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vivado [14]
3 years ago
14

There are 20 entries in the chess tournament. How many ways can they finish in first, second,

Mathematics
1 answer:
Romashka [77]3 years ago
3 0

Answer:

6840

Step-by-step explanation:

Here, the order matters (1st, 2nd, and 3rd), so we need to use permutations.

There are 20 people who can get in first place.  After that, there are 19 people who can get in second place.  Finally, there are 18 people who can get in third place.  So:

20 * 19 * 18 = 6840

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You play the following game against your friend. You have 2 urns and 4 balls One of the balls is black and the other 3 are white
Rom4ik [11]

Answer:

Part a: <em>The case in such a way that the chances are minimized so the case is where all the four balls are in 1 of the urns the probability of her winning is least as 0.125.</em>

Part b: <em>The case in such a way that the chances are maximized so the case  where the black ball is in one of the urns and the remaining 3 white balls in the second urn than, the probability of her winning is maximum as 0.5.</em>

Part c: <em>The minimum and maximum probabilities of winning  for n number of balls are  such that </em>

  • <em>when all the n balls are placed in one of the urns the probability of the winning will be least as 1/2n</em>
  • <em>when the black ball is placed in one of the urns and the n-1 white balls are placed in the second urn the probability is maximum, as 0.5</em>

Step-by-step explanation:

Let us suppose there are two urns A and A'. The event of selecting a urn is given as A thus the probability of this is given as

P(A)=P(A')=0.5

Now the probability of finding the black ball is given as

P(B)=P(B∩A)+P(P(B∩A')

P(B)=(P(B|A)P(A))+(P(B|A')P(A'))

Now there can be four cases as follows

Case 1: When all the four balls are in urn A and no ball is in urn A'

so

P(B|A)=0.25 and P(B|A')=0 So the probability of black ball is given as

P(B)=(0.25*0.5)+(0*0.5)

P(B)=0.125;

Case 2: When the black ball is in urn A and 3 white balls are in urn A'

so

P(B|A)=1.0 and P(B|A')=0 So the probability of black ball is given as

P(B)=(1*0.5)+(0*0.5)

P(B)=0.5;

Case 3: When there is 1 black ball  and 1 white ball in urn A and 2 white balls are in urn A'

so

P(B|A)=0.5 and P(B|A')=0 So the probability of black ball is given as

P(B)=(0.5*0.5)+(0*0.5)

P(B)=0.25;

Case 4: When there is 1 black ball  and 2 white balls in urn A and 1 white ball are in urn A'

so

P(B|A)=0.33 and P(B|A')=0 So the probability of black ball is given as

P(B)=(0.33*0.5)+(0*0.5)

P(B)=0.165;

Part a:

<em>As it says the case in such a way that the chances are minimized so the case is case 1 where all the four balls are in 1 of the urns the probability of her winning is least as 0.125.</em>

Part b:

<em>As it says the case in such a way that the chances are maximized so the case is case 2 where the black ball is in one of the urns and the remaining 3 white balls in the second urn than, the probability of her winning is maximum as 0.5.</em>

Part c:

The minimum and maximum probabilities of winning  for n number of balls are  such that

  • when all the n balls are placed in one of the urns the probability of the winning will be least given as

P(B|A)=1/n and P(B|A')=0 So the probability of black ball is given as

P(B)=(1/n*1/2)+(0*0.5)

P(B)=1/2n;

  • when the black ball is placed in one of the urns and the n-1 white balls are placed in the second urn the probability is maximum, equal to calculated above and is given as

P(B|A)=1/1 and P(B|A')=0 So the probability of black ball is given as

P(B)=(1/1*1/2)+(0*0.5)

P(B)=0.5;

5 0
3 years ago
When a certain valve is open, 281 gallons go through it in one hour. The number of gallons that would go through in 94 hours is
JulsSmile [24]
If 281 gallons go thru in 1 hr......then in 94 hrs, (94 * 281) = 26414 gallons go through
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2 years ago
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Solve the equation for principal values of x. Express solutions in degrees.
Hitman42 [59]

Option C:

x = 90°

Solution:

Given equation:

\sin x=1+\cos ^{2} x

<u>To find the degree:</u>

\sin x=1+\cos ^{2} x

Subtract 1 + cos²x from both sides.

\sin x-1-\cos ^{2} x=0

Using the trigonometric identity:\cos ^{2}(x)=1-\sin ^{2}(x)

\sin x-1-\left(1-\sin ^{2}x\right)=0

\sin x-1-1+\sin ^{2}x=0

\sin x-2+\sin ^{2}x=0

\sin ^{2}x+\sin x-2=0

Let sin x = u

u^2+u-2=0

Factor the quadratic equation.

(u+2)(u-1)=0

u + 2 = 0,  u – 1 = 0

u = –2, u = 1

That is sin x = –2, sin x = 1

sin x can't be smaller than –1 for real solutions. So ignore sin x = –2.

sin x = 1

The value of sin is 1 for 90°.

x = 90°.

Option C is the correct answer.

3 0
2 years ago
Read 2 more answers
The cost of a pizza at the pizza palace depends on the size of the pizza and the number of toppings. For a large pizza, the cost
NeX [460]

Answer:

The 2 represents that each toppings costs $2.

5 0
3 years ago
30 points!<br>please help<br><br>in return brainliest and special thanks
a_sh-v [17]
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22. Distributive Property
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