Consider an invertible n ×n matrix A. Can you write A as A = LQ, where L is a lower triangular matrix and Q is orthogonal? Hint: Consider the QR factorization of A^T

Answer:

Step-by-step explanation:

Combined, it is option C.  {x | x < -4 or x > 4}

Answer:

10/16

Step-by-step explanation:

Perimeter of Rectangle is 44m

A perimeter is a closed path that encompasses, encircles, or delineates a one-dimensional length or a two-dimensional shape.

According to the given information

Area of Rectangle = l × b

Area of Rectangle = 105 \(m^{2}\)

Length of one side = 7 m

Let the length of the adjacent side = b

Area of Rectangle given = 7 × b

                     105   = 7 × b

                       b    =  \(\frac{105}{7}\)

                       b   = 15 m

Perimeter of Rectangle given = 2( l + b )

                                        = 2 ( 7 + 15 )

                                        = 2 × 22

                                        = 44m

Perimeter of Rectangle is 44m

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Answer:

The bait is 14 feet below the water surface

Step-by-step explanation:

Here, we want to know the final position of the bait relative to the surface of the water.

Firstly, he starts with the bait at 2 feet below the water surface. The reels out the bait a further 19 feet, the new position of the bait relative to the water surface will be 2 + 19 = 21 feet

Now, he reels the bait back by 7 feet.

Thus, the new depth of the bait relative to the water surface will be 21-7 = 14 feet

Answer:

4x² -14x - 8

Step-by-step explanation:

(2x - 5)² + 3(2x-5) - 18

Expand brackets.

(2x-5)(2x-5) + 6x -15 - 18

2x(2x-5)-5(2x-5) + 6x - 33

4x² - 10x - 10x + 25 + 6x - 33

Combine like terms.

4x² -14x - 8

Answer:

4x^2 -14x -8

Step-by-step explanation:

( 2x-5)^2 + 3( 2x-5) -18

Foil

(2x-5)(2x-5) = 4x^2 -10x-10x +25 = 4x^2 -20x+25

Distribute

3( 2x-5) = 6x -15

( 2x-5)^2 + 3( 2x-5) -18

Replace with the foil and distribute

4x^2 -20x+25 +6x -15 - 18

Combine like terms

4x^2 -14x -8

Answer:

5 packs of pens and 8 packs of pencils.

Step-by-step explanation:

Let the Pn and Pl stand for the number of packs of pens (Pn) and pencils (Pl) purchased.

We know that each pack of pens is $3 and each pack of pencils is $2.50.

We are also told that Pn + Pl = 13  [In total, 13 packs were purchased].

And we're told that $35 was spent.

The $35 must equal:  $3*Pn + $2.5*Pl  [the sum of the number of packs of each times the price per pack for each]

 3*Pn + 2.5*Pl = 35

Rearrange the first equation:

Pn + Pl = 13

Pn = 13 - Pl

Use this definition of Pn in the second equation:

3*Pn + 2.5*Pl = 35

3*(13 - Pl) + 2.5*Pl = 35

39 - 3Pl + 2.5Pl = 35

-0.5Pl = -4

Pl = 8

8 packs of pencils (Pl) were purchased.

This means the packs of pens purchased must be 5, since a total of 13 packs were purchased.

Check:

Does 5 packs of pens and 8 packs of pencils total $35?

5*($3) + 8*($2.5) = $35  ??

$15 + $20 = $35  ?

YES

You bought  5 packs of pens and 8 packs of pencils.

To find ,we can break down each vector into its horizontal and vertical components. The horizontal component represents the vector's magnitude in the x-axis , and the vertical component the magnitude in the y-axis direction.

To verify the sum of vectors using the components method, we can add the horizontal components together and the vertical components together. If the resultant sum of the horizontal components equals the horizontal component of the resultant vector, and the sum of the vertical components equals the vertical component of the resultant vector, then the components method is verified.

