(b) Factorise fully 9b-3b squared

The true statements from the options provided are:

A. The product Ax is defined as a linear combination of columns of A with the corresponding entries of x as weights.

D. The product Ax is a vector in \(R^n\).

E. Ax is a vector whose ith entry is the sum of the products of the corresponding entries from row i of A and the vector x.

A linear combination in mathematics is an expression created from a group of terms by multiplying each component by a constant and combining the results (for example, an expression of the form axe + by, where a and b are constants, would be a linear combination of x and y).

The true statements from the options provided are:

A. The product Ax is defined as a linear combination of columns of A with the corresponding entries of x as weights.

D. The product Ax is a vector in \(R^n\).

E. Ax is a vector whose ith entry is the sum of the products of the corresponding entries from row i of A and the vector x.

These statements accurately describe properties and definitions related to matrix-vector multiplication. The product Ax is obtained by taking a linear combination of the columns of A, where the entries of x act as weights. The resulting product Ax is a vector in \(R^n\), and its entries are calculated by summing the products of the corresponding entries from row i of A and the vector x.

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Markov chain model with periodic classes of states can be exemplified by a weather model and ergodic system in a Markov chain is the game of Monopoly.

Example of Markov chain with periodic classes of states:

One example of a Markov chain model with periodic classes of states is a weather model that includes seasonal variations. Let's consider a simplified model with three states: sunny, cloudy, and rainy. In this model, the weather is observed over a long period of time, and it is known that the weather tends to follow a cyclic pattern, transitioning from one season to another. The stochastic matrix representing this Markov chain will have non-zero probabilities for transitions between states within the same season (e.g., sunny to sunny, cloudy to cloudy, rainy to rainy), but zero probabilities for transitions between states in different seasons (e.g., sunny to rainy, rainy to cloudy). This creates periodic classes or groups of states that correspond to the different seasons, resulting in a Markov chain with periodic behavior.

Example of ergodic system in a Markov chain:

A common example of an ergodic system in a Markov chain is the game of Monopoly. In Monopoly, players move around the board based on the outcome of rolling dice. The states in this Markov chain correspond to the positions on the board. Each roll of the dice determines the transition probabilities from one state (position) to another. In an ergodic system, it means that it is possible to reach any state from any other state in a finite number of steps. In the context of Monopoly, this means that players can move from any position on the board to any other position by rolling the dice and following the game rules. The stochastic matrix for this Markov chain will have non-zero probabilities for transitions between all states, reflecting the possibility of moving to any position on the board from any other position.

In summary, a Markov chain model with periodic classes of states can be exemplified by a weather model that represents the cyclic nature of seasons, while an example of an ergodic system in a Markov chain is the game of Monopoly, where players can reach any position on the board from any other position through successive dice rolls and gameplay.

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The answer to the question is C. 5,20,80,320

Step-by-step explanation:

5*4=20

20*4=80

80*4=320

Answer:

y = -3/2x + 6

Step-by-step explanation:

Slope m = (y2 - y1)/(x2 - x1)

m = (6 - 0)/(0 - 4) = 6/-4 = -3/2

Slope-intercept form is y = mx + b

Substitue m = -3/2, y = 0, x = 4

0 = -3/2(4) + b

b = 6

y = -3/2x + 6

Answer:

y = -f(x - 5)

Step-by-step explanation:

the function of the dotted graph is f(x) shifted (or translated) 5 units to the right and then reflected across the x-axis.

shifting it to the right is happening by reducing every x value by 5 (so that we get for x the functional value of x-5).

and reflecting it across the x-axis simply means to flip the sign. everything that was originally above the x-axis is now with the same distance below the x-axis (and vice versa).

therefore, the new

y = -f(x - 5)

The length of arc CD, given that the radius, EB = 15 cm, is 29.31 cm

First, we shall determine ∠CED. Details below:

