8. The moment generating function of X is given by Mx(t) = e4e¹-4 and that of W is given by Mw (t) = 2t. Assume also that X and W are independent. Compute 2-et (a) P(W + 2X = 3), (b) E(XW).

(a) Strings in L: "abb", "aabbb". (b) Strings not in L: "aabb", "bb".

(c) State diagram for a deterministic Turing Machine with 10 states is given below.

(a) Two strings that are in L are:

1. `abb` (Here, i = 0, and w is an empty string).

2. `aabbb` (Here, i = 2, and w = "aa").

(b) Two strings over the same alphabet that are not in L are:

1. `aabb` (Here, the length of w is 2, but there are more than two 'a's before the 'bb').

2. `bb` (Here, the length of w is 0, but there are 'b's before the 'bb', violating the condition).

(c) Here is the state diagram for a deterministic Turing Machine with 10 states that decides L:

```START --> A --> B --> C --> D --> E --> F --> G --> H --> ACCEPT

  a      b      b      a      a      b      b      a      b

  |      |      |      |      |      |      |      |      |

  v      v      v      v      v      v      v      v      v

REJECT  REJECT REJECT  A      E      F      REJECT REJECT REJECT

  |      |      |      |      |      |      |      |      |

  v      v      v      v      v      v      v      v      v

REJECT  REJECT REJECT  REJECT REJECT REJECT  G      H      REJECT

  |      |      |      |      |      |      |      |      |

  v      v      v      v      v      v      v      v      v

REJECT  REJECT REJECT  REJECT REJECT REJECT REJECT REJECT REJECT```

In this state diagram, the machine starts at the START state and reads input symbols 'a' or 'b'. It transitions through states A, B, C, D, E, F, G, and H depending on the input symbols.

If the machine reaches the ACCEPT state, it accepts the input, and if it reaches any of the REJECT states, it rejects the input. The machine accepts inputs of the form `a^i b^bw` where the length of w is i.

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The complete question is:

Let L = {a(^i)bbw|w ∈ {a, b} ∗ and the length of w is i}.

(a) Give two strings that are in L.

(b)Give two strings over the same alphabet that are not in L.

(c)Give the state diagram for a deterministic Turing Machine that decides L. To receive full credit, your Turing Machine shall have no more than 10 states.

The answer of the question based on population growth is , the estimated population after one year is approximately 34 deer.

To estimate the population after one year, we can use the formula for exponential growth:

P = P0 * (1 + r)^t.

P0 represents the initial population (20 deer in this case), r represents the growth rate (70% or 0.7 as a decimal), and t represents the time period in years (1 year in this case).

Using these values, we can calculate the population after one year as follows:

P = 20 * (1 + 0.7)¹
P = 20 * 1.7
P ≈ 34

Therefore, the estimated population after one year is approximately 34 deer.

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The algebraic expression representing the cost of t tickets: Cost = (135 * t) + 12.

The cost of purchasing 3 tickets at the Disco is $417.

Part A:

Let "t" be the number of tickets purchased. The cost of one ticket is $135 and there is a one-time transaction fee of $12. So the total cost for "t" tickets can be represented as:

Cost = (135 * t) + 12

Part B:

To calculate the cost of purchasing 3 tickets, we substitute "t" with 3 in the expression we just created:

Cost = (135 * 3) + 12

Cost = 405 + 12

Cost = $417

Therefore, the cost of purchasing 3 Panic! At the Disco tickets is $417.

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Answer:

