Suppose that a given speech signal {UK ER: k= 1,..., n} is transmitted over a telephone cable with input-output behavior given by, Yk = ayk-1 + buk + Uk, where, at each time k, yk E R is the output, u E R is the input (speech signal value) and Uk represents the white noise!. The parameters a, b are fixed known constants, and the initial condition is yo = 0. 'If Ar + w = b, where w is a white noise vector, then the least squares estimate of a given b is the soltuion to the problem minimize || Ac – 6|12. Note than if w is a white noise vector, Dw (where D is a matrix) is not neccesarily a white noise vector. 2 We can measure the signal yk at the output of the telephone cable, but we cannot directly measure the desired signal uk or the noise signal uk. Derive a formula for the linear least squares estimate of the signal {uk, k = 1, ..., n} given the signal {Yk, k = 1,...,n}.

The ordered pair lie on the inverse of the function is (62,−3).

Option A is the correct answer.

A function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

f(x) = -(x - 1)³ - 2

The inverse of f(x).

y = -(x - 1)³ - 2

interchange x and y and solve for y.

x = -(y - 1)3 - 2

(y - 1)³ = -2 - x

(y - 1)³ = -(2 + x)

Cuberoot on both sides.

y - 1 = ∛-(2 + x)

y = ∛-(2 + x) + 1

Now,

Substitute in the inverse of g(x).

(62, -3) = (x, y)

(−4, 123) = (x, y)

(3, 1) = (x, y)

(3,−6) = (x, y)

So,

y = ∛-(2 + x) + 1

y = ∛-(2 + 62) + 1

∛-1 = -1

y = -1∛64 + 1

y = -1 x 4 + 1

y = -4 + 1

y = -3

So,

(62, -3) ______(1)

And,

y = ∛-(2 + x) + 1

y = ∛-(2 - 4) + 1

∛-1 = -1

y = ∛(-2 + 4) + 1

y = ∛2 + 1

y =  1.26 + 1

y = 2.26

So,

(-4, 2.26) _______(2)

And,

y = ∛-(2 + x) + 1

y = ∛-(2 + 3) + 1

∛-1 = -1

y = -1∛5 + 1

y = -1 x 1.71 + 1

y = -1.71 + 1

y = -0.71

So,

(3, -0.71) _______(3)

And,

y = ∛-(2 + x) + 1

y = ∛-(2 + 3) + 1

∛-1 = -1

y = -1∛5 + 1

y = -1 x 1.71 + 1

y = -1.71 + 1

y = -0.71

So,

(3, -0.71) ______(4)

Thus,

From (1), (2), (3), (4) we see that,

(62, -3) is the solution to the inverse of g(x).

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Answer:

A and C are the right statements

Without knowledge of all sides and angles, it is still possible to confirm that two triangles are comparable.

Given:

PQ/XY = QR/YZ and ∠Q ≅ ∠Y

To prove that, △PQR is similar to △XYZ.

Proof: Assume PQ > XY

Draw MN parallel to BC, we find that MQN similar to XYZ

QM/QP = QN/QR --- (1)[using the basic proportionality theorem]

Now △MQN and △XYZ are congruent thus, XY/QP = YZ/QR --- (2)

Since QM = XY from (1) and (2),

XY/QP = QM/QP = QN/QR = YZ/QR

Thus, QN = YZ by SAS congruence criterion.

△MQN ≅ △XYZ

But △MQN congruent to △XYZ,

Thus, △PQR is similar to △XYZ.

