There are $15$ gymnasts in the Olympic women's competition, including $4$ Americans. The gold medal goes to first place, silver to second, and bronze to third. In how many ways can the medals be awarded to three of the $15$ gymnasts, if exactly one of the Americans wins a medal?

Answers

Answer 1

Answer:

There are 220 ways by which the medals can be awarded to three of the 15 gymnast, if exactly one of the Americans wins a medal

Step-by-step explanation:

From the question, we have;

The number of gymnast in the Olympic women's competition = 15

The number of the gymnast who are Americans = 4

The number of medals awarded = 3 medals

The number of ways hat the medals can be awarded to the three of the gymnast if exactly one of the Americans wins a medal is given as follows;

The number of ways one of the medals can be won by one of the four Americans = ₄C₁ = 4 ways

The number of ways the other two medals can be won by the remaining 11 gymnast = ₁₁C₂ = 55 ways

Therefore, the total number of ways, 'N', the medals can be awarded to three of the 15 gymnast, if exactly one of the Americans wins a medal is given as follows;

N = ₄C₁ × ₁₁C₂

∴ N = 4 × 55 = 220


Related Questions

solve the equation below

Answers

Answer:

[tex]\frac{n}{3}[/tex]

how many solutions does the graph above show?
a. one
b. none
c. infinite

Answers

Answer:

infinite

Step-by-step explanation:

The line can be represented by the equation y=-2/3x-2 since there are no other lines it would be infinite. if there was a line with the same slope and a different y-intercept the answer would be none as the lines never intersect.  for the equation there are ifinitly many!  

     for example any point that that lone touches is a solutions so there is not one but many answers.

           

solve the following by completing the square :
x2 - 6x + 7 = 0

Answers

Answer:

Step-by-step explanation:

2x-6x+7=0
-4x+7=0
-4x=-7
x=7/4

Each letter of the word algebra is written on identical slips of paper and placed in a box of a slip of paper selected from the box without looking what is the probability that the slip of paper will not have the letter A on it.

Answers

Answer:

I have no idea sorry

Step-by-step explanation:

what is 500/2000 as a decimal if u get it right u get brainliest!!! pls and thank u

Answers

Answer:

it's 0.25 well good luck and i have a joke

what is the slope for 15 and 15

Answers

Answer:

1

Step-by-step explanation:

15/15=1

Which expression is equivalent to -30 - (8)

Answers

Answer:

Any equation that has an answer of -38

Step-by-step explanation:

A baseball diamond is shaped like a square with each side measuring 30
yards.

Answers

Walter is right cause 30x5 equals 150

What’s the surface area of a cylinder with a height of 6yd and width of 4yd

Answers

Answer: 100.53096 (round if you need to)

Steps:
Surface area of cylinder formula = 2πrh + 2 πr^2

2πrh + 2 πr^2
2(π)(2)(6) + 2(π)(2^2)
2(π)(12) + 2(π)(4)
= 100.53096

Ian has a goal to save $2000. He already has 1/5 of his goal. How much more money must Ian save to achieve his goal?

Answers

Answer:

1,000

Step-by-step explanation:

If Ian has 1/5 of his goal which is $2,000 just divide $2,000 by 1/5 which is 1,000. hope this helped

Answer:

1/5 of 2000 is 400 (2000/5=400)

2000-400 is 1600.

he needs to save another $1600

Solve x + 1 > 3. Graph the solution.

Answers

Answer:

x > 2

> means it's greater (goes in the right direction) than 2 and it's an OPEN circle

The solution of the given inequality is required.

The required graph is attached.

Inequalities

The given inequality is [tex]x+1>3[/tex]

Solving the inequality  we get

[tex]x+1>3\\\Rightarrow x>3-1\\\Rightarrow x>2[/tex]

The points which are greater than 2 all will be the solution set of the inequality.

The solution set will be [tex](2,\infty)[/tex]

In the graph the points towards the right of x = 2 will be in the solution set.

The point x = 2 will not be in the solution set.

Learn more about inequalities:

https://brainly.com/question/24372553

ALGEBRA 2!!!!!!!HELP


Answers

Answer:

x = - 1, x = - 11

Step-by-step explanation:

Given

2| x + 6 | - 4 = 6 ( add 4 to both sides )

2|x + 6 | = 10 ( divide both sides by 2 )

| x + 6 | = 5

The absolute value function always gives a positive result, but the expression inside can be positive or negative, that is

x + 6 = 5 or - (x + 6) = 5

solve both

x + 6 = 5 ( subtract 6 from both sides )

x = - 1

or

- (x + 6) = 5 , that is

- x - 6 = 5 ( add 6 to both sides )

- x = 11 ( multiply both sides by - 1 )

x = - 11

HELP PLZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ i will be very happy if u do. FIRST PERSON TO GET IT CORRECT GETS BRAINLIEST

Answers

Answer:

Step-by-step explanation:

x -12 > 0

x > 12

if x > 12   x-12

if x = 12     0

if x < 12     12-x

You pick a card at random. Without putting the first card back, you pick a second card at random. What is the probability of picking a 5 and then picking a number greater than 4?

Write your answer as a percentage.

Answers

Answer:

I'm sorry I genuinely don't know

Answer:

.33 for 5

Step-by-step explanation:

Can someone plz help me with this one problem plz plz!!!!

Answers

Answer:

the one on the left (the first one)

Answer:

option A

Step-by-step explanation:

the very first image of graph is the one that show the relationship between x and y

Find the values for x and y in rectangle SLIM.

Answers

Answer:

x = 25

y = 65

Step-by-step explanation:

(I did it on Math Nation)

180 = 130 + 2x

50 = 2x

x = 25

180 = 50 + 2y

130 = 2y

y = 65

A bin contains 1 green, 1 blue and 4 black soccer balls. What is the probability of getting NOT blue?

