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3 years ago

Help please! and explain

Mathematics

1 answer:

Mashutka [201]3 years ago

6 0

A square has four equal sides to find he area of a square multiply one side by the other. If the square is 2by2by2by2 multiply 2x2 to get the area. In this case you already have the area. The area of a square can be defined as x^2 x being the length of a side = the area x^2=A substitute the value of the are x^2=37 to simplify this expression you have to cancel out the x^2 to x. Do this by using the square root. Square root of x squared is x remember you have to do this on both sides of the equation so the square root of 37 is something like 6.081937474728774738 or something and you have to round to the nearest tenth of an inch so.. The length of a side would be approximately 6.1 inches

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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

B. What integer(s) when added to -7 give a sum less than 0?

Dmitry_Shevchenko [17]

Answer:

the answer is 6 and below

4 0

3 years ago

Plz help me, plz help deku!?!

DanielleElmas [232]

Answer:

14 cm squared

Step-by-step explanation:

The shaded triangle is clearly half of the rectangle, and half of 28 is 14.

The other way you can look at it is that the dimensions of the rectangle are 4 cm and 7 cm. The area of a triangle equation is $\frac{bh}{2}$ . So $\frac{4(7)}{2}$ is 14.

7 0

3 years ago

A car rental company charges $0.10 per mile plus an initial fee of $120 for the rental of a midsize sedan. If Lawrence rents a v

anzhelika [568]

Answer:

800 miles

Step-by-step explanation:

Set up an equation, where x is the number of miles driven:

0.10x + 120 = 200

Then, solve for x:

0.10x = 80

x = 800

So, the maximum number of miles he can drive is 800 miles

4 0

3 years ago

A circle with area 9 pie has a sector with a central angle of 17/9 pie radians .

zmey [24]

Answer: 8.5π

<u>Step-by-step explanation:</u>

If I understand the question correctly, the entire circle has an Area of 9π and you are looking for the Area of the shaded region which has a central angle of $\dfrac{17}{9}\pi$

the section of the circle that is shaded is $\dfrac{\dfrac{17}{9}\pi}{2\pi}=\dfrac{17\pi}{18\pi}=\dfrac{17}{18}$

Area of the shaded region is: $9\pi \cdot \dfrac{17}{18}=\dfrac{17}{2}\pi=8.5\pi$

5 0

4 years ago

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