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4 years ago

Which of these points lies on the line described by the equation below?

Mathematics

1 answer:

Taya2010 [7]4 years ago

8 0

Answer:

Step-by-step explanation:

The slope-point form of an equation of a line:

$y-y_1=m(x-x_1)$

m - slope

(x₁, y₁) - point on a line

We have the equation:

$y-4=-2(x-6)$

hence

$m=-2,\ x_1=6,\ y_1=4\to(6,\ 4)$

Check other points:

Substitute the coordinates of the points into the equation and check the equality:

A. (-6, -4)

-4 - 4 = -2(-6 - 6)

-8 = 24 FALSE

C. (-4, -6)

-6 - 4 = -2(-4 - 6)

-10 = 20 FALSE

D. (4, 6)

6 - 4 = -2(4 - 6)

2 = 4 FALSE

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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

3-2y-1+5x^2-7y+7+4x^2

MakcuM [25]

Answer: Hi!

The only thing we can do to simplify the equation is combine like terms.

5x^2 + 4x^2 = 9x^2

-2y - 7y = -9y

3 - 1 + 7 = 9

Our equation now looks like this:

9x^2 - 9y + 9

We have nothing left to simplify, so we're done!

Hope this helps!

8 0

3 years ago

How high is a tree that casts a 25 ft shadow at the same time a 7ft pole casts a shadow which is 4 ft long?

Olegator [25]

Answer:

x=12

Step-by-step explanation:

height of tree)/(shadow length of tree) = (height of pole)/(shadow length of pole)

x/26 = 6/13

13x = 26*6

13x = 156

x = 156/13

x = 12

(hope this helps can i plz have brainlist :D hehe)

4 0

3 years ago

What is the product of 25 and (6/5n + 3 1/4)

kiruha [24]

Answer:

999

Step-by-step explanation:

7 0

3 years ago

Please help me thank

Dafna11 [192]

Answer:

laccolith

Step-by-step explanation:

A laccolith is a dome shaped intrusive body that has intruded between layers of sedimentary rock. The rising magma forces the overlying layers to rise up into a dome

6 0

3 years ago