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According to the map, which part of the Iberian Peninsula was under Christian control in the 8th century?

Mandarinka [93]

Answer:

B

Step-by-step explanation:

3 0

3 years ago

Read 2 more answers

Show that if X is a geometric random variable with parameter p, then

Lubov Fominskaja [6]

Answer:

$\sum_{k=1}^{\infty} \frac{p(1-p)^{k-1}}{k}=-\frac{p ln p}{1-p}$

Step-by-step explanation:

The geometric distribution represents "the number of failures before you get a success in a series of Bernoulli trials. This discrete probability distribution is represented by the probability density function:"

$P(X=x)=(1-p)^{x-1} p$

Let X the random variable that measures the number os trials until the first success, we know that X follows this distribution:

$X\sim Geo (1-p)$

In order to find the expected value E(1/X) we need to find this sum:

$E(X)=\sum_{k=1}^{\infty} \frac{p(1-p)^{k-1}}{k}$

Lets consider the following series:

$\sum_{k=1}^{\infty} b^{k-1}$

And let's assume that this series is a power series with b a number between (0,1). If we apply integration of this series we have this:

$\int_{0}^b \sum_{k=1}^{\infty} r^{k-1}=\sum_{k=1}^{\infty} \int_{0}^b r^{k-1} dt=\sum_{k=1}^{\infty} \frac{b^k}{k}$ (a)

On the last step we assume that $0\leq r\leq b$ and $\sum_{k=1}^{\infty} r^{k-1}=\frac{1}{1-r}$ , then the integral on the left part of equation (a) would be 1. And we have:

$\int_{0}^b \frac{1}{1-r}dr=-ln(1-b)$

And for the next step we have:

$\sum_{k=1}^{\infty} \frac{b^{k-1}}{k}=\frac{1}{b}\sum_{k=1}^{\infty}\frac{b^k}{k}=-\frac{ln(1-b)}{b}$

And with this we have the requiered proof.

And since $b=1-p$ we have that:

$\sum_{k=1}^{\infty} \frac{p(1-p)^{k-1}}{k}=-\frac{p ln p}{1-p}$

4 0

4 years ago

Which description best compares the graphs given by the equations:

nexus9112 [7]

x - 5y = -5, -5x - 25y = 25

First, you'll need to get the x variable by itself.

x - 5y = -5
 +5 +5
 x = 0
So x is plotted on the 0.

For the second part of the first equation, you'll be looking for what the y variable represents.

x - 5y = -5
-x -x
 -5y = -5
 5 5
 y = 1
So y is plotted on the 1 on the vertical line above the 0.

For the first part of the second equation, you'll do the same thing as in the first equation.

-5x - 25y = 25
 +25 +25
 -5x = 50
 5 5
x = 10
So the x for this equation is plotted on 10 on the horizontal line.

For the second part of the second equation, you will do the same thing as in the first equation.

-5x - 25y = 25
+5 +5
 -25y = 30
 25 25
y = 1.2
So the y for the second half of the second question is plotted on 1.2 on the vertical line.

<h2>Answer: B) Perpendicular</h2>

Perpendicular means the lines may or may not be of equal length and they will not be perfectly in line with each other.

Parallel means the lines may or may not be of equal length but will be perfectly in line with each other.

Intersecting means the lines may or may not be of equal length but will touch each other.

6 0

3 years ago

Which is the rate of change for the interval between –6 and –3 on the x-axis?

Naya [18.7K]

A. -2 is the correct answer for the rate of change

8 0

4 years ago

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The U.S. Mint produces quarters that weigh about 5.67 grams each. After the

lesantik [10]

The U.S. Mint makes commercial circulation coins including commemorative collection's coins including investor bullion coins.
In the case of circular coins, the quantities were measured in terms of figures for "production" numismatic categories in order "sales" and bullion "mintage" statistics.

$\to \bold{|x-5.67|=0.02}\\\\$

heaviest $\bold{=5.69\ g\\\\}$

lighest $\bold{=5.65\ g\\\\}$

Evaluating the each expression:

$\to \bold{q = -8}\\\\ \to \bold{r = -6}\\\\ \to \bold{t=3}$

Learn more:

brainly.com/question/20845315

8 0

3 years ago