At mayas house they gave out candy to trick-or-treaters

The moment generating function is defined by

[tex]M_X(t) = \mathbb E[e^{tX}][/tex]

Recall the power series expansion for the exponential function:

[tex]\displaystyle \sum_{n=0}^\infty \frac{x^n}{n!} = 1 + x + \frac{x^2}2 + \frac{x^3}6 + \cdots[/tex]

Then by extension, the MGF could be similarly written as

[tex]\displaystyle M_X(t) = \mathbb E \left[1 + Xt + \frac{(Xt)^2}2 + \frac{(Xt)^3}6 + \cdots\right][/tex]

There's a certain theorem (due to Fubini, in case you're interested in learning more about it) that let's us exchange the order of integration (recall the definition of expectation for continuous random variables) and summation, so that

[tex]\displaystyle M_X(t) = \mathbb E[1] + \mathbb E[Xt] + \mathbb E\left[\frac{X^2t^2}2\right] + \mathbb E\left[\frac{X^3t^3}6\right] + \cdots[/tex]

and by the linearity of expectation,

[tex]\displaystyle M_X(t) = 1 + \mathbb E[X] t + \frac12 \mathbb E\left[X^2\right] t^2 + \frac16 \mathbb E\left[X^3\right] t^3 + \cdots[/tex]

and here we see where the name MGF comes from: the coefficient of the n-th order term in the series expansion "generates" the n-th moment, which is defined as E[Xⁿ].

Now, recall the definition of variance:

[tex]\mathrm{Var}(X) = \mathbb E\left[\left(X - \mathbb E[X]\right)^2\right][/tex]

[tex]\mathrm{Var}(X) = \mathbb E\left[X^2\right] - \mathbb E[X]^2[/tex]

and this is exactly the difference between the second moment and the square of the first moment.

So if you know the MGF, then you essentially get the variance for free with little effort. By differentiating the MGF, we get

[tex]\displaystyle M_X''(t) = \mathbb E[X] + \mathbb E\left[X^2\right] t + \frac12 \mathbb E\left[X^3\right] t^2 + \cdots[/tex]

and setting t = 0 lets us recover the first moment, E[X].

Differentiating again gives

[tex]\displaystyle M_X'(t) = \mathbb E\left[X^2\right] + \mathbb E\left[X^3\right] t + \cdots[/tex]

and setting t = 0 once again recovers the second moment.

Then in terms of the MGF, we have

[tex]\boxed{\mathrm{Var}(X) = M_X''(0) - M_X'(0)^2}[/tex]

Answer:

39.1 megabytes

Step-by-step explanation:

Percentages are out of a hundred, so 15.7% is 15.7 out of 100, aka 15.7/100, which is 0.157.

Now, you just need to multiple this number by 249 megabytes to get 0.157 * 249 = 39.093 which rounds to 39.1

Answer:

value of r is 6

Step-by-step explanation:

Given that the slope is 1/2

So we can set up the linear equation like this:

y= 1/2x + b

Since it also goes through (-5, 2)

plug in:

[tex]2 = \dfrac12*-5 + b\\b=2 +2.5 = 4.5\\y = \dfrac12x +4.5[/tex]

Then we plug in x=3 to find out the value of r

[tex]r = \dfrac12*3+4.5=1.5+4.5=6[/tex]

Step-by-step explanation:

from which text book please

Answer:

v=(-4w)/(-w+2)

Answer:

2x² + 2x - 24

Step-by-step explanation:

We can use the FOIL method to multiply the terms together and then find the values in our trinomial. First, the F in FOIL. It stands for first, and we need to multiply the first terms in the two expressions. These terms are 2x and x. Multiplying 2x by x gives us 2x², so that's our first term.

Next, the O in FOIL. It stands for outside, and we need to multiply the terms on the very left and the very right. These are 2x and -3, and multiplying 2x by -3 gives us -6x. That's our second term.

Now, the I in FOIL. It stands for inside, so we need to multiply the terms in the middle of the expressions. Those are 8 and x, and we multiply those together to get 8x. That's our third term.

Finally, the L in FOIL. This stands for last; we need to multiply the last terms of each expression. Those are 8 and -3, and we can multiply those to get -24. Now we can get all our terms added together and simplify as needed.

2x² - 6x + 8x - 24

We can simplify -6x and 8x since they are like terms.

2x² + 2x - 24

And there is our trinomial. Hopefully that's helpful! :)

Answer:

300

Step-by-step explanation:

1. 60/4=15

2. 15x20=300

Step-by-step explanation:

A = 690ft + B

A + B = 1.384ft

(690ft + B) + B = 1.384ft

2B = 1.384ft - 690ft

2B = 694ft

B = 694ft ÷ 2

B = 347ft

A = 690ft + B

A = 690ft + 347ft

A = 1.037ft

Tower A → 1.037 feet

Tower B → 347feet

Any value of

x

makes the equation true.

Always true

Interval Notation:

(−∞,∞)

Answer:

X = 3

Bc = 6

AC = 12

Step-by-step explanation:

Hope it helped

Answer:

y = 4/3x + 4

Step-by-step explanation:

The y intercept is 4. So if we look the 2 points are (-3,0) and (0,4)

So the run is 3 and rise 4

so 4/3 is the slope

Answer:

Distance = 4

Step-by-step explanation:

Given the linear equation of line ℓ, y = 5 which is a horizontal line in which its slope, m = 0 (zero slope), and each of the x-coordinates along the line have the same y-coordinate of y = 5.