6×4

2×12

8×3

Step-by-step explanation:

I know!

Answer:

answer is m = 5 + 2G^2

Step-by-step explanation:

first we have to cancel out the √ by powering both sides by 2

(G) ^2 =(√ m-5/2)^ 2

the 2 on the right side cancels out the √ which will be

G^2 = m - 5/2

we then cross multiply on both sides which will give us:

2*G^2 = m - 5

then carry 5 to the other side

2G^2 +5 = m - 5+5

therefore m = 5 + 2G ^2

clear steps in the picture

hope that helps

Answer:

answer is m = 5 + 2G^2

your welcome

Answer:

The letter "x" is often used in algebra to mean a value that is not yet known. It is called a "variable" or sometimes an "unknown". In x + 2 = 7, x is a variable, but we can work out its value if we try! A variable doesn't have to be "x", it could be "y", "w" or any letter, name or symbol.

Step-by-step explanation:

It is called a "variable" or sometimes an "unknown"

A variable is an abstract storage location paired with an associated symbolic name, which contains some known or unknown quantity of information referred to as a value; or in simpler terms, a variable is a named container for a particular set of bits or type of data.

here, we have,

The letter "x" is often used in algebra to mean a value that is not yet known.

It is called a "variable" or sometimes an "unknown".

In x + 2 = 7, x is a variable, but we can work out its value if we try!

A variable doesn't have to be "x", it could be "y", "w" or any letter, name or symbol.

Hence, x is called a "variable" or sometimes an "unknown".

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Answer:

c

Step-by-step explanation:

x=1 g(x)=-10

x=2 g(x)=-12

x=3 g(x)=-14

f(x)=x+4

=＞ g(x)=-2·(x+4)

Answer:

the  mean and standard error of the mean are 200 and 2 respectively.

Step-by-step explanation:

Given that ;

the sample size n = 81

population mean μ = 200

standard deviation of the infinite population σ = 18

A population  is the whole set of values, or individuals you are interested in, from an experimental study.

The value of population characteristics such as the  Population mean (μ), standard deviation (σ) are said to be known as the population distribution.

From the given information above;

The sample size is large and hence based on the central limit theorem the mean of all the means is same as the population mean 200.

i.e

\(\mu = \bar \mu_x\) = 200

∴ The mean = 200

and the standard error of the mean can be determined via the relation:

\(\mathbf{standard \ error \ of \ mean = \dfrac{\sigma}{\sqrt {n}}}\)

\(\mathbf{standard \ error \ of \ mean = \dfrac{18}{\sqrt {81}}}\)

\(\mathbf{standard \ error \ of \ mean = \dfrac{18}{9}}\)

\(\mathbf{standard \ error \ of \ mean =2}\)

Therefore ; the  mean and standard error of the mean are 200 and 2 respectively.

Answer:

can u plz put a picture

Step-by-step explanation:

Answer:

I think it’s D not sure tho

Step-by-step explanation:

Answer:

D.

Step-by-step explanation:

Try them all out.

0.12/6=0.02

0.03/6=0.005

0.3/6=0.05

1.2/6=0.2

D is the answer.

The volume of the prism as shown in the diagram below is 54 in³.

Volume is the space contained in a solid shape.

To calculate the volume of the prism, we use the formula below

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1

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Answer:

The prime factorization of 110 is: 2 x 5 x 11.

The necessary components to describe a rotation on a coordinate plane include the center of rotation, the shape of the figure, and the number of degrees of rotation.

