3x(x-2)-5x(1-x)-8(x^{2}-3)

The projection matrices and as we have verified that \(P = A(A^TA)^{-1}A^T.\)

Let's start by defining the matrices we will use for this problem. The matrix A is given by A = [1 1 0 1 0 0], which means that A is a 3x6 matrix with three rows and six columns. The vector b is given by b = [2 3 4], which is a 3x1 matrix with three rows and one column.

To project b onto the column space of A, we need to find a vector p that is in the column space of A and is as close as possible to b. We can do this by solving the equation \(A^T Ax = A^T b\), where \(A^T\) is the transpose of matrix A. This equation is known as the normal equation of the least-squares problem, and it gives us the vector p that is the projection of b onto the column space of A.

We can also find the error vector e = b - p, which is the difference between b and its projection onto the column space of A. This error vector is perpendicular to the column space of A, which means that it lies in the null space. To verify this, we can take the dot product of e with each column of A, which should be zero for each column.

To compute the projection matrix P, we can use the formula

\(P = A(A^TA)^{-1}A^T.\)

This matrix projects any vector onto the column space of A.

We can also verify that P² = P and P = \(P^T\), which means that P is an idempotent matrix and a symmetric matrix.

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If the best fit line is nearly horizontal, it suggests no significant relationship between height and head circumference.

In this scenario, the explanatory variable is the child's height, as it is being used to predict the head circumference.

The response variable is the head circumference itself, as it is the variable being predicted or explained by the height.

To draw a scatter diagram of the data, you would plot the child's height on the x-axis and the corresponding head circumference on the y-axis. Each data point would represent a child's measurement pair.

Once all the data points are plotted, you can then draw the best fit line, also known as the regression line, that represents the overall trend or relationship between height and head circumference.

By observing the scatter diagram and the best fit line, you can determine the relationship between a child's height and head circumference.

If the best fit line has a positive slope, it indicates a positive relationship, meaning that as height increases, head circumference tends to increase as well.

If the best fit line has a negative slope, it indicates a negative relationship, meaning that as height increases, head circumference tends to decrease.

By assessing the slope of the best fit line in the scatter diagram, you can determine whether the relationship between height and head circumference is positive, negative, or nonexistent.

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In this case, the alternate interior angles are for example angles 6 and 3 because they are on the inner side of each of the lines (m and l) but on opposite sides of the transversal (t).

m∠6 = m∠3

or

m∠4 = m∠5

Using the normal distribution, it is found that the probability is 0.16.

In a normal distribution with mean \(\mu\) and standard deviation \(\sigma\), the z-score of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

In this problem, the mean and the standard deviation are given by, respectively, \(\mu = 70, \sigma = 3\).

The proportion of students between 45 and 67 inches is the p-value of Z when X = 67 subtracted by the p-value of Z when X = 45, hence:

X = 67:

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{67 - 70}{3}\)

Z = -1

Z = -1 has a p-value of 0.16.

X = 45:

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{45 - 70}{3}\)

Z = -8.3

Z = -8.3 has a p-value of 0.

0.16 - 0 = 0.16

The probability is 0.16.

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The combined present worth of the costs associated with the proposed bridge design, including construction and annual operating costs, is $10,583,333.

To calculate the combined present worth of costs, we need to consider the construction cost and the annual operating cost over the infinite life of the bridge. We will use the concept of present worth, which is the equivalent value of future costs in today's dollars.

The present worth of the construction cost is simply the initial cost itself, which is $9,000,000. This cost is already in present value terms.

For the annual operating cost, we need to calculate the present worth of perpetuity. A perpetuity is a series of equal payments that continue indefinitely. In this case, the annual operating cost of $700,000 represents an equal payment.

To calculate the present worth of the perpetuity, we can use the formula PW = A / MARR,

where PW is the present worth, A is the annual payment, and MARR is the minimum attractive rate of return (also known as the discount rate). Here, the MARR is given as 12%.

Plugging in the values, we have PW = $700,000 / 0.12 = $5,833,333.

Adding the present worth of the construction cost and the present worth of the perpetuity, we get $9,000,000 + $5,833,333 = $14,833,333.

However, since we are looking for the combined present worth, we need to subtract the salvage value, which is zero in this case. Therefore, the combined present worth of the costs associated with the proposed bridge design is $14,833,333 - $4,250,000 = $10,583,333, rounded to the nearest dollar.

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The image of the regular polygon is attached, this is made up of a square with dimension of 1 unit

A polygon with congruent sides and equal angles is referred to as a regular polygon.

Equilateral triangles, squares, regular pentagons, and more are examples of regular polygons.

The regular polygon created form the irregular polygon given is square, there are two squares labelled 1 and 2

The measurement is aided by the grid lines, each side o the square is 1 unit.

Both squares made form the irregular polygon are of same size

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Answer: The value of q is 7.5.

Answer:

7.5

Step-by-step explanation:

Brainliest?

Answer:

11/4

Step-by-step explanation:

4/4 is 1 whole.

We have 2 whole.

So, right now we have: 8/4

We can't forget about the 3/4!

8/4+3/4=11/4

This means your total is 11/4

Hope this helps you out!

-AxekickNebulite

The value of an improper fraction of a mixed number \(2 \dfrac{3}{4}\) would be \(\dfrac{11}{4}\).

Used the concept of the fraction that states that,

A fraction is a part of the whole number and a way to split up a number into equal parts. Or, A number which is expressed as a quotient is called a fraction. It can be written in the form of p: q, which is equivalent to p / q.

Given that the mixed number \(2 \dfrac{3}{4}\).

Now, change the mixed number \(2 \dfrac{3}{4}\)  into an improper fraction as,

\(2 \dfrac{3}{4} = \dfrac{(2\times 4 )+ 3}{4}\)

\(= \dfrac{11}{4}\)

Therefore, The value of an improper fraction would be \(\dfrac{11}{4}\).

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It (B) cannot be determined that there is a statistically significant difference between Mr. Goodman's ratings and those of the History Department in the context of Mr. Goodmain and with all the material provided.

In statistics, a simple random sample (or SRS) is a subset of people (a sample) picked at random from a larger group of people (a population), all with the same probability.

It is a method of choosing a sample at random. Each subset of k people in SRS has the same chance of getting selected for the sample as any other subset of k people.  

An objective sampling strategy is a straightforward random sample. Simple random sampling is a fundamental kind of sampling that can be used in combination with other, more sophisticated sampling techniques.

So, in the given situation of Mr. Goodmain and with all the information given we can conclude that it cannot be concluded that there is a statistically significant difference in Mr. Goodman’s evaluations and the History Department’s.

Therefore, it (B) cannot be determined that there is a statistically significant difference between Mr. Goodman's ratings and those of the History Department in the context of Mr. Goodmain and with all the material provided.

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Complete question:

Students at a high school are asked to evaluate their experience in the class at the end of each school year. The courses are evaluated on a 1-4 scale – with 4 being the best experience possible. In the History Department, the courses typically are evaluated at 10% 1’s, 15% 2’s, 34% 3’s, and 41% 4’s. Mr. Goodman sets a goal to outscore these numbers. At the end of the year, he takes a random sample of his evaluations and finds 11 1’s, 14 2’s, 47 3’s, and 53 4’s. At the 0.05 level of significance, can Mr. Goodman claim that his evaluations are significantly different than the History Departments?

Hypotheses:

H0: There is (no difference /difference) in Mr. Goodman’s evaluations and the History Department’s.

H1: There is (no difference /difference) in Mr. Goodman’s evaluations and the History Department’s.

Enter the test statistic - round to 4 decimal places.

Enter the p-value - round to 4 decimal places.

Can it be concluded that there is a statistically significant difference between Mr. Goodman’s evaluations and the History Department’s?

a. Yes

b. No

Answer:

Lin was better than Clare

Step-by-step explanation:

Clare

Lin

Comparing data for both Clare and Lin, we can see that:

Conclusion

Reason

Assuming that x ≥ 0 and y ≥ 0, the situation is infeasible: True.

In Mathematics, these rules are generally used for writing and interpreting an inequality or system of inequalities that are plotted on a coordinate plane:

In this context, we can logically deduce that the given system of inequalities 5x+3y ≤ 15 and y ≥ 6 would not have a feasible solution set if they are subjected to x ≥ 0 and y ≥ 0:

Assuming the ordered pair (1, 2), we have:

y ≥ 6

2 ≥ 6 (False).

5x+3y ≤ 15

5(1) +3(2) ≤ 15

5 + 6 ≤ 15

11 ≤ 15 (True).

