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3 years ago

Write an equation of the line that passes through the point (3,-2) with slope -2.

Mathematics

1 answer:

Virty [35]3 years ago

4 0

Answer:

y + 4 = -2(x - 3)

Step-by-step explanation:

Use the point-slope formula y - k = m(x - h). Substitute -2 for k and 3 for h, as well as -2 for m:

y + 4 = -2(x - 3).

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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

3 years ago

Is 10 thousands, 5 hundreds greater than or less than 1,050 tens

Olegator [25]

Its greater than 1,050 tens.

4 0

4 years ago

Read 2 more answers

Help please!!!!!!!!!!!!!

kaheart [24]

Answer:

Step-by-step explanation:

6x3=18

8-3=5

6+1=7

7x5=35

35+18=53

I hope this helps!

5 0

3 years ago

Help with #9<br> ASAP PLEASE.

yawa3891 [41]

you add the amount of people in each section that fits into the category. So, 11 people from 6-6:29 and 15 people from 6:30-6:59 and then 8 people from 7:30-7:59 so you get 34 people total

5 0

3 years ago

In the year 2007, a company made $2.2 million in profit. For each consecutive year

balu736 [363]

Answer:

1.7

Step-by-step explanation:

8 0

3 years ago

Read 2 more answers