2∠CED + 2∠BEC = 360

2∠CED + (2 × 68) = 360

2∠CED + 136 = 360

Collect like terms

2∠CED = 360 - 136

2∠CED = 224

Divide both sides by 2

∠CED = 224 / 2

∠CED = 112°

Finally, we shall determine the length of the of arc CD. Details below:

Length of arc = 2πr × (θ / 360)

Length of arc CD = (2 × 3.14 × 15) × (112 / 360)

Length of arc CD = 29.31 cm

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Complete question:

See attached photo

Answer:

0.43* 0.35 = 0.1505 or 0.15 after rounding

Step-by-step explanation:

Based on the probabilities of A and B occurring with conditions, the probability of A and B occurring is 0.15.

This can be found by the formula:

= Probability that A occurs if B occurs x Probability of B occurring if A occurs

Solving gives:

= 0.43 x 0.35

= 0.15

In conclusion, the probability is 0.15.

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Answer:

Let  x=−118  and  y=−114 . On a number line

Which expression has a negative value?

Multiple choice question.

A) x+y

B) x−y

C) x·y

D) xy

Step-by-step explanation:

Answer:

2.48

Step-by-step explanation:

Answer:

8n+10

Step-by-step explanation:

Answer:

10+8n

Step-by-step explanation:

Distribute the 2 to everything in the parenthesis

Complete Question

The area of grandiose rectangular painting is 56 in.² the width of the painting is 7 inches what is the diagonal of the painting

Answer:

The diagonal of the rectangular painting is  \(z = 10.63 \ m\)

Step-by-step explanation:

The diagram for this question is shown on the first uploaded image

From the question we are told that  

    The area is \(A = 56 \ in^2\)

    The width of the painting is \(w = 7 \ in\)

Generally the area of the rectangle is mathematically represented as

          \(A = l * w\)

where \(l\) the length which is mathematically evaluated as

          \(l = \frac{A}{w}\)

substituting value  

         \(l = \frac{56}{7}\)

          \(l = 8 \ in\)

According Pythagoras theorem

     \(z ^ 2 = l^2 +w^2\)

Where z is the diagonal of the rectangular painting

  Now substituting values

      \(z = \sqrt{7^2 + 8^2}\)

      \(z = 10.63 \ m\)

Answer:

I'm not sure about the question, but the one thing that is needed for a function is the "=" sign.  Only option c has an equals sign.  The others, as written, are just expressions, not equations.

Step-by-step explanation:

Even option c doesn't conform to the y = mx + b form, but it is far ahead of the other options.

Answer:

12/5

Step-by-step explanation:

Remember SOH CAH TOA

Answer:

2.4

Step-by-step explanation:

tan= opposite/adjacent

so tan=12/5

P^m-n , 1st option is right answer

The mathematical quantity of the instantaneous velocity is a derivative, specifically the derivative of the distance function d(t) with respect to time.

To find the average velocity of the rock from t = 5 to t = 5.1, we need to calculate the change in distance and time over this interval.

Change in distance = d(5.1) - d(5) = (35(5.1) - 5\((5.1)^{2}\)) - (35(5) - 5\((5)^{2}\)) ≈ -24.5 m

Change in time = 5.1 - 5 = 0.1 s

Average velocity = (change in distance) / (change in time) ≈ -245 m/s

To find the equation for the average velocity from 5 seconds to t seconds, we need to use the formula for average velocity:

average velocity = (d(t) - d(5)) / (t - 5)

Taking the limit of this expression as t approaches 5 gives us the instantaneous velocity at t = 5:

instantaneous velocity = lim (t→5) [(d(t) - d(5)) / (t - 5)]

Using the given function for d(t), we can evaluate this limit as:

instantaneous velocity = lim (t→5) [(35t - 5\(t^{2}\) - 35(5) + 5\((5)^{2}\) / (t - 5)] = -50 m/s

Since the instantaneous velocity is negative, the rock is going down at t = 5. We can tell this because the velocity is the rate of change of distance with respect to time, and the negative sign indicates that the distance is decreasing with time.

