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astraxan [27]
3 years ago
5

How many bottles are needed to hold 3.5 liters of juice?

Mathematics
1 answer:
Kisachek [45]3 years ago
7 0
7 bottles i believe, not rlly sure
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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
The length of the rectangle is 3 cm and the width is 5 cm what will the area be?
WINSTONCH [101]

Answer:

15 cm²

Step-by-step explanation:

3(5)=15 cm²

3 0
3 years ago
What is the discount given on a jacket that was originally priced $90 and is now $72?
torisob [31]

Answer:

Step-by-step explanation:

The disCount will be the differenceb

7 0
3 years ago
If X squared equals 16 then X equals 4
AfilCa [17]
That would be correct because if x times x =16 than that means that the square root of 16 is 4
6 0
3 years ago
PLEASE HELP ME <br> THIS IS DUE IN 10 MINUTES
gizmo_the_mogwai [7]

Answer:

C and D. You're welcome :)

Step-by-step explanation:

7 0
3 years ago
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