer:

The properties of the parabola equation are

Vertex = (-5, -4)

Roots = (-7, 0) and (-3, 0)

Points = (-2, 5) and (-4, -3)

What are parabola equations?

Parabola equations are second-order polynomial equations and they have the form y = ax^2 + bx + c or y = a(x - h)^2 + k

How to plot the graph of the parabola?

The equation is given as

y = x^2 + 10x + 21

Next, we plot the graph on the coordinate plane

On the graph, we can see the following properties

Vertex = (-5, -4)

Roots = (-7, 0) and (-3, 0)

Points = (-2, 5) and (-4, -3)

Step-by-step explanation:

https://brainly.com/question/28729977

Answer:

Step-by-step explanation:

Vertex = (-5, -4)

Roots = (-7, 0) and (-3, 0)

Points = (-2, 5) and (-4, -3)