Therefore, it is not a feasible solution.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

The middle school will host a Talent show.

The goal of the tickets sale is to earn $500

To reach this goal Ms G has to sell a determined number of tickets.

This means that the earnings depend directly on the number of tickets sold.

So the independent/ explanatory variable is the number of tickets sold, and the dependent/ response variable is the money earned

x → Tickets sold

y → Money earned

Answer:

  B/A = 1/2

Step-by-step explanation:

You want the scale factor between the two figures shown.

The scale factor is the ratio of the length in one figure to the corresponding length in the other figure. Often, we're interested in the scale factor B/A, which is what A dimensions need to be multiplied by in order to match the B dimensions.

You can pick any corresponding dimensions. Often, it is convenient to choose a short one, so you don't have to count so many grid squares.

We can choose the line from the center, where the lines cross, up and to the right to the upper right corner. In the A figure, that line goes 2 squares to the right and 2 squares up. In the B figure, that line goes 1 square right and 1 square up. Then the scale factor is ...

  (B dimension)/(A dimension) = 1/2

We can choose to look at the lengths of that line (A: 2√2; B: √2), or the x-dimension (A: 2; B: 1) or the y-dimension (A: 2; B: 1). All the measurements are proportional, so we get the same ratio for any pair of corresponding measures.

The scale factor B/A is 1/2.

__

Additional comment

The horizontal magenta lines in the attached figure are another possibility for determining the scale factor. B/A = 2/4 = 1/2.

You need to be careful to understand what scale factor you want. Sometimes it is described as "A to B", which can be ambiguous.

Here, the ratio of an A dimension to a B dimension is A : B = 2 : 1. The same wording can be interpreted to mean "the scale factor that multiplies A to transform it to B." That is the scale factor we have shown.

P(t1 < t-1 < t²) is the probability that t1 is less than t raised to the power of -1, which is less than t squared.

To calculate the probability P(t1 < t-1 < t²), you need to determine the range of values for t that satisfy this inequality. Start by isolating t:

1. t1 < t-1 → t1 + 1 < t (by adding 1 to both sides)
2. t-1 < t² → 1/t < t (by rewriting t-1 as 1/t)

Now, find the range of t values that satisfy both inequalities. Graph these inequalities on a number line, and identify the intersection of the two ranges. The probability P(t1 < t-1 < t²) will be the proportion of this intersection relative to the total possible range of values for t.

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Are they correct? Is that the question? Well, the first one is correct because Slope (m) = -6/1 =-6

Equation of the line:

y = -6x + 15

When x=0, y = 15

When y=0, x = 2.5

and the other one:

Is incorrect and the correct answer is A because y= 7.5x -2. 7.5 is positive, the slope, and -2 is the y-intercept. Its negative.

Answer:

23/3 or 7 2/3

Step-by-step explanation:

Answer:

23/3

Step-by-step explanation:

So we have the equation:

\(2(3x-1)=9(x-2)-7\)

First, distribute the left:

\(6x-2=9(x-2)-7\)

Now, distribute the right:

\(6x-2=9x-18-7\)

Subtract on the right:

\(6x-2=9x-25\)

Subtract 9x from both sides:

\(-3x-2=-25\)

Add 2 to both sides:

\(-3x=-23\)

Divide both sides by 3:

\(x=23/3\approx7.67\)

And we're done!

Answer:

I got u x= 29.    ( Your welcome )

Step-by-step explanation:

3x+15 +2x+20=180  because a line is 180 duhh

we collect like terms and we get

5x +35=180 we decrease in both sides by 35

5x=145

x=145/5

x=29

Answer:

I,R,I,I,R,I,R,R,I,R,I,R,I,I,R,R,I,I,I,I

Step-by-step explanation:

The following is the expected value of a number of books a student buys at the next book fair is 2.404 books.

The random variable b's expected value is then calculated as follows:

E(X) = 1 x 0.285 + 2 x 0.333 + 3 x 0.168 + 4 x 0.136 + 5 x 0.063 + 6 x 0.015 E(X)  = 2.404 books.

Thus, the expected value of discrete probability distribution is 2.404 books.

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The graph for the question is attached.

Answer:

x = -7

Step-by-step explanation:

First, you must distribute the -3 to the numbers in the parenthesis. You will get -18x - 6. the problem is now 113 = x - 18x - 6. With inverse operations this will become 119 = -17x. Divide 119 by -17 and you will get -7.  x = -7.

Answer:

x = -7

Step-by-step explanation:

113 = x - 3(6x + 2)

113 = x - 18x - 6

x - 18x = 113 + 6

-17x = 119

x = -7

I hope this helped!

a. 36, 000 stadia = 5,664 km. b. 129 yojanas = 1,987 km. Stadia was an ancient unit of length, equal to about 185 meters. It was used in Greece, Rome, and other parts of the Mediterranean world.

Yojana was an ancient unit of length, equal to about 13 kilometers. It was used in India and other parts of Asia.

a. 36, 000 stadia = 5,664 km

1 stadia = 0.1575 km

36,000 stadia x 0.1575 km/stadia = 5,664 km

b. 129 yojanas = 1,987 km

1 yojana = 13.2 km

129 yojanas x 13.2 km/yojana = 1,987 km

To convert from stadia to kilometers, we can use the following conversion factor:

1 stadia = 0.1575 km

To convert from yojanas to kilometers, we can use the following conversion factor:

1 yojana = 13.2 km

In addition to the above, here are some additional information about stadia and yojanas:

Both stadia and yojanas are no longer in use as official units of measurement, but they are still sometimes used in historical and archaeological contexts.

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The amount of money in Iris's checking account can be modeled by a linear function of the form:

y = mt + b

where y is the amount of money in the account, t is the time (measured in years), m is the rate of interest, and b is the initial amount in the account.

In this case, we have m = 0.04 (since the interest rate is 4% per year) and b = 180 (since that's the initial amount in the account). Therefore, the linear function that models the amount of money in Iris's checking account at any time t is:

y = 0.04t + 180

For example, if t = 5 (years), then the amount of money in Iris's checking account is 0.04 * 5 + 180 = 198 dollars.

Answer:

600 g chicken

600 g peppers

120 g onion

15 g spice mix

6 tortillas

Step-by-step explanation:

To make 18 portions, Carly needs to make 3 times the original recipe.

1. Solve for how much of each ingredient is needed.

500 · 3 = 1500 g chicken

600 · 3 = 1800 g peppers

90 · 3 = 270 g onion

25 · 3 = 75 g spice mix

12 · 3 = 36 tortillas

2. Subtract how much of each ingredient Carly already has from how much is needed to find how much more she needs.

1500 - 900 = 600 g chicken

1800 - 1200 = 600 g peppers

270 - 150 = 120 g onion

75 - 60 = 15 g spice mix

36 - 30 = 6 tortillas

Answer:

hjvjhee

Step-by-step explanation:ejbfkwej

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The critical values of a function occur where its derivative is either zero or undefined.

To find the critical values of the function f(x) = 2x^3 + 9x^2 - 60x + 9, we need to determine where its derivative is equal to zero or undefined.

First, we need to find the derivative of f(x). Taking the derivative of each term separately, we get:

f'(x) = 6x^2 + 18x - 60.

Next, we set the derivative equal to zero and solve for x:

6x^2 + 18x - 60 = 0.

We can simplify this equation by dividing both sides by 6, giving us:

x^2 + 3x - 10 = 0.

Factoring the quadratic equation, we have:

(x + 5)(x - 2) = 0.

Setting each factor equal to zero, we find two critical values:

x + 5 = 0 → x = -5,

x - 2 = 0 → x = 2.

Therefore, the critical values of the function f(x) are x = -5 and x = 2.

In more detail, the critical values of a function are the points where its derivative is either zero or undefined. In this case, we took the derivative of the given function f(x) to find f'(x). By setting f'(x) equal to zero, we obtained the equation 6x^2 + 18x - 60 = 0. Solving this equation, we found the values of x that make the derivative zero, which are x = -5 and x = 2. These are the critical values of the function f(x). Critical values are important in calculus because they often correspond to points where the function has local extrema (maximum or minimum values) or points of inflection.

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the solution to the system of equations is x = 2 and y = 1.

To solve the system of equations by substitution, we will solve one equation for one variable and substitute it into the other equation.

Given the system of equations:

1) y = 6x - 11

2) -2x - 3y = -7

Step 1: Solve equation (1) for y.

  y = 6x - 11

Step 2: Substitute the value of y from equation (1) into equation (2).

