Can anyone help me with it?

a)(i) The coefficient matrix A for the system of linear equations is:

A = \(\left[\begin{array}{ccc}1&2&-1\\0&1&1\\0&0&2\end{array}\right]\)

(ii) The inverse of A:

A⁻¹ = (1/2)\(\left[\begin{array}{ccc}1&-1&2\\0&2&-1\\0&0&1\end{array}\right]\)

b)det(B) = 2t + 2, not (t + 7).

c) x is an eigenvector of both matrices A and B, with eigenvalues α and β respectively.

(i) The coefficient matrix A for the system of linear equations is:

A = \(\left[\begin{array}{ccc}1&2&-1\\0&1&1\\0&0&2\end{array}\right]\)

(ii) To find the inverse of matrix A, we can use the formula:

A⁻¹ = (1/det(A)) x adj(A)

First, let's calculate the determinant of A:

det(A) = 1  (1 x 2 - 1 x 0) - 2 (0 x 2 - 1 x 0) + (-1) x (0 x 1 - 1 x 0) = 2

Next, let's calculate the adjoint of A:

adj(A) = \(\left[\begin{array}{ccc}1&-1&2\\0&2&-1\\0&0&1\end{array}\right]\)

Now, we can calculate the inverse of A:

A⁻¹ = (1/2)\(\left[\begin{array}{ccc}1&-1&2\\0&2&-1\\0&0&1\end{array}\right]\)

(iii) To find the solution to the system of linear equations using A⁻¹, we can write it in matrix form:

X = A⁻¹  B

where X is the solution vector and B is the column matrix containing the constants from the right-hand side of the equations.

Substituting the values into the equation:

X =\(\left[\begin{array}{ccc}1&-1&2\\0&2&-1\\0&0&1\end{array}\right]\) . \(\left[\begin{array}{ccc}3\\1\\-2\end{array}\right]\)

Evaluating the matrix multiplication, we get:

X = \(\left[\begin{array}{ccc}9\\3\\-2\end{array}\right]\)

So the solution to the system of linear equations is:

x = 9

y = -3

z = -2

(i) To show that det(B) = (t + 7), we need to calculate the determinant of matrix B and simplify the expression.

det(B) = (t+1) x ((-1)(-2) - (0)(-1)) - 0 x ((t-1)(-2) - (-1)(-1))

      = (t+1) x (2) - 0 x (-2 + t - 1)

      = 2(t + 1) + 0

      = 2t + 2

Therefore, det(B) = 2t + 2, not (t + 7).

(ii) The matrix B does not have an inverse when its determinant is equal to zero. So we need to find the values of t for which det(B) = 0.

2t + 2 = 0

2t = -2

t = -1

Therefore, B does not have an inverse when t = -1.

(c) Let A be an n x n matrix and B be an n x n matrix. Suppose there is a vector x ≠ 0 and scalars α and β such that Ax = αx and Bx = βx.

This means that x is an eigenvector of both matrices A and B, with eigenvalues α and β respectively.

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The slope intercept of the line is y = -1/3x -11

Slope-intercept is one of the special forms of line equation

The slope intercept of a line can be found by solving the slope-intercept equation of a line which is parallel to that line.

Slope-intercept equation is

y = mx + b

where m is the slope and b is the intercept.

The slope-intercept equation of the parallel line is

y = -1/3x + 4

The slope will be the same for both lines as they were parallel to each other.

Thus m = -1/3

The point in which the line passes is given as (-6,-9)

So with these data, We can find the intercept of the line

y = mx + b

where m = -1/3 and (x,y) is (-6,-9),Thus

-9 = -1/3(-6) +b

-9 = 6/3 +b

-9 = 2 + b

b = -9-2

b = -11

Thus the intercept of the line passing through the point (-6,-9) is -11

Thus, the slope-intercept equation of the line we need to find is

y = -1/3x -11

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The distance from the base of the antenna the wire is anchored measuring from the ground level is 461.7 feet.

A 150-ft ham radio antenna is installed in a vertical position on a hillside

that is 18° to the horizontal.  A 200-ft guy wire is attached to the top of

the  antenna and is anchored downhill.

Therefore, the distance form the base of the antenna to the wire anchored can be calculated as follows:

This situation forms a right angle triangle.

using trigonometric ratios,

tan 18 = opposite / adjacent

tan 18 = 150 / x

cross multiply

x = 150 / tan 18

x = 150 / 0.32491969623

x = 461.666307593

x = 461.7 ft

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um if you meant y=2.5 when x=5 then the answer would be y=10 when x=20

Yes, there are experts here in data forecasting methods who can help you with the topics you've mentioned including time series (holts, holts winter), naive method, regression, acf, pacf, arima, stl method and multivariate time series.

Below are brief explanations of each of these terms:

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The projections of the point (0, 3, 3) on the coordinate planes are:

On the xy-plane: (0, 3, 0)

On the yz-plane: (0, 0, 3)

On the xz-plane: (0, 3, 0)

The concept of projections onto coordinate planes.

In a three-dimensional Cartesian coordinate system, each point in space is represented by three coordinates: (x, y, z). The xy-plane, yz-plane, and xz-plane are three separate planes that intersect at right angles and divide the three-dimensional space.

When we talk about the projection of a point onto a coordinate plane, we are essentially finding the point on that plane where the original point would "project" onto if we were to drop a perpendicular line from the original point to the plane.

For the point (0, 3, 3), let's consider its projections onto the coordinate planes:

1. Projection on the xy-plane: To find this projection, we set the z-coordinate to zero. By doing so, we "flatten" the point onto the xy-plane, and the resulting projection is (0, 3, 0).

2. Projection on the yz-plane: To find this projection, we set the x-coordinate to zero. By doing so, we "flatten" the point onto the yz-plane, and the resulting projection is (0, 0, 3).

3. Projection on the xz-plane: To find this projection, we set the y-coordinate to zero. By doing so, we "flatten" the point onto the xz-plane, and the resulting projection is (0, 3, 0).

In summary, the projections of the point (0, 3, 3) onto the coordinate planes are:

- On the xy-plane: (0, 3, 0)

- On the yz-plane: (0, 0, 3)

- On the xz-plane: (0, 3, 0)

These projections help us visualize the point's position on each individual plane while disregarding the coordinate orthogonal to that specific plane.

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Answer:

Step-by-step explanation:

question 13:

the triangle with x is a 30-60-90 triangle which means

x= 17√3

then the traingle with y and z is a 45-45 triangle

z=34

y= 34√2

question 14:

x= 18√3

z=9

y= 18

Answer:

q = p + r + 3s

Step-by-step explanation:

q - r - 3s = p solve for q

q - r - 3s = p

add r to both sides:

q - r - 3s + r = p + r

q - 3s = p + r

add 3s to both sides:

q - 3s + 3s = p + r + 3s

q = p + r + 3s

Amy and Vince must save approximately $323.45 at the beginning of each month to have the $18,000 they need for their trip to Europe in five years  if they can get 5.5% interest in their savings account.

We know that Amy and Vince want to save $18,000 in five years and can earn 5.5% interest in their savings account, we need to adjust the interest rate to a monthly rate.

First, let's calculate the monthly interest rate (r) from the annual interest rate:

r = (1 + annual interest rate)^(1/12) - 1

= (1 + 0.055)^(1/12) - 1

= 0.0045107

Next, let's calculate the number of periods (n) in months:

n = 5 * 12

= 60 months

Using the future value of an ordinary annuity formula, we can solve for the monthly savings (PMT):

PMT = FV / [((1 + r)^n - 1) / r]

where:

FV = Future Value (desired savings amount)

r = Monthly interest rate

n = Number of periods

FV = $18,000

PMT = 18,000 / [((1 + 0.0045107)^60 - 1) / 0.0045107]

≈ $323.45

Therefore, Amy and Vince must save approximately $323.45 at the beginning of each month to have the $18,000 they need for their trip to Europe in five years.

Therefore, the correct option is $323.45.

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Answer:

infinite solutions 0=0

Step-by-step explanation:

solve for x. x=4-2y

input for x from 1st equation

y=-1/2(4-2y) +2

y= -2+y+2

y-y =-2+2

0=0

A couple in Spain was sentenced for stealing nearly $1.7 million worth of restaurant luxury items. The couple from Spain was convicted of stealing almost $1.7 million worth of wine.

According to reports, the wine came from 12 Spanish vineyards, including Penedes, Rioja, and Ribera del Duero. Their stolen wines were primarily expensive, high-end wines that were widely sought after by collectors, like Chateau Petrus and Romanee-Conti. The couple's wine cellar, which was discovered and raided by the authorities in 2014, contained 4,000 bottles of wine worth millions of dollars. The couple was accused of selling the stolen wines to collectors in various parts of Spain, and they were eventually apprehended and brought to justice.

In Spain, the couple was sentenced to a total of 12 years in jail. They were also ordered to pay almost $1.7 million in damages to the vineyards that were robbed. It was discovered that the couple had been doing this for over 10 years before being caught, which indicates that they had accumulated a significant fortune from their heists.

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Answer:

I promise you the app Math. way will save you it will do it for u and show you where to put it on the graph just download it

Answer:

listing method

Step-by-step explanation:

pls make me brainliest pls

Answer:

$2,500

Step-by-step explanation:

divide 30,000 by 12 since there are 12 months in a year.

30000/12=2500

The Excel function used when deciding to reject or fail to reject the null hypothesis is the T.TEST function.

This function is used to calculate the probability of obtaining the observed results or more extreme results, assuming that the null hypothesis is true. If the probability, also known as the p-value, is less than the significance level, typically 0.05, the null hypothesis is rejected, and it is concluded that there is sufficient evidence to support the alternative hypothesis.

Otherwise, if the p-value is greater than the significance level, the null hypothesis is not rejected, and it is concluded that there is not enough evidence to support the alternative hypothesis.

The p-value is the probability of obtaining a test statistic as extreme or more extreme than the observed value, assuming that the null hypothesis is true. If the p-value is less than or equal to the level of significance (alpha) chosen for the test, typically 0.05 or 0.01, then the null hypothesis is rejected in favor of the alternative hypothesis. If the p-value is greater than the chosen alpha level, then the null hypothesis is not rejected.

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It will take approximately 4.4 years to earn enough money to go on the trip if we invest our 2200 in a savings account with a 1.55% interest rate compounded annually.

First, we need to calculate the amount of money that we need to save in order to cover the cost of the trip. This can be done by subtracting the amount we have already saved from the total cost of the trip:

Total cost of trip = 2500

Amount already saved = 2200

Amount to save = 2500 - 2200 = 300

Next, we can use the compound interest formula to calculate how long it will take to earn 300 with an interest rate of 1.55% compounded annually. We can set up the formula as follows:

A = P(1 + i)n

where:

A = accumulated amount = 300 + 2200 = 2500 (the total cost of the trip)

P = principal = 2200

i = interest rate per year = 1.55%

n = number of years we need to save for

We can now solve for n:

2500 = 2200(1 + 0.0155)n

Divide both sides by 2200:

1.13636 = 1.0155n

Take the natural logarithm of both sides:

ln(1.13636) = n ln(1.0155)

Divide both sides by ln(1.0155):

n = ln(1.13636)/ln(1.0155) ≈ 4.4 years

Therefore, it will take approximately 4.4 years to earn enough money to go on the trip if we invest our 2200 in a savings account with a 1.55% interest rate compounded annually.that we rounded our final answer to the nearest tenth as instructed.

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Analysis of variance (ANOVA) is a statistical method of comparing the means of several populations.

ANOVA is used when there are three or more groups or populations that need to be compared. It determines whether there are any statistically significant differences among the means of these groups. The method analyzes the variation within each group as well as the variation between the groups to assess whether the differences observed are due to random chance or if there are true differences in the population means.

The primary goal of ANOVA is to test the null hypothesis that the population means are equal across all groups. If the null hypothesis is rejected, it indicates that at least one group significantly differs from the others.

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The probability of the whole batch getting selected or marked as okay is 0.9030 (most likely).

Probability is the possibility of an event occurring. We can scale the probability of an event between 0 and 1. 0 refers to an improbable event, and 1 refers to an event with the highest possibility.

Now in the given problem statement that in order to evaluate the batch of a product, a sample is selected at random. The sample will be evaluated called the acceptance sampling and if the sample turns out to be undefective, production will be marked okay.

The purpose here is to find the probability that the entire batch will be selected, and it is only possible for all the three random products that are selected to turn out to be okay.

Now we will list down the given data and then solve it,

Total products manufactured = 4500 CDs

Defective pieces = 150 CDs

Good/Undefective CDs = Total products - Defective pieces

= 4500-150

Good/Undefective CDs = 4350

Now the three samples are chosen at random;

P (first good) = 4350/4500 if not replace....

then (one less choice and one less good)

P (the second one is not defective, but it is not)

= 4350/4499

If you don't replace...

If (2 less to choose from and 2 less non-defective)

P(3rd is not defective (1st AND 2nd is not defective ))

= 4350/4498

Just multiply these 3 fractions

(4350 ( 4349 > ) (4348) ) / (4500 (4499) (4498) ) )

= 0.9030

So the probability of the whole batch to get selected or marked as okay is 0.9030 (most likely).

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The true statements among the given options are written below

bc || ad

ba ≅ cd  

∠cba ≅ ∠bcd

In an isosceles trapezoid, there is one pair of legs of equal length and a pair of parallel lines.

Given that quadrilateral abcd is a isosceles trapezoid.

In the given trapezoid abcd

bc || ad ( pair of parallel sides )

So this is correct.

ba ≅ cd  ( For an isosceles trapezoid legs are equal)

So this is correct

∠cba ≅ ∠bcd (According to  the property of isosceles  trapezoid )

So this is correct.

Hence, bc || ad, ba ≅ cd, ∠cba ≅ ∠bcd are correct

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Therefore , the solution of the given problem of equation comes out to be 0.24(d−c) is the required equation.

The equal letter (=) is used to signify equivalence between the statements in a mathematical formula. Using mathematical equation, which are declarations of reality, it is shown that many mathematical variables are equivalent. For instance, the equal sign in the equation y + 6 = 12 divides the values 12 or b + 6 into two halves. The number of words that each side of a symbol corresponds to can be measured. Typically, a symbol's meaning is at odds with itself.

Here,

Given :

$d dollar purchase price

Selling price = $c

25% commission rate

The difference between the selling price and the purchasing price is the profit.

=Buy price - Selling price =d - C

The commission is the result of the profit and the commission rate.

=> Profit = Commission rate * Profit

=> 24% * (d- c)

=>0.24×(d−c)

=> 0.24(d−c)

​

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The polynomial : y = 3.6088 x³  - 0.3494 x² + 7.7644 x + 2.1870

Given,

Table

MATLAB  code :

clc; clear all; x = [1.15; -1.95; 2.15; -0.8; 0.1]; y = [16.42; -41.1; 53.06; -5.8; 2.52]; % taking cube of x p =x³; % taking square of x q = x²; %combining all columns X = [p q x];  % model of the form ax³ + bX² + cx + d % fit model in linear model mdl = fitlm(X,y); % printing coeffecients of matrix mdl.Coefficients

The table is attached below .

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Answer:

The associative property allows us to change groupings of addition or multiplication and keep the same value. (a+b)+c = a+(b+c) and (a*b)*c = a*(b*c).

Step-by-step explanation:

in mathematics, either of two laws relating to number operations of addition and multiplication, stated symbolically: a + (b + c) = (a + b) + c, and a(bc) = (ab)c; that is, the terms or factors may be associated in any way desired.

Answer:

Associative

Step-by-step explanation:

The statement that "Group value theory suggests that fair group procedures are considered to be a sign of respect" is true.

The group value theory is based on the concept that individuals evaluate the fairness and justice of the group procedures to which they are subjected. According to this theory, the perceived fairness of the procedures that a group employs in determining the outcomes or rewards that members receive has a significant impact on the morale and commitment of those members. It provides members with a sense of control over the outcomes they get from their group, thereby instilling respect. Hence, fair group procedures are indeed considered to be a sign of respect.

In conclusion, it can be said that the group value theory supports the notion that fair group procedures are a sign of respect. The theory indicates that members feel more motivated and committed to their group when they perceive that their rewards and outcomes are determined through fair procedures. Therefore, a group's adherence to fair group procedures is essential to gain respect from its members.

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Answer:

\(20a^2-70a\)

Step-by-step explanation:

1) Expand by distributing terms.

\(10\times2a+10a\times-7\)

2) Take out the constants.

\((10\times2)aa+10a\times-7\)

3) Simplify \(10\times2\) to \(20.\)

\(20aa+10a\times7\)

4) Use Product Rule:\(x^ax^b=x^{a+b}\).

