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Gala2k [10]
3 years ago
9

What is the directrix of the parabola defined by 1/4(y+3)=(x-2)^2

Mathematics
1 answer:
Charra [1.4K]3 years ago
4 0
This is a parabola which opens upwards and the directrix will be of the form  
y = k

the general form is 

4p(y - k) = (x - h)^2   we have:-

1/4(y + 3) = (x - 2)^2

so the vertex is at (2, -3)

4p = 1/4  so p =  1/16

so the focus will be at (2 , -2 15/16)

and directrix is  y = -3 1/16
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Baseball's division series is a best of five game series. That is, the first team to win 3 games is the winner. Team A and team
iris [78.8K]

Answer:

1. 27.46% probability that A wins the series in 3 games.

2. There is a 28.84% probability A wins the series in 4 games.

3. There is a 20.18% probability A wins the series in 5 games.

4. There is a 76.48% probability A wins the series.

5. There is a 71.825% probability A wins the series if a "best-of-three" game series is played.

Step-by-step explanation:

For each game, there are these following probabilities:

A 65% probability team A wins.

A 35% probability team B wins.

The combination formula is important to solve this problem:

This is because for example, team A winning games 1,2 and 4 and team B winning game 3 is the same as team A winning games 1,3,4 and team B winning game 2. That is, the order is not important.

C_{n,x} is the number of different combinatios of x objects from a set of n elements, given by the following formula.

C_{n,x} = \frac{n!}{x!(n-x)!}

1. What the probability that A wins the series in 3 games?

This is team A winning all 3 games. For each game, there is a 65% probability that team A wins. So

P = (0.65)^{3} = 0.2746

There is a 27.46% probability that A wins the series in 3 games.

2. What is the probability A wins the series in 4 games?

This is the team A winning three games and the team B 1. The team B win cannot happen in the fourth game, so the number of possibilities is a combination of 3 by 2. So

C_{3,2} = \frac{3!}{2!1!} = 3

The probability that team A wins the series in 4 games is:

P = 3*(0.65)^{3}*(0.35) = 0.2884

There is a 28.84% probability A wins the series in 4 games.

3.What is the probability A wins the series in 5 games?

This is the team A winning three games and the team B 2. The team B second win cannot happen in the fifth game, so the number of possibilities is a combination of 4 by 2. So

C_{4,2} = \frac{3!}{2!1!} = 6

The probability that team A wins the series in 5 games is:

P = 6*(0.65)^{3}*(0.35)^{2} = 0.2018

There is a 20.18% probability A wins the series in 5 games.

4. What is the probability A wins the series (period)?

They can win the series in 3,4 or 5 games. So this is the sum of the answers for 1,2,3.

So

P = 0.2746 + 0.2884 + 0.2018 = 0.7648

There is a 76.48% probability A wins the series.

5. What is the probability A wins the series if a "best-of-three" game series is played?

These three following outcomes are accepted:

A - A

A - B - A

B - A - A

So

P = (0.65)^{2} + 2*(0.65)^{2}*(0.35) = 0.71825

There is a 71.825% probability A wins the series if a "best-of-three" game series is played.

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3 years ago
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Answer:

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Step-by-step explanation:

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Convert 15% to decimal of 0.15
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Formula: (x, -y), when reflecting over the x-axis you keep the x-value the same, but change the sign of the y-value. For example: You have the original coordinates (3, 5), and if you reflect it over the x-axis it’ll be (3, -5).

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