A village fete has a children’s running race each year, run in heats of up to ten children. For each heat the first three contestants past the finishing line qualify for the final. There are three prizes in the final for 1st, 2nd and 3rd places. One year 29 children enter the race so there are three heats, of ten, ten and nine children. One year 29 children enter the race so there are three heats, of ten, ten and nine children. 1) What is the probability that three randomly chosen competitors win prizes? 2) What is the probability that two randomly chosen competitors win prizes? 3) How many ways are there to select ten competitors for the first heat? 4) Once the competitors have been selected for the first heat, how many different groups of three qualifiers are possible from this heat

Answers

Answer 1

Answer:  1) 1/3,654     2) 3/406     3) 72,684,900,288,000      4) 120

Step-by-step explanation:

1)         First       and        Second         and         Third

  [tex]\dfrac{3\ total\ prizes}{29\ total\ people}\times \dfrac{2\ remaining\ prizes}{28\ remaining\ people}\times \dfrac{1\ remaining\ prize}{27\ remaining\ people}=\dfrac{6}{21,924}\\\\\\.\qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \quad =\large\boxed{\dfrac{1}{3,654}}[/tex]

2)         First       and          Second

   [tex]\dfrac{3\ total\ prizes}{29\ total\ people}\times \dfrac{2\ remaining\ prizes}{28\ remaining\ people}=\dfrac{6}{812}=\large\boxed{\dfrac{13}{406}}[/tex]

[tex]3)\quad \dfrac{29!}{(29-10)!}=\large\boxed{72,684,900,288,000}[/tex]

[tex]4)\quad _{10}C_3=\dfrac{10!}{3!(10-3)!}=\large\boxed{120}[/tex]


Related Questions

−3−(−7) Select the point on the number line to plot the answer. https://learning.k12.com/d2l/le/enhancedSequenceViewer/811794?url=https%3A%2F%2Fe02711f5-1353-40b6-af9b-349f7ff846bd.sequences.api.brightspace.com%2F811794%2Factivity%2F122669191%3FfilterOnDatesAndDepth%3D1

Answers

Answer:

The answer is 4

Step-by-step explanation:

Like the other person said

Number lines are used to represent numbers at regular and constant intervals

The point on the number line that represents -3 - (-7) is 4

The expression is given as:

-3 - (-7)

Open the bracket

-3 + 7

Evaluate the expression

4

Hence, the point on the number line that represents -3 - (-7) is 4

Read more about number lines at:

https://brainly.com/question/24644930

what kind of number is 0 and why? if you know the others that'd be great!!

Answers

Answer:

0 is a rational, whole, integer and real number.

Step-by-step explanation:

0 is a rational, whole, integer and real number.

Here’s a chart that I think is super helpful on this subject. It’s a whole, integer, rational and real number

Jasmine is a structural engineer. She designs the lift hill of a roller coaster that models the equation y=x3, where y is the height and x is the length from the start of the lift hill. Using this model, how far from the start of the lift hill does the ride reach a height of 343 meters?​

Answers

Answer:

the anwser is 7 buddy hope it helps

7. Marisa has $26 in her purse. She pays $5 for
lunch Which
expression represents this situation? A. -26 -
(-5) B.-26 + 5 C. 26 + (-5) D. 26 + 5

Answers

Answer: I think the answer is C

Answer:

yea i agree with kassidy

A cliff diver leaps from a 100-foot cliff into the Pacific. The diver’s height above the water is modeled by the function P(x) = –16x 2 + 10x + 100, where x is time in seconds. During which interval is the diver at least halfway down

Answers

Answer:

2.1 < x <2.5

Step-by-step explanation:

i’m taking the test rn i’m not sure if it’s correct i’ll lyk!

Answer:

B on Edge

Step-by-step explanation:

What is the momentum of a 15 kg tire rolling down a hill at 3 m/s?
5 kg. m/s
O 18 kg . m/s
O 45 kg. m/s
60 kg . m/s

Answers

Answer:

45ans

Step-by-step explanation:

p=?

m=15kg

v=3m/s

now,

p=m*v

p=15*3

p=45 ans

Which of the following is equal to 20x + 8y - 80?
A. 3x + y - 10
B. 5x+2y-20
c. 4(5x + 2y - 20)
D. 4(5x + 2y – 40)
E. 4(5x + 8y - 20)

Answers

it would be C because if you take out the four, the coefficients are multiples of 4 so it simplifies down.
It would be C because it make way more sense than the others

What number is 344% of 107

Answers

Answer:

368.08

So I turn the numbers into fractions so 344% would be 344/100 because percentages are out of 100. Since it is 344% OF 107, you'd put 107 on the bottom of the fraction and the answer will go on top. I multiply the IS with the OF (IS is the top number and OF is the bottom) so you'd multiply 107x344 to get 36808. Since 344 is a percent (out of 100) you have to do divide the answer by 100 to get 368.08

I hope that helps!

