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3 years ago

Find the equation of the linear relationship. Help plz :)

Mathematics

2 answers:

STALIN [3.7K]3 years ago

3 0

Answer:

f(x)= -2x+190

Step-by-step explanation:

larisa86 [58]3 years ago

3 0

Answer:

f(x)= -2x+190

Step-by-step explanation:

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Given that set A has 48 elements and set B has 21 elements, determine each of the following. (a) The maximum possible number of

yKpoI14uk [10]

Answer: The required answers are

(a) 69, (b) 21, (c) 21 and (d) 0.

Step-by-step explanation: We are given that the set A has 48 elements and the set B has 21 elements.

(a) To determine the maximum possible number of elements in A ∪ B.

If the sets A and B are disjoint, that is they do not have any common element. Then, A ∩ B = { } ⇒ n(A ∩ B) = 0.

From set theory, we have

$n(A\cup B)=n(A)+n(B)-n(A\cap B)=48+21-0=69.$

So, the maximum possible number of elements in A ∪ B is 69.

(b) To determine the minimum possible number of elements in A ∪ B.

If the set B is a subset of set A, that is all the elements of set B are present in set A. Then, n(A ∩ B) = 21.

From set theory, we have

$n(A\cup B)=n(A)+n(B)-n(A\cap B)=48+21-21=48.$

So, the minimum possible number of elements in A ∪ B is 21.

(c) To determine the maximum possible number of elements in A ∩ B.

If the set B is a subset of set A, that is all the elements of set B are present in set A. Then, n(A ∩ B) = 21.

So, the maximum possible number of elements in A ∩ B is 21.

(d) To determine the minimum possible number of elements in A ∩ B.

If the sets A and B are disjoint, that is there is no common element in the sets A and B . Then, n(A ∩ B) = 0.

So, the maximum possible number of elements in A ∩ B is 0.

Thus, the required answers are

(a) 69, (b) 21, (c) 21 and (d) 0.

6 0

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: