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ololo11 [35]
3 years ago
10

Hey Siri Council consist of eight Democrats and five Republicans if a committee of five people are selected find the probability

of selecting two Democrat and three Republicans
Mathematics
1 answer:
Flura [38]3 years ago
6 0

Answer:

55/2574 ≈ 2.18%

Step-by-step explanation:

There are a total of 13 people on the council.

The probability that the first person is a Democrat is 8/13.

The probability that the second person is a Democrat is 7/12.

The probability that the third person is a Republican is 5/11.

The probability that the fourth person is a Republican is 4/10.

The probability that the fifth person is a Republican is 3/9.

The total probability is:

P = (8/13) (7/12) (5/11) (4/10) (3/9)

P = 56/2574

P ≈ 0.0218

There is a 2.18% probability of selecting two Democrats and three Republicans.

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The focus of a parabola is (0, -3) and the directrix is y = 3. What is the equation of the parabola?
OleMash [197]

Answer:

The equation of the parabola is y = -12\cdot x^{2}.

Step-by-step explanation:

Since the directrix is of the form y = a, the parabola is vertical. The vertex of the parabola (V(x,y)) is the midpoint between the focus (F(x,y)) and a point of the directrix (P(x,y)), that is to say:

V(x,y) = \frac{1}{2}\cdot F(x,y) + \frac{1}{2}\cdot P(x,y) (1)

If we know that F(x,y) = (0, -3) and P(x,y) = (0, 3), then the coordinates of the vertex of the parabola:

V(x,y) = \frac{1}{2}\cdot (0, -3) + \frac{1}{2}\cdot (0, 3)

V(x,y) = (0, 0)

The vertex factor (p) is the distance of the focus with respect to the vertex:

p = \sqrt{[F(x,y)-V(x,y)]\,\bullet \,[F(x,y)-V(x,y)]} (2)

If we know that F(x,y) = (0, -3) and V(x,y) = (0, 0), then the vertex factor is:

p = \sqrt{0^{2}+(-3)^{2}}

p = -3

The equation of the parabola in the vertex form is described below:

y - k = 4\cdot p \cdot (x-h)^{2} (3)

Where:

x - Independent variable.

y - Dependent variable.

h, k - Coordinates of the vertex.

If we know that (h,k) = (0, 0) and p = -3, then the equation of the parabola is y = -12\cdot x^{2}.

6 0
2 years ago
Can someone help me please please please
marissa [1.9K]
Use the Pythagorean theorem a^{2} + b^{2} = c^{2} to find the missing side length of a right triangle 

In this case, after you plug in the given numbers your equation is 12^{2} +  y^{2}  =  20^{2}

Then, Just solve that equation for y.

144 +  y^{2} = 400

x^{2} = 256

\sqrt{} y^{2}  =  \sqrt{256}

y = 16

So the answer is B, 16 cm.

I hope this helps, please feel free to ask questions if you're still confused :)
7 0
3 years ago
How to find the bin size
labwork [276]
To find the area of a rectangular prism multiply length by width by height.


If the problem has a variable take the two other dimensions and multiply them together. Then take that number and subtract it from the total to find the number that the variable equals.
3 0
3 years ago
the ratio of boys to girls at the beach clean up was 7:8 if there are 42 boys how many girls are there
Len [333]
48 girls are there. Given that there is a ratio of boys to girls of 7:8. Then divide 42 boys by 7 boys which equals 6. After, multiply 6 by 8 girls equals 48 girls.

4 0
3 years ago
Find the area of the trapezoid.
ss7ja [257]

\bf \textit{area of a trapezoid}\\\\
A=\cfrac{h(a+b)}{2}~~
\begin{cases}
a,b=\stackrel{bases}{parallel~sides}\\
h=height\\[-0.5em]
\hrulefill\\
a=15.8\\
b=21.8\\
h=11.7
\end{cases}\implies A=\cfrac{11.7(15.8+21.8)}{2}
\\\\\\
A=\cfrac{11.7(37.6)}{2}\implies A=219.96

4 0
3 years ago
Read 2 more answers
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