To find the vector components, we typically use trigonometry. Given a vector with magnitude (r) and an angle (θ) measured counterclockwise from the positive x-axis, we can find the horizontal component (x-component) and the vertical component (y-component) using the following equations:

x-component = r * cos(θ)

y-component = r * sin(θ)

To verify the sum of vectors using the components method, we add the horizontal components together and the vertical components together. Let's say we have two vectors A and B. The components of vector A are (A₁, A₂), and the components of vector B are (B₁, B₂). The components of the resultant vector R would be (A₁ + B₁, A₂ + B₂).

To verify the sum, we check if the sum of the horizontal components (A₁ + B₁) equals the horizontal component of the resultant vector R, and the sum of the vertical components (A₂ + B₂) equals the vertical component of the resultant vector R. If these conditions are satisfied, the sum of vectors using the components method is verified.

In summary, vector components can be found by breaking down vectors into their horizontal and vertical components. To verify the sum of vectors using the components method, we add the horizontal and  vertical components separately and check if they match the components of the resultant vector.

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The values of probabilities P(support children) and P(children | support) are 0.755 and  0.623 respectively.

To determine the probability P(support children) that a randomly selected respondent supports the levy given that he or she has children attending school in the district, we can follow these steps:

1. Find the number of respondents with children attending school in the district who support the levy. In this case, it is 71.

2. Find the total number of respondents with children attending school in the district.

This is 71 (support levy) + 23 (opposed to levy) = 94.

3. Divide the number of respondents supporting the levy with children attending school by the total number of respondents with children attending school:

P(support children) = 71/94 = 0.755

To determine the probability P(children | support) that a randomly selected respondent has children attending school in the district given that he or she supports the levy, follow these steps:

1. Find the number of respondents supporting the levy who have children attending school in the district.

This is 71 (as calculated earlier).

2. Find the total number of respondents who support the levy.

This is 71 (have children attending school) + 43 (have no children attending school) = 114.

3. Divide the number of respondents with children attending school who support the levy by the total number of respondents who support the levy:

P(children | support) = 71/114 = 0.623



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JJonathan spends $14.55 on muffins and cupcakes

Jonathan buys 3 muffins and 4 cupcakes, so we can calculate how much he spends on muffins by multiplying the price of one muffin by the number of muffins he buys:

1.85 * 3 = $5.55

And we can calculate how much he spends on cupcakes by multiplying the price of one cupcake by the number of cupcakes he buys:

2.25 * 4 = $9

To find the total amount of money Jonathan spends, we add the cost of the muffins to the cost of the cupcakes: 5.55 + 9 = $14.55

So, Jonathan spends $14.55 in total.

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1 can only be divided by one other integer except1, hence it is not a prime number.

Any natural number higher than 1 that is not the sum of two smaller natural numbers is referred to be a prime number. A composite number is a natural number greater than one that is not prime.

Given this definition, 1 is not a prime number because it can only be divided by one other integer, which is 1 itself.

Based on the explanation above, we can then conclude that 1 is not a prime number.

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Answer:

A

Step-by-step explanation: add 15+12+7

if im write can i get a brainliest? plss:>

The band director can create a trio in 1,260 different ways.

Hence, option C is correct.

Use the concept of permutations,

The formula for permutations is,

⇒  \(^{n}P_{r}\) = n! / (n - r)!

Where n is the total number of items and r is the number of items we are selecting.

So in this case, we have,

⇒  n = 15 clarinet players

⇒ n = 12 flute players

⇒ n = 7 saxophone players

⇒ r = 1 clarinet player,

1 flute player, and 1 saxophone player

To find the number of ways we can create a trio with one player from each instrument, we need to calculate,

⇒ (\(^{15}P_{1}\)) x (\(^{12}P_{1}\)) x (\(^{7}P_{1}\))

⇒  (\(^{15}P_{1}\))   = 15! / (15 - 1)!

                = 15! / 14!

                = 15  

This represents the number of ways we can choose one clarinet player out of 15.  

(\(^{12}P_{1}\)) ) = 12! / (12 - 1)!

           = 12! / 11!

