Mathematics Middle School

Three research departments have 8 ,10 , and 7 members, respectively. Each department is to select a delegate and an alternate to represent the department at a conference. In how many ways can this be done?

Answers

Answer 1

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

Answer 2

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.

Related Questions

Help ASAP pls -screenshot-

Answers

Number 1 is .6 (60 in total and 40 are not red so 30/50=.6)

Number 2 is 40% because 8/20=0.4

I’m almost 100% sure this is right but i could be wrong

The answers to the questions should be
1. 0.6
2. 40%

Pls help! Will give brainliest!!

Answers

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

I need help ASAP -screenshot-

Answers

Answer:

3.A

4. 3

Step-by-step explanation:

4 15x20=300/100=3

3.72% vs 75%

Answer:
3. (A)
4. (A)
Explanation:
I used critical thinking and it was easy.

Graph the equation y= -x^2 +10x-21 on the accompanying set of axes. You must plot 5 points including the roots and vertex. Using the graph, determine the vertex of the parabola

Answers

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)

Someone help with this one too :(

Answers

Answer :it is the cone and sphere

Look back in the question and look back in math notes

Answer:

1= 4th shape , 2= 3rd shape

Step-by-step explanation:

You answer, you win 100 points

Answers

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.

__________________________________________________________

Which is the correct answer

Answers

Answer:

The mode is equal to the minimum

Is the correct answer

Step-by-step explanation:

In this case,

Mean = (52+48+48+54+50)/5

Mean = 50.4

The Median = 50,(the middle value)

Mode = 48 (the value that appears most often)

Now, the minimum value(smallest value) of the data set is 48

so,

The mode is equal to the minimum

Answer: the mode is equal to the minimum

Step-by-step explanation:

Can someone help me with this question!!

Answers

The answer I got is somehow 5

Answer:

Step-by-step explanation:

area = bh/2

32.4 yd² = 8.1 yd × s / 2

s = 8 yd

Please help with this question please.

Answers

M < 7 is the answer because if m was equal to seven the equation would be 19 > 19 which cannot be correct so m must be less than 7

Option d. m>7 is the correct answer.

Given,

2m+5>19

or, 2m+5+(-5)>19+(-5) [adding both side with a negative number doesn't

change the inequality sign]

or, 2m>14

or, (2m/2)>(14/2) [also dividing both sides by a non-negative number doesn't change the inequality sign]

or, m>7.

Hence, m>7 is the correct answer to the given question.

Learn more about inequality problems,

brainly.com/question/33962875

Pls help :D screenshot

Answers

First one is C and the second one is A (not sure tho)

The first one is c and I don’t know the second one

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?

Answers

C(7, 4) = 7! / (4!(7-4)!) = (7 * 6 * 5) / (3 * 2 * 1) = 35

and

C(13, 5) = 13! / (5!(13-5)!) = (13 * 12 * 11 * 10 * 9) / (5 * 4 * 3 * 2 * 1) = 1287

Multiply these two combinations since the faculty members and students are selected independently:

Total number of ways to form the committee = C(7, 4) * C(13, 5) = 35 * 1287 = 45,045

Therefore, there are 45,045 ways to form the committee consisting of 4 faculty members and 5 students.

To determine the number of ways to form the committee with 4 faculty members and 5 students, we need to calculate the combinations of faculty members and students separately and then multiply them together.

For faculty members:
There are 7 eligible faculty members, and we need to select 4 of them for the committee. This can be done using the combination formula:

C(7, 4) = 7! / (4!(7 - 4)!) = 35.

So, there are 35 ways to select 4 faculty members from the 7 eligible ones.

For students:
There are 13 eligible students, and we need to select 5 of them for the committee. Using the combination formula again:

C(13, 5) = 13! / (5!(13 - 5)!) = 1287.

Therefore, there are 1287 ways to select 5 students from the 13 eligible ones.

To form the committee, we multiply the number of ways to select faculty members by the number of ways to select students:

35 * 1287 = 44,895.

Hence, there are 44,895 ways to form the committee consisting of 4 faculty members and 5 students from the eligible candidates.

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