Answers

Answer: 5/6

Step-by-step explanation:

First find total number of soccer balls.

1 + 1 + 4 = 6

4 + 1 = 5 non-blue soccer balls

5/6 = around 0.83

What is the perimeter of the figure? Use 3.14 for pi

Answers

Answer:

42.84 cm

Step-by-step explanation:

It would be easiest to split this first. To find the circumference of a circle, it is 2πr.

d= 12

r= 6

C= 2π6

C= 12π

Divide by 2 because you are only trying to get the circumference of half the circle.

C= 6π

Now you can add all the other sides to find the total perimeter.

P= 6(3.14) + 10 + 6 + 8

P= 42.84 cm

Answer:

61.68cm

Step-by-step explanation:

semicircle=12x2x3.14x1/2=37.68

trapezium=10+6+8=24

s+t=61.68cm

Please help me!
[One Step Inequalities]

Answers

Answer:

C

Step-by-step explanation:

I really really need help with this and no one is answering. I've looked everywhere for how to do this and I fell like its simple but I can't find it. given -2+4i, express the complex number in polar form. I know the answer is 2 root 5(cos2.03 + isin2.03), but I don't know where the 2.03 comes from. Can someone explain please?

Answers

Result:

Complex number:

The polar form of z is:

Explanation:

z = −2 + 4i

z = 4.4721 · (cos 117o + i · sin 117o)

The polar form of the complex number z = a + bi is:

z = r · (cos θ + i · sin θ)

where, r is the modulus of z and θ is an argument of z. The moduo for a = −2 and b = 4 is:

r = a2 + b2 = · · · = 4.4721 To find argument θ we use one of the following formulas:

b θ=arctan a ifa>0

b o θ=arctan a +180 ifa<0

θ=90o ifa=0andb>0 θ=270o ifa=0andb<0

Inthisexample: a=−2andb=4so:

θ=arctan a +180

θ=arctan 4 +180o −2

b o

θ = arctan (−2) + 180o θ ≈ 117o

Try this website it’s really helped me!

www.mathportal.org/calculators/complex-numbers-calculator/complex-unary-operations-calculator.php?val1=-2&combo1=1&val2=4&rb1=pol&ch2=useDecimals

Answer:

Step-by-step explanation:

a+bi = -2+4i

arctan(b/a)=arctan(4/-2)=-1.071

Because this falls in quardant 2, you have to add pi

1.071+pi=2.03

I hope this helps.

The sum of two numbers is 17 and their difference is 5, what are the two numbers?

Answers

Answer:

11, 8

Step-by-step explanation:

x + y = 17

x - y = 5

The "y" cancels out when you add the two equations and you end up with:

2x = 22

x = 11

Then, plug the "x" back into one of the equations to find "y":

11 + y = 17

y = 6

if its height is y, then what polynomial represents the length of a side of the square base​

Answers

Answer:

Hello your question is incomplete attached below is the complete question

answer :  3y + 6cm

Step-by-step explanation:

attached below is the detailed solution to the given question

The polynomial that represents the side of the square base = 3y + 6cm

Maya has a brown poster board to color. She colors part of it green and part of it orange.
Which fraction of the poster board does Maya color?

Answers

Answer:

d

Step-by-step explanation:

3/5

5 poster boards in total and 3 are colour so...

it is  3/5

Hope this helps!

I need help please!!!!!

Answers

Answer:

y-intercept is (0, -2) and asymptote of y = -2.5

Step-by-step explanation:

If you substitute 0 in for x and simplify, then you will have the y-intercept

y = [tex]\frac{1}{2} (7)^{0} - 2.5 = \frac{1}{2} (1) - 2.5 = \frac{1}{2} - 2.5 = -2[/tex]

The y-intercept is (0, -2)

If the -2.5 were not there, then the graph would have an asymptote at y = 0 or the x-axis

The -2.5 moves the graph down 2.5 units so that y = -2.5 is the asymptote

Therefore, the first answer is correct

4 2/7+2 /2/7
you'll get brainless​

Answers

Answer:

i don't know here is what i got in a calculator 4.42857142857

Step-by-step explanation:

Improper Fraction: 46/7

Mixed Number: 6 4/7

Who can answer this??

Answers

Answer:Answer below in description:Step-by-step explanation:

Ths question is not complete but I will try my best to guide you through it so you can answer it. So what the question is asking you to do is that you have to plug in the coordinates into the equation. I don't want to give you an incorrect answer so I will explain it and you can do it yourself with the full question. First use the second equation as it is a full equation with an equal sign. Once plugged in you can find that c and d do not make the second equation true. A and B both complete the second equation. This means that either A or B is the answer. Since the first equation does not have an equal sign meaning it is not complete I can not answer it and I am sorry. But I have cut the answer down for you to A and B. If this answer helped you in the slightest please check out my channel The Game Rater. Thank you and I appreciate it.

-The Game Rater(Nitroid444)

Some one pls helps ASAP plsss I’ll give brainiest

Answers

Answer:

A is the answer

Step-by-step explanation:

The answer is A like he said above

Help me! I’ll mark brainliest

Answers

Answer:

help me first,help me first

Step-by-step explanation:

A triangle has side lengths of 6, 7, and 10. Is it a right triangle? Explain

Answers

Answer:

As 6^2 + 8^2 = 10^2  

Therefore, triangle is a right angle triangle

Step-by-step explanation:

thank you for your help

Answers

Answer:

I'm not completely sure but if they want exponents for 6 * 6 * 6 then it should be [tex]6^{3}[/tex]

Step-by-step explanation:

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