2 – 1 + 5 x 4 x 11 Solve with PEMDAS

Answers

Answer:

221

Step-by-step explanation:

2-1+5*4*11

2-1+20*11

2-1+220

1+220

221

Complete the statements to verify that f(x) = 10x and g(x) = log10x are inverses of each other. f(g(x)) = 10log10x Using the law of logarithms blogbn = , we have that f(g(x)) = . We also need to show that is also equal to x. g(f(x)) = log10(10x) Using the law of logarithms logbbn = , which means that g(f(x)) = x. Therefore, f and g are inverses of each other.

Answers

Complete the statements to verify that f(x) = 10x and g(x) = log10x are inverses of each other. f(g(x)) = 10log10x

The answer is given below in the image.

What are the two laws of logarithms?

The laws apply to logarithms of any base but the identical base needs to be used at some point in a calculation. This regulation tells us a way to add logarithms collectively. Adding log A and log B results in the logarithm of the product of A and B, that is log AB. The same base, in this situation 10, is used throughout the calculation.

What is the fundamental law of logarithms?

A logarithm of more than a few raised to a power is identical to the power expanded via the logarithm of the wide variety to the same base. that is, loga(mn) = nlogam.

Learn more about logarithms here: https://brainly.com/question/247340

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If you get this you are a critical thinker. I enter the garden. There are 34 people. You kill 30. How many people are in the garden. Good luck! If you get it correct your answer will be deleted and I will message you to continue the game. Don't play if you are not going to continue.

Answers

1 person is in the garden. Me

Answer:

35 counting yourself.........34 not

Factor 8x3 − 343.
A) (2x − 7)(4x2 + 14x + 49)
B) (2x − 7)(4x2 + 28x + 49)
C) (2x − 7)(4x2 −14x + 49)
D) (2x − 7)(4x2 − 28x + 49)

Which expression is equivalent to 27x3 + 125?
A) (3x – 5)(9x2 – 15x + 25)
B) (3x – 5)(9x2 + 15x – 25)
C) (3x + 5)(9x2 – 15x + 25)
D) (3x + 5)(9x2 + 15x – 25)
please explain if you could, thank you

Answers

Answer:

A) (2x − 7) (4x² + 14x + 49)

C) (3x + 5) (9x² − 15x + 25)

Step-by-step explanation:

Sums and differences of cubes factor as:

a³ + b³ = (a + b) (a² − ab + b²)

a³ − b³ = (a − b) (a² + ab + b²)

8x³ − 343 is a difference of cubes.

(2x)³ − 7³

(2x − 7) (4x² + 14x + 49)

27x³ + 125 is a sum of cubes.

(3x)³ + 5³

(3x + 5) (9x² − 15x + 25)

3. Fill in the blanks so that the answer to this number sentence is correct: 2ab​

Answers

Answer:

where's the question or the picture of the question

Can someone please help me?

Answers

Answer:

2/5 so 4/10

THE ANSWER IS A

Answer:

4/10

Step-by-step explanation:

get a common denominator (which is 10) then subtract

help um. Order the set of numbers from least to greatest

Answers

5/2 , √5 , 2¾ , 2.71 (bar)

am not really sure but i guess that is what I know.

Answer:

 [tex]2\frac{3}{4}, 2.71, \sqrt{5}, \frac{5}{2}[/tex]

Step-by-step explanation:

Just convert them all to a decimal, I'm too lazy to write it all out...

An insurance company offers two types of insurance: health insurance and life insurance. Let X be the annual claim on the health insurance and Y be the annual claim on the life insurance. The joint density function of X and Y is: Find the probability that the total claims exceed 0.5 but is less than 2 and the claim on the life insurance is less than 1.5.

Answers

The joint density equation is missing in the question. The equation is [tex]f(x,y)=\left\{\begin{matrix}2x^3, 0\leq x\leq 1,0\leq y\leq 2\\ 0, \text{ otherwise}\end{matrix}\right.[/tex]

Probability is 0.59

Step-by-step explanation:

We have

x -- denotes the annual claim health insurance

y -- denotes the annual claim life insurance

And joint density of x and y is given to us

[tex]f(x,y)=\left\{\begin{matrix}2x^3, 0\leq x\leq 1,0\leq y\leq 2\\ 0, \text{ otherwise}\end{matrix}\right.[/tex]

Event that the claim exceeds 0.5 but less than 2 can be written as 0.5≤ x+y ≤2

and claim of life insurance less than 1.5 can be written as 0 ≤ y ≤ 1.5

Required probability

= P( 0.5≤ x+y ≤2  ∩ 0 ≤ y ≤ 1.5 )

Lets plot this, to find the common region

For common region

when 0≤ x ≤ 0.5, then 0.5 ≤ y ≤ 1.5  ---- for region I

when 0.5≤ x ≤ 1, then 0 ≤ y ≤ 2-x  ---- for region II

The required probability

= [tex]\int_{0}^{0.5} \int_{0.5-x}^{1.5}2x^3 dy dx+\int_{0.5}^{1} \int_{0}^{2-x}2x^3 dy dx[/tex]