The mathematical quantity of the instantaneous velocity is a derivative, specifically the derivative of the distance function d(t) with respect to time.

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The algebraic expression that represents the given phrase is b + 15 = 180.

The algebraic expression that represents the phrase "the sum of the number of boys and 15 girls is 180" is:b + 15 = 180Explanation:Let's assume that the number of boys is "b".

According to the question, the total number of students in the class can be calculated by adding the number of boys (b) to the number of girls (15) which is equal to 180 students.Using algebra,

we can write this statement as an equation: b + 15 = 180Hence, the algebraic expression that represents the given phrase is b + 15 = 180

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Answer:

61

Step-by-step explanation:

11^2 + 60^2 = 3721

square root of that is 61

put it in a calculator

f^-1(x) is the inverse of f(x) as the composite functions f(f^-1(x)) and f^-1(f(x)) are both equal to x.

A function is composite when the co- domain of the first mapping is the domain of the second mapping.

We shall evaluate the functions f(f^-1(x)) and f^-1(f(x)) as follows:

f(f^-1(x)) = [(3x+5 / x+1) - 5] ÷ [3 - (3x+5 / x+1)]

changing division to multiplication;

f(f^-1(x)) = [3x + 5 - 5(x + 1)]/(x + 1) × (x + 1)/[3(x + 1) - (3x + 5)]

(x + 1) is common and will cancel out

f(f^-1(x)) = (3x + 5 - 5x - 5)/(3x + 3 - 3x - 5)

f(f^-1(x)) = -2x/-2

f(f^-1(x)) = x

f^-1(f(x)) = [3(x-5 / 3 -x) + 5] ÷ [(x-5 / 3 -x) + 1]

changing division to multiplication;

f^-1(f(x)) = [3(x - 5) + 5(3 - x)]/(3 - x) × (3 - x)/[x - 5 + (3 - x)]

(3 - x) is common and will cancel out

f^-1(f(x)) = (3x - 15 + 15 - 5x)/(x - 5 + 3 - x)

f^-1(f(x)) = -2x/-2

f^-1(f(x)) = x

Therefore, since composite functions; f(f^-1(x)) = x and f^-1(f(x)) = x, then f^-1(x) is the inverse of f(x).

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Answer:

the answer is 56.

Step-by-step explanation:

2 for every 4 = 1 for every two, so 28 multiplied by two.

The value of angle Q using the concept of similar quadrilaterals is: ∠Q = 91°

Two quadrilaterals are said to be similar quadrilaterals provided that three corresponding angles are equal (the sum of the interior angles is 360 degrees, so the fourth angle is automatically equal) and if the proportions of the two adjacent sides are equal is.

Now, we ware told that the wo given quadrilaterals GHIJ and RQPS are similar.

This tells us that corresponding angles and sides are equal to each other and therefore, we can say that:

∠G = ∠R

∠H = ∠Q

∠I = ∠P

∠J = ∠S

Thus:

∠Q = 91°

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We should use the chi-square test of independence to test whether the political ideology of voters in Tampa is associated with their opinion on workers who have illegally entered the US.

The null hypothesis for this test is that there is no association between political ideology and opinion on workers who have illegally entered the US. The alternative hypothesis is that there is an association between political ideology and opinion on workers who have illegally entered the US.

Symbolically, we can write the hypotheses as follows:

H0: Political ideology and opinion on workers who have illegally entered the US are independent.

Ha: Political ideology and opinion on workers who have illegally entered the US are not independent.

To perform the chi-square test of independence, we would need to create a contingency table showing the frequencies of each combination of political ideology and opinion on workers who have illegally entered the US. We would then calculate the expected frequencies for each cell under the assumption of independence, and use these values to calculate the chi-square test statistic. Finally, we would compare the calculated test statistic to the critical value from the chi-square distribution with (r-1)(c-1) degrees of freedom, where r is the number of rows in the contingency table and c is the number of columns.