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Answer:

\(its \: dimensions \: are \to \\\boxed{w = 17.6cm} \: \boxed{l = 78.4cm} \)

Step-by-step explanation:

\(if \to l = 4w + 8 \\ but \\ \: perimeter(p )= l + w = 96 \\ 4w + 8 + w = 96 \\ 5w + 8 = 96 \\ 5w = 96 - 8 \\ 5w = 88 \\ w = \frac{88}{8} \\ \boxed{w = 17.6cm} \boxed{l = 78.4cm}\)

Answer:

2 I think i might be wrong

Answer: hers the answer

g(r)= - 3r

a) The variable x ≈ 0.958

b) x = 2/3

(a) We can rewrite the equation as follows:

\(x - x^3/3! + x^5/5! - ... = 0.4\)

Let's group the terms with even exponents together and the terms with odd exponents together:

\((x^2/2! - x^4/4! + x^6/6! - ...) - (x^3/3! - x^5/5! + x^7/7! - ...) = 0.4\)

Now we can recognize the series expansions for sine and cosine:

cos(x) - sin(x) = 0.4

Using a calculator, we can solve for x to get:

x ≈ 0.958

(b) We can rewrite the series as follows:

\(1/(3x) + 1/(9x^2) + 1/(27x^3) + ... = 3\)

Let's multiply both sides by 3x:

\(1 + 3/(3x) + 3/(9x^2) + 3/(27x^3) + ... = 9x\)

Now we can recognize the series expansion for the geometric series:

\(1 + r + r^2 + r^3 + ... = 1/(1 - r)\)

where r = 1/3x. So we have:

\(1 + 3/(3x) + 3/(9x^2) + 3/(27x^3) + ... = 1/(1 - 1/3x)\)

Multiplying both sides by (1 - 1/3x), we get:

\((1 - 1/3x) + 3/(3x)(1 - 1/3x) + 3/(9x^2)(1 - 1/3x) + 3/(27x^3)(1 - 1/3x) + ... = 1\)

Simplifying the right-hand side gives:

1 - 1/3 + 1/3 = 1

And simplifying the left-hand side gives:

2/3x = 1

So we have:

x = 2/3

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Store B sells 12591 products.

An equation is a mathematical statement that demonstrates the equality of two mathematical expressions.

Let the number of products Store A sells be x, the number of products store B sells be y, and the number of products store C be z.

Now,

Store C sells 125910 products.

z = 125910 products

Store A sells one-half as many as store C.

x = ( 1/2 )z

x = ( 1/2) × 125910

x = 62955 products

Store A sells five times as many products as store B can be expressed as the equation,

x = 5y

62955 = 5y

Dividing each side by 5,

y = 62955 / 5

y = 12591 products

Store A, B, and C sell 62955, 12591, and 125910 products.

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The percentage of tires that will have a life of 45,000 to 55,000 miles is  68.27%. So the correct option is 68.27%.

To find the percentage of tires that will have a life of 45,000 to 55,000 miles, we can use the concept of the normal distribution.

First, we calculate the z-scores for both values using the formula:
z = (x - mean) / standard deviation

For 45,000 miles:
z1 = (45,000 - 50,000) / 5,000 = -1

For 55,000 miles:
z2 = (55,000 - 50,000) / 5,000 = 1

Next, we look up the corresponding values in the standard normal distribution table. The table will provide the proportion of data within a certain range of z-scores.

The percentage of tires with a life between 45,000 and 55,000 miles is the difference between the cumulative probabilities for z2 and z1.

Looking at the standard normal distribution table, the cumulative probability for z = -1 is 0.1587, and the cumulative probability for z = 1 is 0.8413.

Therefore, the percentage of tires that will have a life of 45,000 to 55,000 miles is:
0.8413 - 0.1587 = 0.6826

Converting this to a percentage, we get:
0.6826 * 100 = 68.26%

So the correct answer is 68.27%.

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Answer:

B

Step-by-step explanation:

If we count the number of points we find out that there are 36 employees

so the fraction must go like x/36

x is the numbers of dots that are less than a 1/2 which are 1/8, 1/4 and 3/8

so x=6

6/36

1/6

so option B

Answer:

The first step when rewriting \(y = 6\cdot x^{2}+18\cdot x + 14\) consists in applying distributive property. (Step 2).