To describe a rotation of a figure on a coordinate plane, the necessary components include the center of rotation, the shape of the figure, and the number of degrees of rotation.

a. The center of rotation is a fixed point around which the figure rotates. It serves as the anchor for the rotation and determines the position of the figure after the rotation is applied.

b. The shape of the figure refers to its size, proportions, and geometric characteristics. This information is crucial as the figure retains its original shape during the rotation.

c. The number of degrees of rotation determines the magnitude of the rotation. It specifies how much the figure is rotated around the center of rotation. Positive angles indicate counterclockwise rotations, while negative angles represent clockwise rotations.

d. The direction of rotation is not necessary to describe a rotation on a coordinate plane. The rotation can be defined solely by the center, shape, and angle of rotation.

In summary, the essential components to describe a rotation on a coordinate plane include the center of rotation, the shape of the figure, and the number of degrees of rotation. The direction of rotation is not required to define the rotation.

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the answer is 165 I think because I didn't understand the question

Answer:

Step-by-step explanation:

y = 1/3x - 1 -7

y = 1/3x - 8

Trinomials are expressions with three terms

The factor is not an intelligent guess, because the expression can be further simplified

The factor is given as:

(4x - 2)(3x + 5)

The above factor can further be factorized.

This is shown below

(4x - 2)(3x + 5) = 2(2x - 1)(3x + 5)

Hence, the factor is not an intelligent guess, because the factor can still be further simplified

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Using linear functions, the cost will be the same, of $70, when there are 5 students.

A linear function is modeled by:

y = mx + b

In which:

In this problem, the functions are:

The costs are the same when:

45 + 5x = 35 + 7x

2x = 10

x = 5.

The cost is:

y = 45 + 5 x 5 = $70.

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Answer:

-32

Step-by-step explanation:

7^2 = 49

3^4 = 81

49-81=

-32

Answer: -6x + -9y

Step-by-step explanation:

You just distribute the negative with each term

Answer:

\(f(x)=16x^4+96x^{3}+216x^{2}+216x+81\)

Step-by-step explanation:

The function f(x) = (2x + 3)⁴ is a fourth-degree polynomial function.

It can be expanded using the binomial theorem.

\(\boxed{\begin{minipage}{5cm} \underline{Binomial Theorem}\\\\$\displaystyle (a+b)^n=\sum^{n}_{k=0}\binom{n}{k} a^{n-k}b^{k}$\\\\\\where \displaystyle \binom{n}{k} = \frac{n!}{k!(n-k)!}\\\end{minipage}}\)

Comparing the given function with (a + b)ⁿ:

Substitute these values into the binomial theorem formula:

\(\displaystyle (2x+3)^4=\binom{4}{0}(2x)^{4-0}3^{0}+\binom{4}{1}(2x)^{4-1}3^{1}+\binom{4}{2}(2x)^{4-2}3^{2}+\binom{4}{3}(2x)^{4-3}3^{3}+\\\\\\\phantom{wwww}\binom{4}{4}(2x)^{4-4}3^{4}\)

Solve:

\(\begin{aligned}\displaystyle (2x+3)^4&=\binom{4}{0}(2x)^4\cdot3^0+\binom{4}{1}(2x)^{3}\cdot3^1+\binom{4}{2}(2x)^2\cdot3^2+\binom{4}{3}(2x)^{1}\cdot3^3+\binom{4}{4}(2x)^0\cdot3^4\\\\&=\binom{4}{0}16x^4\cdot1+\binom{4}{1}8x^3\cdot3+\binom{4}{2}4x^2\cdot9+\binom{4}{3}2x\cdot27+\binom{4}{4}\cdot81\\\\&=\binom{4}{0}16x^4+\binom{4}{1}24x^3+\binom{4}{2}36x^2+\binom{4}{3}54x+\binom{4}{4}81\\\\&=1\cdot16x^4+4\cdot24x^3+6\cdot36x^2+4\cdot54x+1\cdot81\\\\&=16x^4+96x^3+216x^2+216x+81\end{aligned}\)

Therefore, the expanded function is:

\(f(x)=16x^4+96x^{3}+216x^{2}+216x+81\)

\( \Large{\boxed{\sf F(x) = (2x + 3)^4 = 16x^4 + 96x^3 + 216x^2 + 216x + 81 }} \)