           = 12  

This represents the number of ways we can choose one flute player out of 12.

\(^{7}P_{1}\) = 7! / (7 - 1)!

     = 7! / 6!

     = 7

This represents the number of ways we can choose one saxophone player out of 7.

So the total number of ways we can create a trio consisting of one clarinet player, one flute player, and one saxophone player is,

⇒ 15 x 12 x 7 = 1,260

Therefore,

The band director can create a trio in 1,260 different ways.

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The trigonometric expression in terms of sine and cosine and simplified is -sec^2 x.

We can use the trigonometric identity:

tan^2 x + 1 = sec^2 x

to rewrite the expression as:

tan^2 x − sec^2 x = tan^2 x − (tan^2 x + 1) = -1 - tan^2 x

Using the identity:

1 = sin^2 x + cos^2 x

we can rewrite tan^2 x as:

tan^2 x = sin^2 x / cos^2 x

Substituting this into the expression, we get:

-1 - tan^2 x = -1 - (sin^2 x / cos^2 x) = (-cos^2 x - sin^2 x) / cos^2 x

Using the identity:

cos^2 x + sin^2 x = 1

we can simplify the expression to:

(-cos^2 x - sin^2 x) / cos^2 x = (-1) / cos^2 x = -sec^2 x

Therefore, the trigonometric expression in terms of sine and cosine and simplified is -sec^2 x.

To write the trigonometric expression tan^2(x) - sec^2(x) in terms of sine and cosine, we first need to recall the definitions of tangent and secant:

tan(x) = sin(x) / cos(x)
sec(x) = 1 / cos(x)

Now, we can substitute these definitions into the given expression:

tan^2(x) - sec^2(x) = (sin(x) / cos(x))^2 - (1 / cos(x))^2

Now let's simplify the expression:

= (sin^2(x) / cos^2(x)) - (1 / cos^2(x))

To combine the two terms, we need a common denominator, which is cos^2(x):

= (sin^2(x) - 1) / cos^2(x)

Now, recall the Pythagorean identity: sin^2(x) + cos^2(x) = 1. We can rearrange this identity to express sin^2(x) in terms of cosine:

sin^2(x) = 1 - cos^2(x)

Now, substitute this expression for sin^2(x) in the given expression:

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

Finally, simplify the expression:

= -cos^2(x) / cos^2(x)

The result is:

= -1

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Answer:

d

Step-by-step explanation:

The predicted win for 17000 attendance is 98.5.

Option (B) is correct.

To find the predicted number of wins for a team

science that deals with the addition, subtraction, multiplication, and division of numbers and properties and manipulation of numbers.

Given that:

A sports statistician was interested in the relationship between game attendance (in thousands) and the number of wins for baseball teams.

Attendance = 17,000

The regression equation is

\(y=4.9x+15.2\)

where x represents the attendance (in thousands) and ŷ is the predicted number of wins.

The required predicted number of wins can be calculated as,

\(y=4.9x+15.2\\\\\\y=4.96*17+15.2\\\\y=98.5 wins\)

Therefore, the predicted win for 17000 attendance is 98.5.

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Therefore, the maximum height to which water could be squirted with the hose, when it emerges from the nozzle, is approximately 146.86 meters.

To calculate the maximum height to which water could be squirted with the hose, we can use the principles of fluid mechanics, specifically Bernoulli's equation.

a. When the water emerges from the nozzle attached to the hose, we can assume that the velocity of water at the nozzle is the maximum, and the pressure is atmospheric pressure. At the highest point of the water stream, the velocity will be zero, and the pressure will be atmospheric pressure.

Using Bernoulli's equation, we can write:

P₁ + 1/2 ρ v₁² + ρgh₁ = P₂ + 1/2 ρ v₂² + ρgh₂

Since the water is squirting vertically upwards, the velocity at the highest point will be zero (v₂ = 0) and the pressure at the highest point will be atmospheric pressure (P₂ = P₀, where P₀ is atmospheric pressure). Also, the pressure at the nozzle (P₁) can be considered to be approximately atmospheric pressure.