\(20a^2+10a\times-7\)

5) Simplify \(10a\times-7\) to \(-70a.\)

\(20a^2-70a\)

Thank you,

Eddie

Answer:

20a² - 70a

Step-by-step explanation:

(10a)(2a-7)

= 10a*2a + 10a*-7

= 20a² - 70a

Answer:

Current price $50eax135hats= $6750

Step-by-step explanation:

If he sells the hats at $52 he sells 3 less hats so $52x132=$6864

if he sells the hats at $54 he has 6 less hats= 54x129=6966 etc

$56 x 126=$7056

The parameter of interest is the proportion of people in the original group who had not smoked over the past 6 months.

We can calculate the parameter of interest by taking the number of people in the sample who had not smoked over the past 6 months (210) and dividing it by the total number of people in the sample (1000). This gives us a proportion of 0.21, or 21%. This tells us that 21% of people in the original group had not smoked over the past 6 months. This proportion is the parameter of interest in this scenario.

210/1000 = 0.21 or 21%

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If 1472cm² of wrapping paper is needed to cover the smaller box, approximately 1672cm² of wrapping paper is needed to cover the larger box (assuming the surface area is directly proportional to the length).

Since the smaller and larger boxes have exactly the same shape, we can assume that their dimensions are proportional.

Let's denote the width and height of the smaller box as "w" and "h," respectively, and the width and height of the larger box as "W" and "H," respectively.

We know that the length of the smaller box is 16 cm, so we have:

Length of smaller box = 16 cm

Width of smaller box = w

Height of smaller box = h

To find the dimensions of the larger box, we can set up a proportion based on the lengths of the boxes:

16 cm / 18 cm = w / W

From this proportion, we can solve for W:

\(W = (18 cm \times w) / 16 cm\)

Now, let's consider the surface area of the boxes.

The surface area of a box is given by the sum of the areas of its six faces. Since the boxes have the same shape, the ratio of their surface areas will be equal to the square of the ratio of their lengths:

Surface area of smaller box / Surface area of larger box = (16 cm / 18 cm)^2.

We know that the surface area of the smaller box is 1472 cm^2, so we can set up the equation:

\(1472 cm^2\) / Surface area of larger box \(= (16 cm / 18 cm)^2\)

To find the surface area of the larger box, we rearrange the equation:

\(Surface $area of larger box = 1472 cm^2 / [(16 cm / 18 cm)^2]\)

Now we can substitute the value of W into the equation to find the surface area of the larger box:

Surface area of larger box \(= 1472 cm^2 / [(16 cm / 18 cm)^2] = 1472 cm^2 / [(18 cm \times w / 16 cm)^2]\)

\(= 1472 cm^2 / [(18 \times w / 16)^2] = 1472 cm^2 / [(9w / 8)^2]\)

\(= 1472 cm^2 / [(81w^2 / 64)]\)

Simplifying further:

Surface area of larger box \(= (1472 cm^2 \times 64) / (81w^2)\)

So the amount of wrapping paper needed to cover the larger box is given by the surface area of the larger box, which is:

\((1472 cm^2 \times 64) / (81w^2)\)

Note that we don't have enough information to calculate the exact value of the wrapping paper needed to cover the larger box since we don't know the width "w" of the smaller box.

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Answer:

1) fraction

2)denominator

3)quotient

4)remainder

i hope this helps

A score of x = 60 on an exam with μ = 72 and σ = 12 is comparatively better than a score of x = 70 on an exam with μ = 82 and σ = 8.

To compare the two scores, we can convert them to z-scores, which tell us how many standard deviations a particular value is from the mean. The formula for z-score is:

z = (x - μ) / σ

where x is the value, μ is the mean, and σ is the standard deviation.

For the first score of x = 70 on an exam with μ = 82 and σ = 8, the z-score is:

z = (70 - 82) / 8 = -1.5

For the second score of x = 60 on an exam with μ = 72 and σ = 12, the z-score is:

z = (60 - 72) / 12 = -1.0

The z-score for the first score is lower than the z-score for the second score, which means that the first score is further below its mean than the second score is below its mean. Therefore, we can say that a score of x = 60 on an exam with μ = 72 and σ = 12 is comparatively better than a score of x = 70 on an exam with μ = 82 and σ = 8.

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Answer:

It costs 2.25 to rent a movie

Step-by-step explanation:

11.50-4.75=6.75

6.75/3=2.25