How many ways are there to choose a soccer team consisting of 3 forwards, 4 midfield players, and 3 defensive players, if the players are chosen from 8 forwards, 6 midfield players and 8 defensive players?

Answers

Answer 1

Using the combination formula, it is found that there are 47,040 ways to form a soccer team.

What is the combination formula?

Each of the different groups or selections can be formed by taking some or all of a number of objects, irrespective of their arrangments is called a combination.

[tex]^mC_k = \dfrac{m!}{k! \times (m-k)!}[/tex]

A soccer team consisting of 3 forwards, 4 midfield players, and 3 defensive players, if the players are chosen from 8 forwards, 6 midfield players and 8 defensive players

Since they are independent of each other, the total number of combinations will be;

[tex]^mC_k = \dfrac{8!}{3! \times (5)!} \times \dfrac{6!}{4! \times (2)!} \times \dfrac{8!}{3! \times (5)!} \\\\^mC_k =47,040[/tex]

Hence, There are 47,040 ways to form a soccer team.

More can be learned about the combination at brainly.com/question/25821700

#SPJ1


Related Questions

ustrating the fine basic
1. Future Value or Present Value of a Single Sum
Compute the future value of $2,250 at a 17 percent annual rate for
30 years.

Answers

Answer:$249895.46

Step-by-step explanation:

Well, if 2250 dollars increase by 17% every year for 30 years, then it will be 2250*(1.17)^30

which would be $249895.46

so if you could increase money by 17% every year, 2250 dollars now will be worth a lot in 30 years!

Find the missing side of this right triangle.
X

8

16
VI?]
X =
Enter the number that belongs in the green box.

Answers

Step-by-step explanation:

the missing side is given by sqrt(16² - 8²)

hence,

the number that belongs in the green box is 192

1+ cos^4 x-sin^4 x = 2 cos² x​

Answers

[tex]\text{L.H.S}\\\\=1+ \cos^4 x - \sin^4 x\\\\=1+ (\cos^2 x)^2 - (\sin^2 x)^2\\\\=1+(\cos^2 x + \sin^2 x)(\cos^2 x- \sin^2 x)\\\\=1+1\cdot(\cos 2x)\\\\=1+\cos 2x\\\\=2\cos^2 x\\\\=\text{R.H.S}\\\\\text{Proved.}[/tex]

Which functions are one to one ? The mapping diagram or the set of ordered pairs

Answers

The functions that are one to one are the set of ordered pairs.

What are the set of ordered pairs?

It should be noted that the set of ordered pairs simply means an object that the pairs are significant.

On the other hand, a mapping diagram simply consists of two parallel columns that represents the domain and the range.

In this case, the functions that are one to one are the set of ordered pairs.

Learn more about ordered pairs on:

brainly.com/question/1208726

#SPJ1

In a class test(3+) marks are given for every correct answer and (-2) marks are given for every incorrect answer (-2) marks are given for every incorrect answer and no marks for not attempting any question. (i) Radhika scored 20 marks. If she got 12 correct answers, how many questions has she attempted incorrectly? (ii) Mohini scores -5 marks in this test, though she has got 7 correct answers.How many questions has she attempted incorrectly?

Answers

Radhika attempted 8 questions incorrectly, while Mohini attempted 13 questions incorrectly.

The number of Radhika's incorrect attempt

The given parameters are:

Correct = +3

Wrong = -2

Let the correct attempt be x and the incorrect attempt be y.

The equation that represents the total score is:

Total = 3x - 2y

She scored a total of 20.

So, we have:

3x - 2y = 20

She got 12 correctly.

So, we have:

3 * 12 - 2y = 20

Evaluate the product

36 - 2y = 20

Subtract 36 from both sides

-2y = -16

Divide by -2

y = 8

Hence, Radhika attempted 8 questions incorrectly.

The number of Mohini's incorrect attempt

In (a), we have the equation that represents the total score is:

Total = 3x - 2y

She scored a total of -5

So, we have:

3x - 2y = -5

She got 7 correctly.

So, we have:

3 * 7 - 2y = -5

Evaluate the product

21 - 2y = -5

Subtract 21 from both sides

-2y = -26

Divide by -2

y = 13

Hence, Mohini attempted 13 questions incorrectly.