  -2x - 3(6x - 11) = -7

Step 3: Simplify and solve for x.

  -2x - 18x + 33 = -7

  -20x + 33 = -7

  -20x = -7 - 33

  -20x = -40

  x = (-40)/(-20)

  x = 2

Step 4: Substitute the value of x into equation (1) to find y.

  y = 6(2) - 11

  y = 12 - 11

  y = 1

Therefore, the solution to the system of equations is x = 2 and y = 1.

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The solution to the system of equations y = 6x - 11 and -2x - 3y = -7 is x = 2 and y = 1. This is achieved by substituting y into the second equation, simplifying, and solving for x, then substituting x back into the first equation to solve for y.

To solve the system of equations y = 6x - 11 and -2x - 3y = -7 by substitution, we start by substituting the equation y = 6x - 11 into the second equation in place of y, giving us -2x - 3(6x - 11) = -7. Next, simplify the equation by distributing the -3 inside the parentheses to get -2x - 18x + 33 = -7. Combine like terms to get -20x + 33 = -7. Subtract 33 from both sides to obtain -20x = -40, and finally, divide by -20 to find x = 2.

Once we find the solution for x, we substitute it back into the first equation y = 6x - 11. Substituting 2 in place of x gives y = 6*2 - 11, which simplifies to y = 1.

Therefore, the solution to the system of equations is x = 2 and y = 1.

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Answer:

15 miles= 3 hours

   x         =    2.5

37.5/3= 3x/3

         12.5 miles   =  x

Answer:

1a. y = $10 + $5x (With $10 as the flat fee, Company A charges $5 an hour, so the equation should be $10, base, plus $5x, the amount charged after you paid the flat fee.)

1b. y = $7x (Every hour $7 translates to $7x as the total. Nothing more, nothing less.)

1c. Substitution (This will allow us to substitute in one of the equations with y, since the question asks for the same amount charged, with the other equation.)

1d. $10 + $5x = $7x

    $7x - $5x = $10

    $2x = $10

    x = \(\frac{\$10}{\$2}\)

    x = 5

Therefore, after 5 hours, both companies charge $35 dollars.

1e. To check whether this is correct, let's sub in the amount of hours for both equations.

For Company A:

y = $10 + $5x

y = $10 + $5(5)

y = $35

For Company B:

y = $7x

y = $7(5)

y = $35

Since both are equal to $35, we can definitively say the answer is 5 hours.

Step-by-step explanation:

Hope this helped!

The steps for subtracting mixed numbers are the transformation of improper fractions, subtraction of denominator, then subtracting numerator, making it the smallest term, and reverse.

Finding the difference between two mixed numbers is required when subtracting mixed numbers. The steps for subtracting mixed numbers are as follows:

Step 1: Transform the mixed values into improper fractions in step 1. To achieve this, divide the total by the denominator, then add the numerator. The new numerator is the outcome, and it is positioned above the denominator.

Step 2: Identify a common denominator in step two. You must identify a common denominator to subtract fractions with various numerators.

Step 3: Subtract the fractions in step three. Subtract the numerators from the fractions while maintaining the same denominator.

Step 4: Make the outcome simpler. Simplify the outcome if you can by breaking the fraction down into its smallest terms. 13/4 in this instance may be expressed as 3 1/4.

Step 5: Reverse the incorrect fraction to a mixed number in step 5. Divide the numerator by the denominator to return the improper fraction to a mixed number. The full number serves as the numerator, and the remainder serves as the quotient.

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The question is -

How to Subtract mixed numbers?

Answer: y = -6x - 2  

Step-by-step explanation:

54x + 15 = -3(3y + 1)   To solve for y distribute on the right side to get,

54x + 15 = -9y -3        Add 3 to both sides

      +3             +3

54x  + 18 = -9y        Divide each term by -9 on each side.

y = -6x - 2

Answer______

54x + 15 = -3 (3y + 1)

54x + 15 = -9y -3

+3 +3

54x + 18 = -9y

y = -6x - 2

Answer:

C. 18

Step-by-step explanation:

Let's say the first number is x so the second will be x+1 and the third will be x+2

x+ x+1+x+2=51

3x+3=51

3x=51-3

3x=48

3x/3=48/3

X=16 this is the first number

The second number will be x+1=16+1=17

The third number will be x+2=16+2=18

So the greatest number will be 18