\( \\ \)

To expand the given function, we will apply the binomial theorem, which is the following:

\(\sf(a+b)^n =\sf\sum\limits_{k=0}^{n} \binom{n}{k}a^{n-k}b^{k} \\ \\ \sf \:Where\text{:} \\ \star \: \sf n \: is \: a \: positive \: integer. \: ( n \in \mathbb{N}) \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \sf \star \: k \: is \: a \: positive \: integer \: less \: than \: or \: equal \: to \: n. \: (k \leqslant n, \: k \: \in \: \mathbb{ N}) \\ \\ \\ \sf \star \: \displaystyle\binom{ \sf \: n}{ \sf \: k} \: \sf is \: a \: \underline{binomial \: coefficient} \: and \: is \: calculated \: as \: follows\text{:} \\ \\ \\ \sf \displaystyle\binom{ \sf \: n}{ \sf \: k} = \sf \dfrac{n! }{(n - k)! k ! }\)\( \\ \\\)

\( \\ \)

\( \\ \)

\( \sf F(x) = (\underbrace{\sf 2x}_{\sf a} + \underbrace{3}_{\sf b})^{\overbrace{\sf 4}^{n}} \\ \\ \implies \sf a = 2x \: \: ,b = 3 \: \: ,n = 4 \)

\( \\ \)

\( \\ \)

\( \sf (2x + 3)^4 = \displaystyle\sum\limits_{ \sf k=0}^{ \sf 4} \binom{ \sf 4}{ \sf k}( \sf 2x)^{4-k}(3)^{k} \\ \\ \\ \sf = \binom{ \sf 4}{ \sf 0}( \sf 2x)^{4-0}(3)^{0} + \binom{ \sf 4}{ \sf 1}( \sf 2x)^{4-1}(3)^{1} + \binom{ \sf 4}{ \sf 2}( \sf 2x)^{4-2}(3)^{2} + \binom{ \sf 4}{ \sf 3}( \sf 2x)^{4-3}(3)^{3} + \binom{ \sf 4}{ \sf 4}( \sf 2x)^{4-4}(3)^{4} \\ \\ \\ \sf = \binom{ \sf 4}{ \sf 0}( \sf 2x)^{4}(3)^{0} + \binom{ \sf 4}{ \sf 1}( \sf 2x)^{3}(3)^{1} + \binom{ \sf 4}{ \sf 2}( \sf 2x)^{2}(3)^{2} + \binom{ \sf 4}{ \sf 3}( \sf 2x)^{1}(3)^{3} + \binom{ \sf 4}{ \sf 4}( \sf 2x)^{0}(3)^{4} \\ \\ \\ \sf = \binom{ \sf 4}{ \sf 0}( \sf 16 {x}^{4} ) + \binom{ \sf 4}{ \sf 1}( \sf 24 {x}^{3}) + \binom{ \sf 4}{ \sf 2}( \sf 36x^{2}) + \binom{ \sf 4}{ \sf 3}( \sf 54x) + \binom{ \sf 4}{ \sf 4}(81) \)

\( \\ \)

\( \\ \)

\( \\ \star \: \displaystyle\binom{ \sf 4}{\sf \: 0} = \sf \dfrac{4! }{(4-0)!0 ! } = \dfrac{4!}{4!0!} = \dfrac{4!}{4!} = \boxed{\sf 1} \\ \\ \star\:\displaystyle\binom{ \sf 4 }{ \sf \: 1} =\sf \dfrac{4! }{(4 - 1)!1 ! } = \dfrac{4!}{3!1!}= \dfrac{2\times 3 \times 4}{2 \times 3} = \boxed{\sf 4} \\ \\ \star \: \displaystyle\binom{ \sf 4 }{ \sf \: 2} =\sf \dfrac{4! }{(4-2)!2!} = \dfrac{4!}{2!2!}=\dfrac{2 \times 3 \times 4}{2 \times 2} = \boxed{\sf 6} \\ \\ \star \:\displaystyle\binom{ \sf 4 }{ \sf \: 3}= \sf \dfrac{4! }{(4 - 3)!3!} =\dfrac{4!}{1!3!} = \dfrac{2 \times 3 \times 4}{2 \times 3 } = \boxed{\sf 4}\\ \\ \star \:\displaystyle\binom{ \sf 4 }{ \sf \: 4}= \sf \dfrac{4! }{(4 - 4)!4 !} =\dfrac{4!}{0!4!} = \dfrac{2 \times 3 \times 4}{2 \times 3 \times 4 } = \boxed{\sf 1} \)

\( \\ \)

\( \\ \)

\( \sf (2x + 3)^4 = \binom{ \sf 4}{ \sf 0}( \sf 16 {x}^{4} ) + \binom{ \sf 4}{ \sf 1}( \sf 24 {x}^{3}) + \binom{ \sf 4}{ \sf 2}( \sf 36x^{2}) + \binom{ \sf 4}{ \sf 3}( \sf 54x) + \binom{ \sf 4}{ \sf 4}(81) \\ \\ \\ \sf = (1)(16x^4) + (4)(24x^3) + (6)(36x^2) + (4)(54x) + (1)(81) \\ \\ \\ \boxed{\boxed{\sf = 16x^4 + 96x^3 + 216x^2 + 216x + 81}} \)

\( \\ \\ \\ \)

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Answer:

hgoahdjfgggfhhfjfhfjf mark me brainliestplz

Step-by-step explanation:

Solution of the non linear equations are (-5, √11) , (-5,-√11) and (6,0)

When two or more equations are being solved concurrently, at least one of them must be a system of nonlinear equations. Be aware that just one of your equations—not all of them—can be linear in a nonlinear system.

Any function whose graph is NOT a line is said to be nonlinear. It has the equation f(x) = ax + b. With the exception of the form f(x) = ax + b, its equation can take any form. Any two points on the curve have the same slope. Every pair of points on the graph do not have the same slope.

The non linear equations are :