Read more about linear equations at:

https://brainly.com/question/14323743

#SPJ1

Arrange the samples in order starting with the sample that gives the least variation from the expected value and ending with the sample that gives the
greatest variation.
Tiles
sample A: a sample of
10 people
sample B: a sample of
50 people
sample C: a sample of
100 people
sample D: a sample of
20 people
Sequence
C

Answers

On the basis of least variation from the expected value is:

   Sample A ⇒ Sample D ⇒ Sample B ⇒ Sample C

What is Variance?

Variance is the expectation of the squared deviation of a random variable from its population mean or sample mean.

Here, on the basis of least variation,

we had arranged the given sample as per their expected value.

Thus, On the basis of least variation from the expected value is:

   Sample A ⇒ Sample D ⇒ Sample B ⇒ Sample C

Learn more about Variance from:

https://brainly.com/question/16269880

#SPJ1

√-361 what is the answer

Answers

Answer:

19i

Step-by-step explanation:

note that [tex]\sqrt{-1}[/tex] = i

[tex]\sqrt{-361}[/tex]

= [tex]\sqrt{361(-1)}[/tex]

= [tex]\sqrt{361}[/tex] × [tex]\sqrt{-1}[/tex]

= 19 × i

= 19i

the sharks are fed three times a day. During the morning feeding, 2/15 of a ton of fish is fed. During the afternoon feeding, the weight of the fish fed will be 1/15 of a ton more than the fish fed during the morning. If the total weight of fish fed in a day is 1/2 of a ton, how much is fed during the feeding at night?

Answers

Fish fed during night  is equal to  1/6 tons

Let the weight of the fish fed at night = X tons

In the morning, the weight of the fish fed Wm = 2/15 tons.

In the afternoon, 1/15 ton more fish fed during the morning.

∴ Weight of fish fed in afternoon Wa

= 2/15 + 1/15

= 3/15 tons

Given that,

What is the total weight?

Wm + Wa + Wn = 1/2 tons

∴ 2/15 + 3/15 + Wn = 1/2

∴Wn = 1/2 - 5/15

∴ Wn = 3/6 - 2/6

∴ Wn = 1/6 tons

Fish fed during night = 1/6 tons.

To learn more about the weight visit:

https://brainly.com/question/2337612

#SPJ1

A soccer league has $6,333 to buy new soccer balls. If each ball costs $3, how many balls can the league buy?

Answers

Answer: 2,111 soccer balls

Step-by-step explanation:

         We will divide the total amount of money by the price per ball to find how many balls the league can buy.

        $6,333 / $3 = 2,111

        The league can buy 2,111 soccer balls.

ZA and B are supplementary and vertical angles. What is m<B

A.180
B.135
C.45
D.90​

Answers

Answer:  90

Reason:

Vertical angles are equal to each other. Call them x. They must add to 180 degrees because they are supplementary (they are able to form a straight line).

x+x = 180

2x = 180

x = 180/2

x = 90

Ellis is going on a tour that costs $65 while on vacation. He was told to bring $118 to pay for the cost of the tour and dinner. Which of the following inequalities represents the money Ellis can spend on dinner?

A. $118 + d < $65
B. $118 + d > $65
C. $65 + d > $118
D. $65 + d < $118

Answers

Answer:

The answer should be D.

4n² +7n=0 what do I do if there is no part c?

Answers

Answer:

Find the coefficients using ax^2 + bx + c = 0

a = 4

b = 7

c = 0

Make the coefficient equal 1. But how do we do that? Division.

4n² + 7n = 0

4/4n² + 7n/4 = 0/4

Simplify

= n² + 7/4n = 0

a = 1

b = 7/4

c = 0

Complete the square using b/2².

b = 7/4

(b/2)² = (7/4 ÷ 2)²

Use fraction rule.

7/4 ÷ 2² = 7/4² / 2²

square the numbers

7/4² / 2² = 49/16 ÷ 4

49/16 ÷ 4 = 49/16 × 1/4

49/16 × 1/4 = 49/64

Add to both sides of the equation using 49/64

b = 7/4

b/2 = 7/4 ÷ 2

simplify

b/2 = 7 ÷ (4 × 2)

simplify(arithmetic)

b/2 = 7/8

n² + 7/4n + 49/64 = 49/64

(n + 7/8)² = 49/64

Solve for the unknown x

[tex](n+\frac{7}{8})^2=\frac{49}{64}\\\sqrt{(n+\frac{7}{8})^2}=\sqrt{\frac{49}{64}}\\[/tex]

Next, cancel out the square on the left side.