The equation simplifies to:

1/2 ρ v₁² + ρgh₁ = ρgh₂

ρ is the density of water, which is approximately 1000 kg/m³.

v₁ is the velocity of water at the nozzle.

h₁ is the height of the nozzle above the ground.

h₂ is the maximum height to which water is squirted.

Since the density and the velocity are constant, we can rewrite the equation as:

v₁²/2 + gh₁ = gh₂

Solving for h₂:

h₂ = (v₁²/2g) + h₁

To calculate h₂, we need to determine the velocity v₁ at the nozzle. The flow rate through the hose and nozzle is given as 0.75 L/s. We can convert this to m³/s:

Flow rate = 0.75 L/s

= 0.75 x 10^(-3) m³/s

The flow rate (Q) is given by Q = A₁v₁, where A₁ is the cross-sectional area of the nozzle.

The cross-sectional area of the nozzle can be calculated using the radius (r₁) of the nozzle:

A₁ = πr₁²

Substituting the given radius value (0.21 cm = 0.0021 m), we have:

A₁ = π(0.0021)²

≈ 1.385 x 10⁻⁵ m²

Now we can calculate the velocity v₁:

v₁ = Q / A₁

\(= (0.75 x 10^{(-3)}) / (1.385 x 10^{(-5)})\)

≈ 54.18 m/s

Substituting the values into the equation for h₂:

h₂ = (v₁²/2g) + h₁

= (54.18² / (2 x 9.8)) + 0

= 146.86 m

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On the interval [0, 2π], the minimum values of f(x) = 12cos^2(x) - 1 are -1, and the maximum values are 11.

To find the minimum and maximum values of the function f(x) = 12cos^2(x) - 1 on the interval [0, 2π], we need to determine the critical points and endpoints within that interval.

First, let's differentiate the function f(x) with respect to x to find the critical points. The derivative of f(x) is f'(x) = -24cos(x)sin(x).

Next, we set f'(x) equal to zero and solve for x:

-24cos(x)sin(x) = 0

This equation is satisfied when cos(x) = 0 or sin(x) = 0.

For cos(x) = 0, we have x = π/2 and x = 3π/2 as critical points.

For sin(x) = 0, we have x = 0 and x = π as critical points.

Now, we evaluate the function f(x) at these critical points and the endpoints of the interval [0, 2π]:

f(0) = 12cos^2(0) - 1 = 11

f(π/2) = 12cos^2(π/2) - 1 = -1

f(π) = 12cos^2(π) - 1 = 11

f(3π/2) = 12cos^2(3π/2) - 1 = -1

f(2π) = 12cos^2(2π) - 1 = 11

From the evaluations, we see that the minimum values of f(x) are -1, occurring at x = π/2 and x = 3π/2, while the maximum values are 11, occurring at x = 0, x = π, and x = 2π.

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Answer:

Step-by-step explanation:

Measure of an inscribed angle intercepted by an arc is half of the measure of the arc.

From the picture attached,

m(∠A) = \(\frac{1}{2}m(\text{arc BD})\)

           = \(\frac{1}{2}[m(\text{BC})+m(\text{CD}]\)

           = \(\frac{1}{2}[55^{\circ}+145^{\circ}]\)

           = 100°

m(∠C) = \(\frac{1}{2}[(360^{\circ})-m(\text{arc BCD})]\)

           = \(\frac{1}{2}(360^{\circ}-200^{\circ})\)

           = 80°

m(∠B) + m(∠D) = 180° [ABCD is cyclic quadrilateral]

115° + m(∠D) = 180°

m(∠D) = 65°

m(arc AC) = 2[m(∠D)]

m(arc AB) + m(arc BC) = 2(65°) [Since, m(arc AC) = m(arc AB) + m(arc BC)]

m(arc AB) + 55° = 130°

m(arc AB) = 75°

m(arc ADC) = 2(m∠B)

m(arc AD) + m(arc DC) = 2(115°)

m(arc AD) + 145° = 230°

m(arc AD) = 85°

The surface area of a square pyramid is 2619 m².