Step-by-step explanation:

We present the procedure, in which \(y = 6\cdot x^{2}+18\cdot x + 14\) is transformed into the form \(y = a\cdot (x-h)^{2} + k\):

1) \(y = 6\cdot x^{2}+18\cdot x + 14\) Given

2) \(y = 6\cdot \left( x^{2}+3\cdot x + \frac{7}{3}\right)\) Distributive property/\(\frac{a\cdot c}{b\cdot c} = \frac{a}{b}\)

3) \(y = 6\cdot \left[x^{2}+3\cdot x + \frac{7}{3}+\left(-\frac{1}{12} \right)+\frac{1}{12} \right]\) Modulative property/Existence of the additive inverse.

4) \(y = 6\cdot \left(x^{2}+3\cdot x+\frac{9}{4} \right)+6\cdot \left(\frac{1}{12}\right)\) Definition of subtraction/Associative and distributive properties.

5) \(y = 6\cdot \left(x+\frac{3}{2} \right)^{2}+\frac{1}{2}\) Perfect square trinomial/\(a \cdot \frac{b}{c} = \frac{a\cdot b}{c}\)/Result.

As we can see, the first step when rewriting \(y = 6\cdot x^{2}+18\cdot x + 14\) consists in applying distributive property. (Step 2).

Marshall is wondering whether he can participate in the LLP again next year. The statement that is true is "He can participate in the LLP again, but only to the extent that his existing LLP balance is less than $20,000.

The Lifelong Learning Plan is a program that helps Canadian residents finance their post-secondary education through their registered retirement savings plans (RRSP). If an individual is attending school full-time, they can withdraw up to $10,000 a year from their RRSP under the program, or up to $20,000 in total. There are certain rules that must be followed by an individual participating in the LLP. For example, withdrawals must be made within four years of enrolling in an eligible educational program, and repayments must begin within the same period.

Here are the statements: Provided he repays his LLP balance in full by the end of this year, Marshall can participate in the LLP again next year.Marshall can only participate in the LLP once over his lifetime. However, his wife can make a LLP withdrawal from her RRSP on his behalf. He can participate in the LLP again, but only to the extent that his existing LLP balance is less than $20,000. He can only participate in the LLP a second time if he repays his LLP balance in full and waits 5 years before he returns to school.The correct statement is: He can participate in the LLP again, but only to the extent that his existing LLP balance is less than $20,000.

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Answer:

Point Y

Step-by-step explanation:

This dilation is an expansion, so in order for it to expand, the center of dilation need to be in the middle or near the middle of the pre-image.

What is a pre-image?

Noun. preimage (plural preimages) (mathematics) For a given function, the set of all elements of the domain that are mapped into a given subset of the codomain; (formally) given a function ƒ : X → Y and a subset B ⊆ Y, the set ƒ−1(B) = {x ∈ X : ƒ(x) ∈ B}.

What is an Image?

The new position of a point, a line, a line segment, or a figure after a transformation is called its image.

Center of Dilation:

The center of a dilation is a fixed point in the plane about which all points are expanded or contracted. The center is the only invariant (not changing) point under a dilation (k ≠1), and may be located inside, outside, or on a figure.

I hope this helps! :)

Answer:

17

Step-by-step explanation:

6x7= 42

42 divided by 2 = 21

21 - 4 = 17

answer = 17

The marginal cost, revenue, and profit functions can be written as:

C'(x) = 7

R'(x) = 9 - 0.02x

P'(x) = 2 - 0.02x

To find the marginal cost, revenue, and profit functions, we need to take the first derivative of the cost and revenue functions with respect to x.