[tex]n+\frac{7}{8}=+/-\sqrt{\frac{49}{64}}[/tex]

Subtract 7/8 from both of the sides.

[tex]n+\frac{7}{8}-\frac{7}{8}=-\frac{7}{8}+/-\sqrt{\frac{49}{64}}[/tex]

Simplify the left side.

[tex]n=-\frac{7}{8}+/-\sqrt{\frac{49}{64}}\\n=-\frac{7}{8}+/-\frac{\sqrt{49}}{\sqrt{64}}\\n=-\frac{7}{8}+/-\frac{7}{8}\\n_1=0\\n_2=-\frac{7}{4}[/tex]

That wraps it up for this equation. Hope it helped!

Question 6(Multiple Choice Worth 1 points)
(02.02 MC)
Given the function f(x) = -5x² + 2x + 9, find f(1) and f(2). Choose the statement that is true concerning these two values.
O The value of f(1) cannot be compared to the value of f(2).
O The value of f(2) is larger than the value of f(1).
O The value of f(2) is smaller than the value of f(1).
O The value of f(1) is the same as the value of f(2). help

Answers

Answer:

O The value of f(2) is smaller than the value of f(1).

Step-by-step explanation:

First, let's solve for both. When the problem says f(1) or f(2), this just means that the x value is equal to that. So:
f(1) = -5(1)^2 + 2(1) + 9 = 6
f(2) = -5(2)^2 + 2(2) + 9 = -7
Since f(1) = 6 and f(2) = -7, we know that f(1) is greater than f(2). Therefore, the value of f(2) is smaller than the value of f(1)

Which number line represents the solution set for the inequality 2x-62 6(x-2) + 8?
-1.5 -1
-0.5
0
0.5
1
1.5
-1.5 -1
-0.5
0
0.5
1
1.5
-1.5
-1 -0.5
0.5
1.5
-1.5
-1
-0.5
0.5
1.5
Mark this and return
04
O
0
O
1
Save and Exit
Next
Submit

Answers

The THIRD number line represents the solution of that inequality.

The correct number line which represents the solution set for the inequality is shown in option 2.

What is Inequality?

A relation by which we can compare two or more mathematical expression is called an inequality.

We have to given that;

Inequality is,

⇒ 2x - 6 ≥ 6 (x - 2) + 8

Now, We cam simplify as;

⇒ 2x - 6 ≥ 6 (x - 2) + 8

⇒ 2x - 6 ≥ 6x - 12 + 8

⇒ 2x - 6x ≥ - 12 + 8 + 6

⇒ - 4x ≥ 2

⇒ 4x ≤ - 2

⇒ x ≤ - 1/2

⇒ x ≤ - 0.5

Hence, The correct number line which represents the solution set for the inequality is shown in option 2.

Learn more about the inequality visit:

https://brainly.com/question/25944814

#SPJ7

The following scatter plot shows the data for NCAA quarterbacks comparing their attempted passes to completed passes.

Draw in the line of best fit/ trend line!

Hint: A line of best fit follows the pattern of the data and is in the middle of the points.

Answers

The line of the best fit is shown in the picture which is approximate near the dots.

What is the line of best fit?

A mathematical notion called the line of the best fit connects points spread throughout a graph. It's a type of linear regression that uses scatter data to figure out the best way to define the dots' relationship.

The slope and y-intercept can be found using the formula below:

[tex]\rm m = \dfrac{n\sum xy-\sum x \sum y}{n\sum x^2 - (\sum x)^2} \\\\\rm c = \dfrac{\sum y -m \sum x}{n}[/tex]

We have a given a scatter plot shows the data for NCAA quarterbacks comparing their attempted passes to completed passes.

We can draw a line of best fit y = mx + c

Thus, the line of the best fit is shown in the picture which is approximate near the dots.

