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DiKsa [7]
4 years ago
9

Solve the inequality. Show your work 6y -8 ≤ 10

Mathematics
2 answers:
emmainna [20.7K]4 years ago
6 0

6y-8≤10

Add 8 to both sides

6y-8+8≤10+8

Simplify

6y≤18

Divide both sides by 6

6y/6  ≤   18/6

Simplify

y  ≤ 3

prohojiy [21]4 years ago
4 0
6y - 8 ≤ 10   Add 8 to both sides
     6y ≤ 18   Divide both sides by 6
       y ≤ 3

Y is less than or equal to 3.

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What is the coefficient in the following expression?
frosja888 [35]

Answer:

5

Step-by-step explanation:

A coefficient is a number used to multiply a variable. in "5a" 5 is the coefficient.

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3 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
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7 0
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S:
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Answer:

A

Step-by-step explanation:

5 0
3 years ago
What is (3.5 x 10^-5) (3 x 10^-10)
Kryger [21]
It is 1.05 E-14 that's the answer

7 0
3 years ago
Read 2 more answers
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