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avanturin [10]
3 years ago
5

Six Republicans and four Democrats have applied for two open positions on a planning committee. Since all the applicants are qua

lified to serve, the City Council decides to pick the two new members randomly. What is the probability that both come from the same party?
Mathematics
1 answer:
Dafna11 [192]3 years ago
3 0

Answer:

\displaystyle P=\frac{7}{15}=0.467

Step-by-step explanation:

<u>Probabilities</u>

When we choose from two different sets to form a new set of n elements, we use the so-called hypergeometric distribution. We'll use an easier and more simple approach by the use of logic.

We have 6 republicans and 4 democrats applying for two positions. Let's call R to a republican member and D to a democrat member. There are three possibilities to choose two people from the two sets: DD, DR, RR. Both republicans, both democrats and one of each. We are asked to compute the probability of both being from the same party, i.e. the probability is

P=P(DD)+P(RR)

Let's compute P(DD). Both democrats come from the 4 members available and it can be done in \binom{4}{2} different ways.

For P(RR) we proceed in a similar way to get \binom{6}{2} different ways.

The total ways to select both from the same party is

\displaystyle \binom{4}{2}+\binom{6}{2}=4+15=21

The selection can be done from the whole set of candidates in \binom{10}{2} different ways, so

\displaystyle P=\frac{21}{\binom{10}{2}}

\displaystyle P=\frac{21}{45}=\frac{7}{15}=0.467

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bearhunter [10]

Answer:

The inverse is 1/2x -3/2

Step-by-step explanation:

y =2x+3

Exchange x and y

x = 2y+3

Solve for y, subtracting 3 from each side

x-3 = 2y+3-3

x-3 =2y

Divide each side by 2

(x-3)/2 = 2y/2

1/2x - 3/2 =y

The inverse is 1/2x -3/2

7 0
3 years ago
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What value from the set {6, 7, 8, 9, 10} makes the equation 5x + 2 = 47 true? Show your work. (5 points)
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Answer:

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3 years ago
What is the decimal equivalent of 4/9?
NemiM [27]
What is the decimal equivalent of 4/9?


Answer is: 0.44444444
7 0
1 year ago
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If X and Y are independent continuous positive random
Leni [432]

a) Z=\frac XY has CDF

F_Z(z)=P(Z\le z)=P(X\le Yz)=\displaystyle\int_{\mathrm{supp}(Y)}P(X\le yz\mid Y=y)P(Y=y)\,\mathrm dy

F_Z(z)\displaystyle=\int_{\mathrm{supp}(Y)}P(X\le yz)P(Y=y)\,\mathrm dy

where the last equality follows from independence of X,Y. In terms of the distribution and density functions of X,Y, this is

F_Z(z)=\displaystyle\int_{\mathrm{supp}(Y)}F_X(yz)f_Y(y)\,\mathrm dy

Then the density is obtained by differentiating with respect to z,

f_Z(z)=\displaystyle\frac{\mathrm d}{\mathrm dz}\int_{\mathrm{supp}(Y)}F_X(yz)f_Y(y)\,\mathrm dy=\int_{\mathrm{supp}(Y)}yf_X(yz)f_Y(y)\,\mathrm dy

b) Z=XY can be computed in the same way; it has CDF

F_Z(z)=P\left(X\le\dfrac zY\right)=\displaystyle\int_{\mathrm{supp}(Y)}P\left(X\le\frac zy\right)P(Y=y)\,\mathrm dy

F_Z(z)\displaystyle=\int_{\mathrm{supp}(Y)}F_X\left(\frac zy\right)f_Y(y)\,\mathrm dy

Differentiating gives the associated PDF,

f_Z(z)=\displaystyle\int_{\mathrm{supp}(Y)}\frac1yf_X\left(\frac zy\right)f_Y(y)\,\mathrm dy

Assuming X\sim\mathrm{Exp}(\lambda_x) and Y\sim\mathrm{Exp}(\lambda_y), we have

f_{Z=\frac XY}(z)=\displaystyle\int_0^\infty y(\lambda_xe^{-\lambda_xyz})(\lambda_ye^{\lambda_yz})\,\mathrm dy

\implies f_{Z=\frac XY}(z)=\begin{cases}\frac{\lambda_x\lambda_y}{(\lambda_xz+\lambda_y)^2}&\text{for }z\ge0\\0&\text{otherwise}\end{cases}

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f_{Z=XY}(z)=\displaystyle\int_0^\infty\frac1y(\lambda_xe^{-\lambda_xyz})(\lambda_ye^{\lambda_yz})\,\mathrm dy

\implies f_{Z=XY}(z)=\lambda_x\lambda_y\displaystyle\int_0^\infty\frac{e^{-\lambda_x\frac zy-\lambda_yy}}y\,\mathrm dy

I wouldn't worry about evaluating this integral any further unless you know about the Bessel functions.

6 0
3 years ago
The Poe family bought a house for $240,000. If the value of the house increases at a rate of 4% per year, about how much will th
Eddi Din [679]

Answer:

  about $525,900

Step-by-step explanation:

Each year, the value is multiplied by (1 +4%) = 1.04. After 20 years, it will have been multiplied by that value 20 times. That multiplier is 1.04^20 ≈ 2.19112314.

The value of the house in 20 years will be about ...

  $240,000×2.19112314 ≈ $525,900 . . . . . rounded to hundreds

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2 years ago
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