Learn more about the line of best fit here:

brainly.com/question/14279419

#SPJ1

50 POINTS!!!! PLSSS HELPPP URGENTTTT!!!! Although 300° is a special angle on the unit circle, Amanda wanted to determine its coordinates using the sum and difference formulas.

Part A: Determine cos 300° using the cosine sum identity. Be sure to include all necessary work. (5 points)

Part B: Determine sin 300° using the sine difference identity. Be sure to include all necessary work. (5 points)

Answers

Answer:

a) 1/2, b) = - sqrt(3) / 2

Step-by-step explanation:

a) Let A = 120 degree, B = 180 degree

Using cosine sum is cos(120+180) = cos(120)*cos(180) - sin(120)* sin(180)

which will give you 1/2

b) Let A = 360, B = 60 degree

Using sine difference: sin(360-60) = sin(360) cos(60) - cos(360) sin (60)

gives you -sqrt(3)/2

Cos (300°) using the cosine sum identity is 1/2.

sin (300°) using the sine difference identity is √3/2.

What are Trigonometric Ratios?

Trigonometric ratios are the ratios which is described for two sides of a right angled triangle.

The main three trigonometric ratios are sine, cosine and tangent functions.

Part A :

The cosine sum identity is,

cos (A + B) = cos (A) cos (B) - sin (A) sin (B)

We can write cos (300°) as,

cos (300°) = cos (180° + 120°)

                  = cos (180°) cos (120°) - sin (180°) sin (120°)

sin (180°) = 0 and cos (180°) = -1

So,  cos (300°) = -cos (120°) = -(-1/2) = 1/2

Part B :

Sine difference identity is,

Sin (A - B) = sin (A) cos (B) - cos(A) sin (B)

We can write sin (300°) as,

sin (300°) = sin (360° - 60°)

                = sin (360°) cos(60°) - cos(360°) sin (60°)

                = - sin (60°)

                = -√3 / 2

Hence the value of Cos (300°) using the cosine sum identity is 1/2 and the sin (300°) using the sine difference identity is √3/2.

Learn more about Trigonometric Ratios here :

https://brainly.com/question/29081149

#SPJ2

[tex]\frac{1}{2} - x + \frac{3}{4} = x - 4[/tex]

Answers

Answer:

[tex]x = \dfrac{21}8[/tex]

Step-by-step explanation:

[tex]~~~~~~~~\dfrac 1 2 -x + \dfrac 34 = x-4\\\\\\\implies \dfrac 24 + \dfrac 34 - x =x-4\\\\\\\implies \dfrac 54+4=x+x\\\\\\\implies 2x = \dfrac{21}{4}\\\\\\\implies x = \dfrac{21}{4 \cdot 2}\\\\\\\implies x = \dfrac{21}8[/tex]

pls help!!! Let theta equals negative 9 times pi over 4 period


Part A: What is a coterminal angle of θ such that 0 ≤ θ ≤ 2π? (5 points)


Part B: What are the exact values of all six trigonometric functions evaluated at θ?

Answers

A coterminal angle of θ such that 0 ≤ θ ≤ 2π is equal to 7π/4 and the exact value of Sin(θ) = -1/√2.

What is a coterminal angle?

A coterminal angle can be defined as an angle that share the terminal side of an angle which occupies the standard position i.e it has the same initial side.

In this scenario, all angles that are multiples of 2π and added to the given angle (-9π/4) would be coterminal. For the range [0, 2π], 8π should be added to the given angle as follows:

Coterminal angle = -9π/4 + 4π

Coterminal angle = -9π/4 + 16π/4

Coterminal angle = 7π/4.

Part B.

The reference angle is given by:

7π/4 -π = 3π/4.

Therefore, the exact values of all six (6) trigonometric functions evaluated at θ are:

Sin(θ) = -1/√2.Cosec(θ) = √2.Cos(θ) = 1/√2Sec(θ) = -√2.Tan(θ) = -1.Cot(θ) = -1.

Read more on coterminal angles here: https://brainly.com/question/23093580

#SPJ1

The large rectangle below represents one whole.

A large rectangle with 25 equal sections, 11 of which are shaded

What percent is represented by the shaded area? is it 2.27

Answers

Answer:

See below

Step-by-step explanation:

If the whole rectangle were shaded (all 25 parts) that would be 100%

So, we can set up a proportion.