If the calculated test statistic exceeds the critical value, we would reject the null hypothesis and conclude that there is evidence of an association between political ideology and opinion on workers who have illegally entered the US. If the calculated test statistic does not exceed the critical value, we would fail to reject the null hypothesis and conclude that there is insufficient evidence to conclude that there is an association.

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A multiple-choice quiz contains 5 questions. Each question has answer choices labeled a, b, c, and d. There are 256 different ways can a student answer the five questions.

Permutation and Combination:

Permutations and combinations form counting principles, which are applied in many different situations. A permutation is the number of different arrangements that can be made from a given set. When it comes to permutations, the details matter because the order or order matters. The three country names are spelled differently: {US, Brazil, Australia} or {Australia, US, Brazil) or {Brazil, Australia, US}, and the order in which the country names appear is important. In combination, the names of the three countries are just one group, and the order or sequence does not matter.

When asked how many ways an object can be combined, dispersed, mixed or split, in this case the answer is to use the counting method to calculate the number of ways.

In this case, DDDD can be answered from AAAA, AAAB, AAAC, AAAD, AABA, AABB, ..., CADB. To calculate that number, we have to consider that for every possible answer to one question, there are four alternatives to the other question. So for the 4 choices for question 1, there are 4 choices for question 2, and for each question 3, and so on.

Therefore, the answer is 4*4*4*4 = 256 questions.

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Answer:

168 deg

Step-by-step explanation:

Assuming the increase in temperature in constant during the 3 weeks, we do the following calculations-

8 deg * 7 = 56 deg / week (Since there are 7 days in a week)

56 * 3 = 168 deg in 3 weeks.

Answer:

29 mililiters

Step-by-step explanation:

3 + 3x = 90

3x = 87

x = 29

The original volume of the solution is 29 ml.

Given,

After the addition of an acid, a solution has a volume of 90 milliliters.

The volume of the solution is 3 milliliters greater than three times the volume of the solution before acid was added.

We need to find what was the original volume of the solution.

Find the volume of the solution after the acid is added.

V(acid) = 90 ml

Find the volume of the solution before the acid was added.

= V( no acid)

We have,

The volume of the solution is 3 milliliters greater than three times the volume of the solution before acid was added.

V ( acid ) = 3 V ( no acid ) + 3 ml

90 ml = 3 V ( no acid ) + 3 ml

90 ml - 3 ml = 3 V ( no acid )

87 ml = 3 V ( no acid )

Dividing by 3 on both sides.

87/3 ml = 3/3 V ( no acid )

29 ml = V ( no acid )

V ( no acid ) = 29 ml

Thus the original volume of the solution is 29 ml.

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Step-by-step explanation:

D I think sorry if it's wrong :(

Answer:

The answer would be 1/6

The probability that both jurors selected are female is 1/6.

For a criminal trial, 8 active and 4 alternate jurors are selected.

Two of the alternate jurors are male and two are female.

During the trial, two of the active jurors are dismissed.

The judge decides to randomly select two replacement jurors from the 4 available alternates.

Total numbers of selected candidates is;

8 + 4 = 12

The judge decides to randomly select two replacement jurors from the 4 available alternates.

Therefore,

The probability that both jurors selected are female is;

\(= \dfrac{2}{12}\\\\= \dfrac{1}{6}\)

Hence, the probability that both jurors selected are female is 1/6.

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Transitional forms in the fossil record, including Archaeopteryx, provide evidence for the pattern of evolution known as "gradualism."

This pattern suggests that species change over time through a slow and continuous process of accumulation of small, incremental changes. Transitional fossils like Archaeopteryx exhibit characteristics that are intermediate between two different groups of organisms, indicating a gradual transition from one form to another.

The presence of transitional fossils supports the idea that species do not undergo abrupt transformations but instead evolve gradually over long periods of time.

These fossils provide a tangible link between different groups of organisms, such as dinosaurs and birds in the case of Archaeopteryx, and offer evidence for the gradual transformation of one group into another. This supports the broader concept of evolution as a slow and continuous process of change in populations over generations.

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