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meriva
3 years ago
13

Describe the differences between a parabola that has a horizontal directrix and a parabola that has a vertical directrix.

Mathematics
1 answer:
Readme [11.4K]3 years ago
4 0
 <span>A parabola that has a horizontal directrix is a parabola that opens up or down. 

Here are some of its components: 
1) Standard equation of a parabola with a horizontal directrix: (x-h)^2 = 4a(y-k), 
a = distance from vertex to focus 
2) Vertex at (h,k) 
3) Focus(h,k+a) 
4) Directrix: y = k-a 
5) Axis of symmetry: x = h 

A parabola that has a vertical directrix opens to the right or left and is on its side. 

Here are some components 
1) Standard equation of a parabola with a vertical directrix: (y-k)^2 = 4a(x-h) 
2) vertex (h,k) 
3) focus (h+a,k) 
4) directrix: x = h-a 
5) Axis of symmetry: y = k

Hopes this helps :)</span>
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Suppose you pay a dollar to roll two dice. if you roll 5 or a 6 you Get your dollar back +2 more just like it the goal will be t
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(a)$67

(b)You are expected to win 56 Times

(c)You are expected to lose 44 Times

Step-by-step explanation:

The sample space for the event of rolling two dice is presented below

(1,1), (2,1), (3,1), (4,1), (5,1), (6,1)\\(1,2), (2,2), (3,2), (4,2), (5,2), (6,2)\\(1,3), (2,3), (3,3), (4,3), (5,3), (6,3)\\(1,4), (2,4), (3,4), (4,4), (5,4), (6,4)\\(1,5), (2,5), (3,5), (4,5), (5,5), (6,5)\\(1,6), (2,6), (3,6), (4,6), (5,6), (6,6)

Total number of outcomes =36

The event of rolling a 5 or a 6 are:

(5,1), (6,1)\\ (5,2), (6,2)\\( (5,3), (6,3)\\ (5,4), (6,4)\\(1,5), (2,5), (3,5), (4,5), (5,5), (6,5)\\(1,6), (2,6), (3,6), (4,6), (5,6), (6,6)

Number of outcomes =20

Therefore:

P(rolling a 5 or a 6)  =\dfrac{20}{36}

The probability distribution of this event is given as follows.

\left|\begin{array}{c|c|c}$Amount Won(x)&-\$1&\$2\\&\\P(x)&\dfrac{16}{36}&\dfrac{20}{36}\end{array}\right|

First, we determine the expected Value of this event.

Expected Value

=(-\$1\times \frac{16}{36})+ (\$2\times \frac{20}{36})\\=\$0.67

Therefore, if the game is played 100 times,

Expected Profit =$0.67 X 100 =$67

If you play the game 100 times, you can expect to win $67.

(b)

Probability of Winning  =\dfrac{20}{36}

If the game is played 100 times

Number of times expected to win

=\dfrac{20}{36} \times 100\\=56$ times

Therefore, number of times expected to loose

= 100-56

=44 times

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3 years ago
Please decrease 90 by 20%
Mashcka [7]

Answer:

Step-by-step explanation:

90 by 20%

10%=9

20%=18

90-18=62

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