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3 years ago

Which sequence is modeled by the graph below?

2 answers:

6 0

First, we inspect what type of sequence is the order of the coordinates:
a2 = 1
a3 = 2
a4 = 4

Getting the difference,
a3 - a2 = 1
a4 - a3 = 2

The differences are not equal; hence, the sequence is not arithmetic.

Getting the ratio:
a3/a2 = 2
a4/a3 = 2

The common ratio is 2. Using the general form for a geometric series:
an = a1 r^(n-1)
If n = 2
1 = a1 (2)^(2-1)
a1 = 1/2

So,
an = (1/2) (2)^(n-1)

The answer is the first option.

strojnjashka [21]3 years ago

6 0

Answer:

an = one half(2)n − 1

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Exercise 5.2. Suppose that X has moment generating function

soldi70 [24.7K]

Answer:

a) Mean, E(X) = - 0.5

Variance = = 9.25

b) $M_{X}(t)=E(e^{tX})$

⇒ $=\sum e^{tx}p(x)$

⇒ $=\frac{1}{2}+\frac{1}{3}e^{-4t}+\frac{1}{6}e^{5t}$

Step-by-step explanation:

Given:

moment generating function of X as:

MX(t) = $\frac{1}{2} + \frac{1}{3}e^{-4t} + \frac{1}{6} e^{5t}$

a) Now

Mean, E(X) = $M_{X}'(t=0)$

Thus,

$M_{X}'(t)=\frac{1}{3}(-4)e^{-4t}+\frac{1}{6}(5)e^{5t}$

$M_{X}'(t)=\frac{-4}{3}e^{-4t}+\frac{5}{6}e^{5t}$

also,

$E(X^{2})=M_{X}''(t=0)$

Thus,

$M_{X}''(t)=\frac{-4}{3}(-4)e^{-4t}+\frac{5}{6}(5)e^{5t}$

$M_{X}''(t)=\frac{16}{3}e^{-4t}+\frac{25}{6}e^{5t}$

Therefore,

Mean, E(X) = $M_{X}'(t=0)=\frac{-4}{3}e^{-4(0)}+\frac{5}{6}e^{5(0)}$

Mean, E(X) = - 0.5

and

$E(X^{2})=M_{X}''(t=0)=\frac{16}{3}e^{-4(0)}+\frac{25}{6}e^{5(0)}$

$E(X^{2})$ = 9.5

also,

Variance(X) = E(X²) - E(X)²

⇒ 9.5 - (-0.5)²

= 9.25

b) Now,

Let f(x) be the PMF of X

Thus,

$M_{X}(t)=E(e^{tX})$

⇒ $=\sum e^{tx}p(x)$

⇒ $=\frac{1}{2}+\frac{1}{3}e^{-4t}+\frac{1}{6}e^{5t}$

Therefore,

at x = 0, P(x) = $\frac{1}{2}$

at x= - 4 ,P(x) = $\frac{1}{3}$

at x = 5, P(x) = $\frac{1}{6}$

Thus,

E(X) = $\sum xP(x)=0(\frac{1}{2})+(-4)(\frac{1}{3})+5(\frac{1}{6})$

E(X) = - 0.5

also, $E(X^{2})=\sum x^{2}P(x)=0^{2}(\frac{1}{2})+(-4)^{2}(\frac{1}{3})+5^{2}(\frac{1}{6})$

$E(X^{2})$ = 9.5

Hence,

Var(X) = E(X²) - E(X)²

⇒ 9.5 - (-0.5)²

= 9.25

4 0

4 years ago

-2x + 4 = 3<br>how would you solve this problem?

ikadub [295]

-2x+4=3
move the 4

-2x+4=3
-4 -4

-2x=-1
then you would move the -2 by using division

-2x=-1
__ __
-2 -2

x=0.5

4 0

3 years ago

Solve -3(x-2) <8 or -3(x-2)>12

dsp73

The solution is: x >-2/3 or x< -2

Step-by-step explanation:

we will solve the inequalities one by one

So,

First inequality is:

$-3(x-2)$

Second inequality is:

$-3(x-2)>12\\-3x+6>12\\-3x+6-6>12-6\\-3x>6\\\frac{-3x}{3} >\frac{6}{3}\\-x> 2\\x$

The solution is: x >-2/3 or x< -2

Keywords: Inequalities, compound inequalities

Learn more about inequalities at:

#LearnwithBrainly

5 0

3 years ago

Brainly for step by step correct answer ❤️

Alik [6]

Take the radius squared 10*10=100 then times that by pi which equals 314 then by 16 which is 5,024 then multiply that by 75 and get 376,800

3 0

3 years ago

Find the measure of angle A

omeli [17]

Answer:

Step-by-step explanation:

A and B are along a straight line

(3x - 20) + 2x = 180

5x = 200

x = 40

3(40) - 20 = 100°

7 0

3 years ago