25 = 100%

11 = x

Then, cross-multiply to get,

25x = 1100

Divide both sides by 25 to solve for x

x = 44.

The x value represents the percentage shaded.

44%

Which point is not included in the solution set for the inequality? (–1, 3) (0, 4) (1, 5) (2, 4)

Answers

The point that is not included in the solution set for the inequality in the graph is (-1, 3).

How to explain the graph?

In the information given, (h, k) is the vertex point. In the graph, the vertex point will be (1, 2). The equation will be:

y = a(x + 1)² + 2

By the point of the graph(0, 3) the value of a will be:

3 = a(0 - 1)² + 2

3 = a + 2

a = 3 - 2

a = 1

The equation this becomes:

y = 1(x - 1)² + 2.

y = x² - 2x + 1 + 2

y = x² - 2x + 3

Therefore, the point that is not included in the solution set for the inequality is (-1, 3).

Learn more about graph on:

brainly.com/question/19040584

#SPJ1

-5(x+2)=-4x-12-x+2

3x-4+2x=5(x-4)

5(x+7)=-5(x-7)

6x+2-x=-2x-2+7x

Which equation has infinitely many solutions?

Answers

Answer:

−5(x+2)=−4x−12−x+2

Step-by-step explanation:

1) −5(x+2)=−4x−12−x+2

−5x−10=−4−10−x

-5x= -5x

0=0

so, it is true for all values

what is a factor of 84 but not a multiple of 3

Answers

Answer:

2

Step-by-step explanation:

Answer to this math question?

Answers

Answer:

Option 4

Step-by-step explanation:

Volume of Cone:

                h = x units

   diameter = x units

                 r = (x/2) units

    [tex]\sf \boxed{\text{ \bf Volume of cone = $\dfrac{1}{3} \pi r^2h$}}[/tex]

                                   [tex]\sf =\dfrac{1}{3}*\pi * (\dfrac{x}{2})^2*x\\\\=\dfrac{1}{3}*\pi*\dfrac{x^2}{4}*x\\\\=\dfrac{1}{12}\pi x^3[/tex]

PLEASE HELP!!! 25 POINTS!!!

Answers

6 4
5

2 3
6

7 5
3

2 4
8

3 5
7

One number is 2 less than a second number. Twice the second number is 7 less than 3 times the first. Find the two numbers.

Answers

Answer : 11 and 13

Step-by-step explanation:

Let the numbers be X and Y then,

By question

X= Y - 2 .....................(i)

2Y = 3X - 7 ...............(ii)

putting the value of X from (i) on equation (ii) we get,

2Y = 3(Y - 2) - 7

2Y = 3Y - 6 - 7

2Y - 3y = - 13

-Y = - 13

Y = 13

now putting value of Y in equation (i)

X = 13 - 2= 11

hence those numbers are 11 and 13 respectively

Find the equation of the linear relationship.
The equation that represents the linear relationship is y = ___

Answers

Answer: The equation of a linear relationship is y = mx + b, where m is the rate of change, or slope, and b is the y-intercept (The value of y when x is 0).

Step-by-step explanation:

a) A market researcher investigating consumers' preference for three brands of beverages namely coffee, tea and cocoa, in Ongata town gathered the following information: From a sample of 800 consumers, 230 took coffee, 245 took tea and 325 took cocoa, 30 took all the three beverages, 70 took coffee and cocoa, 110 took coffee only, 185 took cocon only. Required: Present the above information in a Venn Diagram. The number of customers who took tea only. (4 marks) (2 marks) (0) (2 marks) iv) The number of customers who took coffee and tea only. The number of customers who took tea and cocoa only. The number of customers who took none of the beverages. (2 marks) 1) (2 marks)​

Answers

The sample of 800 consumers, 230 took coffee, 245 took tea and 325 took cocoa are shown in the picture by the Venn diagram.

What is the Venn diagram?

It is defined as the diagram that shows a logical relation between sets.

The Venn diagram consists of circles to show the logical relation.

We have:

From a sample of 800 consumers, 230 took coffee, 245 took tea and 325 took cocoa, 30 took all the three beverages, 70 took coffee and cocoa, 110 took coffee only, and 185 took cocoon only.

We can represent the above data by the Venn diagram as shown in the picture.

From the Venn diagram:

The number of customers who took none of the beverages

= 800 - 580 = 220

The number of customers who took tea only = 95

The number of customers who took tea and cocoa only = 70

The number of customers who took tea and coffee only = 50

The number of customers who took none of the beverages = 220

Thus, in the sample of 800 consumers, 230 took coffee, 245 took tea and 325 took cocoa are shown in the picture by the Venn diagram.

Learn more about the Venn diagram here:

brainly.com/question/1024798

#SPJ1

Harry buys a ream of computer paper priced at $9.99 before a 6.0%
sales tax. He uses a coupon at checkout for a 10% discount. After the
purchase he mails in a form for a $5.00 rebate. What is Harry's final
cost?

Answers

Answer:

Step-by-step explanation:

Harry buys a ream of computer paper priced at $9.99 before a 6.0%

sales tax. He uses a coupon at checkout for a 10% discount. After the

purchase he mails in a form

Simplify (5x+6)(6x-4)

Answers

Answer:

I think it's 35x^2 +16x-24 listen I'm not sure yet I could be wrong

using the the polynomial using the FOIL method. you would get:
3022 + 16.0 - 24

Solve the following system of equations
3x - 4y + z = -5
x-y-z = -10
6x - 8y + 2z = 10

Answers

Notice that the left side of the third equation is 2 times the left side of the first equation:

6x - 8y + 2z = 2 (3x - 4y + z)

The first equation says

3x - 4y + z = -5

while the third equation would reduce to

2 (3x - 4y + z) = 10   ⇒   3x - 4y + z = 5

but -5 ≠ 5, so there is no solution to the system.

Other Questions
What was the purpose of the federalist papers Water is made of polar molecules, and oil is made of nonpolar molecules. Based on your observations, which molecules attract each other more strongly, polar molecules or nonpolar molecules? Explain your reasoning. How many people watched the champions league final?. PLEASE HELP ILL MAKE YOU THE BRAINIEST What is the value of x how many died in the battle of the battle of Cerro Gordo on each side Determine a series of transformation that would map polygon ABCDE onto polygon A'B'C'D'E' which number is equal to 4 half Prove that 2 is an irrational number and hence show that 3+53 is also irrational comparison of faith? judaism, christianity, and islam. Image is attached Find x and y of 2 similar polygons !20 PTS!Find point Z that partitions the directed line segment XY in the ratio of 2:1 where X(1, 2) and Y(7, 5). EXPLAIN IN STEPS.Find the coordinates of P so that P partitions segment AB in the part-to-whole ratio of 1 to 5 with A(-9, 3) and B(1, 8). EXPLAIN IN STEPS. How did television contribute to a culture of conformity in the United Statesduring the 1950s? A 4.0-kg object has 72 J of kinetic energy.Determine its speed. Read the excerpt from "The Gift of the Magi.""Isn't it a dandy, Jim? I hunted all over town to find it. You'll have to look at the time a hundred times a day now. Give me your watch. I want to see how it looks on it."Instead of obeying, Jim tumbled down on the couch and put his hands under the back of his head and smiled."Dell," said he, "let's put our Christmas presents away and keep 'em a while. They're too nice to use just at present. I sold the watch to get the money to buy your combs. And now suppose you put the chops on."Which best describes the use of irony in this excerpt?The excerpt is an example of verbal irony, as Jim tells Della to put the presents away.The excerpt is an example of dramatic irony, as the audience knows something that Jim does not.The excerpt is an example of situational irony, as Jim has sold the watch for which Della bought a chain.The excerpt is an example of dramatic irony, as the audience knows something that neither one of the couple knows. Choose the correct answer (picture included)GIVING BRAINLIEST15 POINTS! Motte and bailey castles, such as bedford castle, were built in which period A cast iron pipe used as a water main for a home has an outer diameter of 8 in. If the pipe has a thickness of 0.25 in, what volume of iron does 24 in of pipe contain? Answer in cubic inches. Sheryl makes $7 per pair ofearrings, e, and $13 per necklace,n, she sells. What expressionrepresents her total income? Why would you advise someone to quit smoking ( according to the histology of the respiratory system) the author of this passage would most likely cite which factor as contributing to the phenomenon described?