= [tex]\int_{0}^{0.5} 2x^3[\int_{0.5-x}^{1.5}dy] dx+\int_{0.5}^{1} 2x^3[\int_{0}^{2-x}dy] dx[/tex]

= [tex]\int_{0}^{0.5} 2x^3(1.5-0.5+x) dx+\int_{0.5}^{1} 2x^3 (2-x) dx[/tex]

= [tex]\int_{0}^{0.5}2x^3 dx+\int_{0}^{0.5}2x^4 dx+\int_{0.5}^{1}4x^3 dx-\int_{0.5}^{1}2x^4[/tex]

= [tex][\frac{2x^4}{4}]_0^{0.5}+[\frac{2x^5}{5}]_0^{0.5}+[\frac{4x^4}{4}]_{0.5}^1-[\frac{2x^5}{5}]_{0.5}^1[/tex]

= [tex]$\frac{1}{32}+\frac{1}{80}+\frac{1}{16}-\frac{31}{20}$[/tex]

= 19/32

=0.59    

0.2, 0.19, 3/5
Greatest to least

Answers

3/5, 0.2, 0.19

3/5 is equal to 0.6

Answer:

3/5 , .2, .19

Step-by-step explanation:

.2= 20/100

.19 = .19/100

3/5 = .6= 60/100

Which angle pairs are supplementary? Check all that
apply.
Angle 1 and angle 2
Angle 4 and angle 3
Angle 4 and angle 5
Angle 7 and angle 5
Angle 3 and angle 6

Answers

Here, Angle 1 and angle 2, Angle 4 and angle 3 and Angle 7 and angle 5 are supplementary angles.

We need to identify which angle pairs are supplementary.

What are supplementary angles?

Supplementary angles are two angles with a sum of 180°.

Here, Angle 1 and angle 2, Angle 4 and angle 3 and Angle 7 and angle 5 are supplementary angles.

To learn more about supplementary angles visit:

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Factorize 6p2 - 7p + 2​

Answers

Answer:

(2p - 1)(3p - 2)



what is equal to
[tex] \frac{( {2}^{3} ) {}^{3} }{( {3}^{3} ) {}^{3} } [/tex]


A.
[tex]( \frac{2}{3} ) {}^{6} [/tex]
B.
[tex]( \frac{2}{3} ) {}^{9} [/tex]
C.
[tex]( - 6) { }^{6} [/tex]
D.
[tex]( - 6) {}^{9} [/tex]

Answers

Answer:

B.

Step-by-step explanation:

At a dance supply store dance pants cost $30 each and leotards cost $18 each you have $175 to spend you are going to buy 3 pairs of pants what is the greatest number of leotards you can buy

Answers

answer

4 pairs

Step-by-step explanation:

total is $175

when you buy three pairs of pants you have wasted $90

175-90 equals 85

find the value of each variable. write your answers in simplest radical form

Answers

Answer:

y=3.364

x=4

Step-by-step explanation:

hope this helps

what is does p equal if 8-p = -12 -3p

Answers

Answer:

8-p=-12-3p

8+12-p = -3p

20 = -3p + p

20 = -2p

20/-2 = p

-10 = p

ans. p = -10

...

Short answers is p=-10 hope this helps :)

How many planes appear in this figure? Name three points that are collinear. Are points a, b, c, and d coplanar? Explain. At what does and ca interest db

Answers

D, B, and A are collinear. Yes they are coplanar because they all lay on the same plane. And I don’t understand the last question

5(5z - 7), when z = -1

Answers

Answer:

5(5(-1)-7)

-25-35

-60

Step-by-step explanation:

Answer: -60

Step-by-step explanation:

Image!!

What is 28 rounded to the nearest 10

Answers

Question:

What is 28 rounded to the nearest 10?

Answer:

28 rounded to the nearest 10 is 30.

28 rounded to the nearest 10 is 30

Evaluate x^3– y^2 if x = 2 and y= 3/4

Answers

Answer:

2³-3/4²

Step-by-step explanation:

Please answer fast will make you brainlest

Answers

Answer:

if i'm correct its the second one

Step-by-step explanation:



If 11 boxes of chocolates contain 220 chocolates in total, calculate how many chocolates 5 box of chocolates will contain
chocolates

Answers

Answer:100 chocolates

Step-by-step explanation:

20 chocolate in each box so 20 time 5 is 100 so 20 time 11 is 220

The perimeter of a playing field for a certain sport is 190 ft. The field is a rectangle, and the length is 43 ft longer than the width. Find the dimensions

Answers

Answer:

2(L+w) = 190ft (Perimeter)

L + W = 95ft (190 divided by 2)

L = W + 43ft (Given)

W + 43 + W = 95ft

2W + 43 = 95ft

2W = 52ft

W = 26ft

L = 26ft + 43 = 69ft

Answer: The feild is 69ft by 26ft

Hope this helps!!!

- Jarrett Lane

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