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2 years ago

Which expression is equivalent to 15n – 20?

Mathematics

2 answers:

crimeas [40]2 years ago

7 0

Answer:

5(3n-4)

Step-by-step explanation:

because(5*3n)-(5*4)=15n-20

Semenov [28]2 years ago

3 0

The only thing you can do with this expression is to factor a 5 out of the two terms: we have

$15n-20 = 5(3n-4)$

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Name the property illustrated by each statement:

aniked [119]

both are correct.

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8 0

2 years ago

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

You plan to set up an endowment at your alma mater that will fund $209,000 of scholarships each year indefinitely. If the princi

Leto [7]

Answer:

$199,047.62

Step-by-step explanation:

PV = X(1+i)^nm

X=$209000

i=5% = 0.05

n=1

m=1

Pv=$209000(1+0.05)^-1x1

Pv=$209000(1.05)^-1

Pv=$209000(1/1.05)

Pv=$209000/1.05

Pv=$199,047.62

$199,047.62 is needed to be donated for investment at 5.0% compounded annually rate for a year so as to get $209,000 at end of the year for the purpose of funding the scholarship.

6 0

2 years ago

Simplify the following expression.<br><br> 99 - 3[15 - (2 + 1)]

Vikki [24]

Answer:

Step-by-step explanation:

2+1= 3

15-3= 12

12 x 3 = 36

99 - 36

= 63

6 0

2 years ago

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What is the area of a circle with a diameter of 9.2 centimeters? Round your answer ro the nearest hundredth.

nika2105 [10]

The answer the the problem is A.

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3 years ago