Is 3/7 and 10/21 proportional ? 15 points

Any value of

x

makes the equation true.

Always true

Interval Notation:

(−∞,∞)

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:

2 is the variable

Step-by-step explanation:

8(2) = 16

16-27 = -11

Answer:

Step-by-step explanation:

Step-by-step explanation:

from which text book please

Answer:

1. 46

2. 307.3

3. 40

4. 0

5. 4

6. 0

7.

8. 400

9. -1000

10. 10582

expand: Evaluate:

11. -216 21. 0.015625

12. 81 22. -216

13. 0.03125 23. 2¹.⁹²

14. -81 24. 729

15. 25. 64

16. 343

simplify.

17. 68526

18. 262144

19. 5.960464 x 10¹⁶

20. 0.003906

Step-by-step explanation:

sana maka tulong to sayo

Answer:

300

Step-by-step explanation:

1. 60/4=15

2. 15x20=300

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:

6lbs

Step-by-step explanation:

7.50 can only go into 20, two times

7.50

×   2

-------

15.00

Answer:

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

Answer:

X = 3

Bc = 6

AC = 12

Step-by-step explanation:

Hope it helped

Answer:

im pretty sure its 2025

Answer:

2025

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

v666

Answer:

16)  7⁻²

17) -1⁻²

Step-by-step explanation:

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

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

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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:

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:

2.91 Kg

Step-by-step explanation:

Tin weighs 60g, it contains 425g of baked beans, add that together to get a full tin of baked beans

= 485.

Multiply by 6 to get the total amount in grams

= 2910g.

Turn that into Kg.

2.91 kg.

The weight of 6 tins will be 2.19 Kg,

The unitary technique involves first determining the value of a single unit,  followed by the value of the necessary number of units.

For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.

12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.

As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.

This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.

Given:

Tin weighs 60g, it contains 425g of baked beans,

So, the total weight along with tin

= 425 + 60

= 485 g

Now, the weight of 6 tins

= 485 x 6

= 2190 g

= 2190/1000 Kg

= 2.19 Kg

Hence, the weight is 2.19 Kg.

Learn more about Unitary Method here:

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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:

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:

He has 31 students

Step-by-step explanation:

You know this because 49.6 ÷ 1.6 = 31

Answer:

-1/7

Step-by-step explanation:

1/5 · (-2/7) = -2/35

= -2/35 · 5/2 = -10/70

simplified -10/70

-1/7

Answer:

C=78.5

Step-by-step explanation:

C=πr²

r=1/2 of diameter

π=3.14

C=π5²

C=78.5

The circumference and the area of the circular flower bed are 31.4 feet and 78.5 square feet respectively.

It is described as a set of points, where each point is at the same distance from a fixed point (called the center of a circle).

It is given that:

A gardener makes a new circular flower bed. The bed is ten feet in diameter.

D = 10 feet

The radius r = D/2 = 10/2 = 5 feet

A = πr²

π = 3.14

A = π(5)²

A = 78.5 square feet

The circumference:

C = 2πr

C = 2(3.14)(5)

C = 31.4 feet

Thus, the circumference and the area of the circular flower bed are 31.4 feet and 78.5 square feet respectively.

Learn more about circle here:

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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:

24

Step-by-step explanation:

S = ½ × 12 × 4

S = 24

._._._._._._.

Answer:

a) 60

Step-by-step explanation:

sorry I know only of one

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:

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