In order to determine the distance of the horizontal line from the given point Q, (0, 1), use the following distance formula:

[tex]d = \sqrt{(x_2 - x_1)^{2} + (y_2 - y_1)^{2}}[/tex]

Choose any x-coordinate to pair with the y-coordinate, y = 5. Let's use the y-intercept, (0, 5).

Let  (x₁, y₁) = (0, 1)  

      (x₂, y₂) = (0, 5)  

Substitute these values into the distance formula:

[tex]d = \sqrt{(x_2 - x_1)^{2} + (y_2 - y_1)^{2}}[/tex]

[tex]d = \sqrt{(0 - 0)^{2} + (5 - 1)^{2}}[/tex]  

[tex]d = \sqrt{(4)^{2}}[/tex]

[tex]d = \sqrt{16}[/tex]

d = 4  

Therefore, the distance of line ℓ from point Q is 4.

Step-by-step explanation:

We know ,

=> Sum = a / 1 - r

=> 15 = 3/1-r

=> 15 - 15r = 3

=> 15r = 18

=> r = 18/15

=> r = 6/5

Answer:

19 to 21

Step-by-step explanation:

Head table is for 6 attendants

158 to 174 - 6 attendants

152 to 168 people for round tables

each round table can sit 8 guests

so, 152/8  168/8

19 to 21

Answer:

D. 21 to 23

Step-by-step explanation:

1. First, you use the biggest number of guests just to be safe. Since there will be about 174 guests attending

2. you divide 174 by the number of seats a round table can hold. Since the number is 8, you 174/8 which is 21.75.

3. You round up to the biggest number of tables that has the number 21 in it.

4. Your answer is D. 21 to 23

Answer:

try kopo

Step-by-step explanation:

55+1200+300=1555

Answer:

Step-by-step explanation:

start by graphing it (see picture)

formula for a parabola: y=ax²

using the coordinates (600,55) we get

55=a*600²

a=55/(600²)

so now it's just a matter of plugging in 300 for x

(55/600²)*300²= 13.75

Answer:

130

Step-by-step explanation:

(x - 129) * 129 = 129

x - 129 = 129/129

x - 129 = 1

x = 129 + 1

x = 130

Answer:

x could equal 130 but I'm not sure about this one

Step-by-step explanation:

you take 130-129 which equal 1 then times 1 by 129 and it equals 129... again sorry if it's not right because I'm not entirely sure how to do this I'm pretty sure I did it correct though

Answer:

2 is the variable

Step-by-step explanation:

8(2) = 16

16-27 = -11

Answer:

A

Step-by-step explanation:

v666

Answer:

im pretty sure its 2025

Answer:

2025

Step-by-step explanation:

Answer:

16)  7⁻²

17) -1⁻²

Step-by-step explanation:

plug in the x=, y=, and n= into the equation.

Answer:

The total value of toys the factory produces in a day is $10,000.

Step-by-step explanation:

One Toy = $10

Workers = 40

Toys Made By Each Worker Per Day = 25

The factory makes 1,000 toys per day and 5,000 toys per week. Each toy has a value of $10 so the value of toys in one day would add up to $10,000. The toy factory would also make $50,000 a week.

Answer:

I think it is parallel

Step-by-step explanation:

Answer:

He has 31 students

Step-by-step explanation:

You know this because 49.6 ÷ 1.6 = 31

Answer:

19j-9

HOPE THIS HELPS

- Todo ❤️

Step-by-step explanation:

10+9=19j

-7-2=9

Answer:

a) 60

Step-by-step explanation:

sorry I know only of one

The solutions to the questions if y is represented by the formula y = a(x - 100)(x - 200) are:

a) The value of a = -2000

b) The maximum profit the company can make = $5,000,000

To make maximum profit, 150 computers must be produced

c) The company must produce between 140 and 160 computers to make at least $4,800,000

The equation representing the company's profit is:

y = a(x - 100)(x - 200)  for x > 20

If 120  computers are produced, the profit will be $3,200,000

That is, y = 3,200,000 if x = 120

a) Find the value of a

3,200,000 = a(120 - 100)(120 - 200)

3200000 = -16000a

a = -3200000/1600

a = -2000

b) Maximum profit the company can make

The equation becomes:

y = -2000(x - 100)(x - 200)

y = -2000(x² - 200x - 100x + 20000)

y = -2000(x² - 300x + 20000)

y = -2000x² + 600000x - 40000000

dy/dx = -4000x + 600000

dy/dx = 0 at maximum value

-4000x  +  600000 = 0

4000x  =  600000

x  =  600000/4000

x   =  150

To make maximum profit, 150 computers must be produced

Substitute x = 150 into y = -2000x² + 600000x - 40000000 to find the maximum profit

y  = -2000(150²) + 600000(150) - 40000000

y = 5000000

The maximum profit the company can make = $5,000,000

c) Calculate the range of the number of computers to be produced If the company targets to make at least $4,800,000

-2000x² + 600000x - 40000000 ≥ 4800000

-2000x² + 600000x - 40000000 - 4800000 ≥ 0

-2000x² + 600000x - 44800000 ≥ 0

Divide through by -2000

x² - 300x +22400 ≤ 0

(x - 140)(x - 160) ≤ 0

140 ≤ x ≤ 160

The company must produce between 140 and 160 computers to make at least $4,800,000

Learn more here: https://brainly.com/question/25471478

Answer:

equilateral triangle is a triangle in which all 3 sides have the same length