C(x) = 7x

Taking the derivative of C(x) gives us:

C'(x) = 7

R(x) = 9x − 0.01x^2

Taking the derivative of R(x) gives us:

R'(x) = 9 - 0.02x

The marginal profit is calculated by subtracting the marginal cost from the marginal revenue. Therefore, the marginal profit function can be written as:

P'(x) = R'(x) - C'(x)

P'(x) = 9 - 0.02x - 7

P'(x) = 2 - 0.02x

The marginal cost function C'(x) tells us the rate of change of the cost with respect to the quantity produced. It means that for each additional ounce of the commodity produced, the cost increases by $7.

The marginal revenue function R'(x) tells us the rate of change of the revenue with respect to the quantity produced. It means that for each additional ounce of the commodity sold, the revenue increases by $9 - 0.02x.

The marginal profit function P'(x) tells us the rate of change of the profit with respect to the quantity produced. It means that for each additional ounce of the commodity produced, the profit increases by $2 - 0.02x.

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54  pages are needed to hold all of his cards , if  Ricky has 648 baseball cards he wants to put them in an album if each page of the album holds 12 cards

Ricky has 648 cards , and each page of the album holds 12 cards. Which means, if each page holds 12 cards; One page will hold 12 cards, the second page, another 12 cards and so on.

Hence, 2 pages will hold 12+12 cards which is 24 cards. 3 pages will hold, 12+12+12 = 36 cards

Now, to get how much pages will hold 648 cards, we divide 648 by 12

648/12= 54 pages

Hence, if  Ricky has 648 baseball cards he wants to put them in an album if each page of the album holds 12 cards then 54  pages are needed to hold all of his cards

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The result of the Commission on Wartime Relocation and Internment of Civilians was C. In the 1980s, a commission held investigations and made recommendations.

The Commission on Wartime Relocation and the Internment of Civilians reviewed details surrounding the forced relocation and the internment of "aliens."

The commission discovered that the internment badly impacted American citizens and permanent resident aliens.

The commission recommended the payment of compensation to those who suffered the War Relocation.

Thus, the result of the Commission on Wartime Relocation and Internment of Civilians was Option C.

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The area of the polygon with the given vertices: (-3,3) (-3,-1) (4,-1) (4,3) is 28 square units

A rectangle is a polygon with four sides. The opposite sides of a rectangle are equal while the angles at the vertex is orthogonal

The following are the data given in the question

polygon with the given vertices' as:

(-3,3)

(-3,-1)

(4,-1)

(4,3)

plotting the given polygon shows it is a rectangle with sides

Length, L =  7 units

Width, w = 4 units

Area if a rectangle is given by

= L * w

= 7 * 4

= 28 square units

The area of the polygon is 28 square units

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Answer:

solving we get Solution set = {4,0}

Step-by-step explanation:

We are given system of equation:

\(9x + 4y = 36---eq(1)\\6x + 2.5y = 24---eq(2)\)

Multiply eq(1) by 2 and eq(2) by -3

\(18x \ \ + 8y \ \ \ = 72\\-18x - 7.5y = -72\\---------\\0.5y=0\\y=0\)

We get y=0,

Now finding x by putting value of y in eq(1)

\(9x + 4y = 36\\9x+4(o)=36\\9x=36\\x=\frac{36}{9}\\x=4\)

So, solving we get Solution set = {4,0}

Answer:

Step-by-step explanation:

9 + 6x = 9 + 9x - 3x

and

4x - 7 - 2x = 2x - 9

Answer:

the 1st one and last one don't have solutions

Step-by-step explanation:

Answer:

21

Step-by-step explanation:

the perimeter equals the sum of the 3 sides of the triangle so 50=15+10+x+4

x=50-29

x=21

Answer:

b. Data mining

Step-by-step explanation:

Data mining is the process of searching and analyzing a large batch of raw data in order to identify patterns and extract useful information.

The correct answer is b. Data mining. Data mining refers to the process of exploring and analyzing large datasets to discover patterns, relationships, and insights that can be used for various purposes.

Such as decision-making, predictive modeling, and identifying trends. It involves applying various statistical and computational techniques to extract valuable information from the data.