(i)      y² = 6 - x

(ii)     x² + y² = 36

From , (i) putting y² = 6 - x in equation (ii) we get

x² + 6 - x = 36

⇒ x² - x - 30 = 0

⇒x² +5x - 6x -30 =0

⇒x(x+5) -6(x+5) = 0

⇒(x+5)(x-6) = 0

so, x = -5 and x = 6

when x = -5

y² = 6 - x is

y² = 6 + 5 = 11

⇒ y = ±√11

and when x = 6

y² = 6 - x is

y² = 6-6

y = 0

Solution of the non lineae equations are (-5, √11) , (-5,-√11) and (6,0).

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Answer:

If a number is not a rational number, then it is not a whole number. The converse is true. ---> the sentence above is the only one that has a true condition, true hypothesis and a true conclusion.

The correct answer is option B which is (-4-√11) and (-4+√11).

Inequality is the relationship between two expressions that are not equal, employing a sign such as ≠ “not equal to,” > “greater than,” or < “less than.”.

The inequality is given as x² + 8x + 5 < 0 for we will draw a graph of the inequality and find the range of x which ranges from ( -7.31,- 0.68) So these points in the options will be equal to (-4-√11) and (-4+√11).

(-4 - √11)  = -4 -3.31 =-7.31

(-4 + √11) = -4 +3.31 = -0.68

Therefore the correct answer is option B which is (-4-√11) and (-4+√11).

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Rashawn experienced a temperature change of 85 degrees Fahrenheit given that the temperature of New York was -1 degree Fahrenheit.

Rashawn flew from his New York home to Hawaii for a week of vacation.

He left blizzard conditions and a temperature of -1 degree Fahrenheit and stepped off the airplane into 84°F weather.

Rashawn experienced a temperature change of 85 degrees Fahrenheit since he left blizzard conditions and a temperature of -1 degree Fahrenheit and stepped off the airplane into 84°F weather.

It is given that the temperature in New York was -1 degrees Fahrenheit and the temperature in Hawaii was 84 degrees Fahrenheit.

To find the temperature change, we have to subtract the temperature of New York from Hawaii.

84 - (-1) = 85

Therefore, Rashawn experienced a temperature change of 85 degrees Fahrenheit.

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Answer: 0.049

Step-by-step explanation:

Answer:

Step-by-step explanation:

0.061

For the matrix given , the element a₂₃ is the number at 2nd row and 3 column ,which is 6 , Option B is the correct answer.

It is a table or a rectangular array of numbers or expressions arranged in rows and columns ,

For a Matrix of m x n , m is the no. of rows and n is the no. of column

For the matrix given the element a₂₃ is the number at 2nd row and 3 column ,

which is 6 ,

Therefore Option B is the correct answer.

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Answer:

24.7cm^2

Step-by-step explanation:

Line PQ = 5.413590865cm

BQ = 9cm

Angle BPQ =  

5.413590865² = 9² + 9² - 2 × 9 × 9 × cos(x)

29.30696605 = 81 + 81 - 162 × cos(x)  

29.30696605 = 162 - 162 × cos(x)

-132.693034 = -162 × cos(x)

cos(x) = 0.8190928022

x = 35.00591739˚

Area of sector = 24.7cm^2

When  point B is at the centre of the circle.  So the area of the shaded sector is 24.7 \(cm^2\).

Since

Line PQ = 5.413590865cm

BQ = 9cm

Now

\(5.413590865^2 = 9^2 + 9^2 - 2 \times 9 \times 9 \times cos(x)\\\\29.30696605 = 81 + 81 - 162 \times cos(x) \\\\29.30696605 = 162 - 162 \times cos(x)\\\\-132.693034 = -162 \times cos(x)\\\\\)

cos(x) = 0.8190928022

x = 35.00591739˚

Now finally the

Area of sector = 24.7cm^2

Hence, When  point B is at the centre of the circle.  So the area of the shaded sector is 24.7 \(cm^2\).

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