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3 years ago

I NEED HELP ASAP!!! Question: Which equation applies the associative property of multiplication?

Mathematics

1 answer:

Aleks [24]3 years ago

8 0

I’m not 100% but from what i know i think it’s (C.)

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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:

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

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3 years ago

9. Which transformation will place the trapezoid onto

galben [10]

Answer: B

The rotation will go back to the place where the trapezoid started

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3 years ago

David uses 1/2 cup of apple juice for every 1/4 cup of cranberry juice to make a fruit drink. Enter the number of cups of apple

mario62 [17]

Answer:

2 cups of apple juice

Step-by-step explanation:

In order to get one cup of cranberry juice, you would need to add the ratio, 1/4, four times. Since for every 1/4 cup of cranberry juice there is 1/2 cup of apple juice, add 1/2 four times

1/2 + 1/2 + 1/2 + 1/2 = 4/2 = 2 cups

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2 years ago

Mike's grandmother opened a savings account in Mike's name and deposited some money into the account. The account pays an annual

Snowcat [4.5K]

SI = prt/100
1440 = (p*9*8)/100
⇒p=2000

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3 years ago

Ivy walks from the store to her friend's house. Write the fraction that represent her constant speed, C, if she walks y miles in

dlinn [17]

Answer:

Step-by-step explanation:

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2 years ago