Data visualization (a) is the representation of data in graphical or visual formats to facilitate understanding. Data analysis (c) refers to the examination and interpretation of data to uncover meaningful patterns or insights. Data interpretation (d) involves making sense of data analysis results and drawing conclusions or making informed decisions based on those findings.

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Answer:

y=300-7x

Step-by-step explanation:

since monthly budget for gasoline=$300

Per day, he uses an average of $7 of gasoline

after x days he will use $7x of gasoline.

remaining amount after x days of driving= 300-7x

the equation will be y= 300-7x

To solve the equation 15 + 2x = 36, we can start by subtracting 15 from both sides of the equation to get 2x = 21. Then, we can divide both sides by 2 to get x = 10.5. Rounded to the nearest ten-thousandth, the solution is x = 10.5000.

Answer:

DCC

Step-by-step explanation:

CDDCDC

Different type of spaghetti dinners is 8

What is combination ?

"The number of possible arrangements in a collection of items where the order does not matter."

For 4 different shaped of noodles = ⁴c₁

                                             ⁴c₁ = 4        

For two kinds of cheese = ²c₁

                                         ²c₁ = 2

Now , multiplying these  4×2 = 8

Hence, 8 type of spaghetti dinners

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Answer:

x = 20

Step-by-step explanation:

X = 20 Because the values are Corresponding Angles This means that they are congruent

Using the center-of-gravity technique, the best site location for the new distribution center in Charlotte is determined to be at coordinates (X, Y) = (27.92, 19.08).

The center-of-gravity technique is used to find the optimal location for a facility based on the distribution of demand. In this case, we will calculate the weighted average of the coordinates (X, Y) of the three sites, with the weights being the number of weekly packages flowing to each site.

To calculate the X-coordinate of the center of gravity, we use the formula:

Xc = (X1 * W1 + X2 * W2 + X3 * W3) / (W1 + W2 + W3)

Similarly, for the Y-coordinate:

Yc = (Y1 * W1 + Y2 * W2 + Y3 * W3) / (W1 + W2 + W3)

Substituting the given values:

Xc = (16 * 26000 + 35 * 12000 + 40 * 10000) / (26000 + 12000 + 10000) ≈ 27.92

Yc = (28 * 26000 + 10 * 12000 + 18 * 10000) / (26000 + 12000 + 10000) ≈ 19.08

Therefore, the best site location for the new distribution center in Charlotte is approximately at coordinates (X, Y) = (27.92, 19.08) based on the center-of-gravity technique.

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The computation shows that the time will be 11:05 am.

The friends entered the amusement park at 10:05 AM, the wait time it took 35 minutes to ride the FLIP-A-Trip and it took 23 minutes to ride the Slippery Slope.

Therefore, the time will be:

= 10.05 + 35 + 25

= 10:05 + 60 minutes

= 10:05 + 1

= 11:05

.It should be noted that 60 minutes= 1 hour. Therefore, you'll add 1 hour to the original time.

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Answer: 1.8 L/h

Step-by-step explanation:

To convert the rate of water dripping from a tap from millilitres per second (ml/sec) to litres per hour (L/h), we need to use conversion factors.

Step 1:

First, let's convert the rate from millilitres per second to litres per second.

There are 1000 millilitres in a litre, so we can divide the rate in millilitres per second by 1000 to get the rate in litres per second:

\(\LARGE \boxed{\textsf{0.5 ml/sec $\div$ 1000 = 0.0005 L/sec}}\)

Step 2:

We can convert the rate from litres per second to litres per hour. There are 3600 seconds in an hour, so we can multiply the rate in litres per second by 3600 to get the rate in litres per hour:

\(\LARGE \boxed{\textsf{0.0005 L/sec $\times$ 3600 = 1.8 L/h}}\)

Therefore, the rate of water dripping from the tap is 1.8 L/h.

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