The surface area of a square pyramid given by the formula:

A = a² + 2al

where,

a = base length of square pyramid

l = slant height or height of each side face

We have:

a = 27 m

l = 35 m

A = a² + 2al

A =  27² + (2*27*35)

A = 729 + 1890

A = 2619 m²

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Answer:

correct choice is option 3 - figure C.

Step-by-step explanation:

When you reflect a point across the line y = x, the x-coordinate and y-coordinate change places. This gives you such reflection rule:

From the diagram:

L(3,1), M(4,3), N(5,3) and P(4,1).

Using the reflection rule, you can find coordinates of image points:

L'(1,3), M'(3,4), N'(3,5) and P'(1,4).

As you can see, these are coordinates of vertices of the figure C.

on e2020 its c

give brainliest if this helps please (;

Answer:

Figure C

Thanks for actually attaching a picture, it's helpful!

Answer:

The correct options are;

The amplitude of f(x) is greater than the amplitude of g(x)

Step-by-step explanation;

The given functions are plotted

From the graphs, we have;

The amplitude of f(x) is larger than the amplitude of g(x)

The graphs of g(x) and f(x) are not identical

The period (the time taken to complete one cycle) of g(x) is half the period of f(x)

The observed properties are due to the fact that the maximum value of the sine function are ±1, and the period of the sine function is 2·π or 360°.

The total number of seeds that Josiah would plant would be = nR×S

To determine the total number of seeds that Josiah will plant will be to add the seeds in the total number of rooms he planted.

Let each row be represented as = nR

Where n represents the number of rows planted by him.

Let the seed be represented as = S

The total number of seeds he planted = nR×S

Therefore, the total number of seeds that was planted Josiah would be = nR×S.

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The graph of the equation Y = 4X - 1 (or Y = -1 + 4X) represents (A) a line that slopes gradually up to the right.

The equation Y = 4X - 1 (or Y = -1 + 4X) is in the form of a linear equation, where the coefficient of X is 4. This indicates that for every increase of 1 in the X-coordinate, the Y-coordinate will increase by 4. This results in a positive slope.

When graphed on a Cartesian plane, the line represented by this equation will slope gradually up to the right. The slope of 4 means that the line rises 4 units for every 1 unit it moves to the right. This creates a steady and consistent upward trend as X increases.

Therefore, (A) the pattern observed in the graph is a line that slopes gradually up to the right.

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The expected value of the "Buy New" option is 724732.60.

Decision Tree:

To solve the given problem, the first step is to create a decision tree. The decision tree for the given problem is shown below:

Expected Value Calculation: The expected value of the "Buy New" option can be calculated using the following formula:

Expected Value = (Prob. of Prosperity * Payoff for Prosperity) + (Prob. of Recession * Payoff for Recession)

Substituting the given values in the above formula, we get:

Expected Value for "Buy New" = (0.7 * 1,035,332) + (0.3 * -150,000)Expected Value for "Buy New" = 724,732.60

Therefore, the expected value of the "Buy New" option is 724,732.60.

Conclusion:

To conclude, the decision tree is an effective tool used in decision making, especially when the consequences of different decisions are unclear. It helps individuals understand the costs and benefits of different choices and decide the best possible action based on their preferences and probabilities.

The expected value of the "Buy New" option is 724,732.60.

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The height of the box can be represented as a function of the width, h = 4/w², where the domain of the function is (0, +∞).

Let's assume the width of the rectangular box is represented by the variable 'w'. Given that the length of the box is twice the width, we can express the length as '2w'. The height of the box can be represented by the variable 'h'.

The volume of a rectangular box is given by the formula: V = lwh, where V represents the volume, l represents the length, w represents the width, and h represents the height.

We are given that the volume of the box is 8 ft³. Substituting the values into the formula, we have:

8 = (2w)(w)(h)

Simplifying, we get:

8 = 2w²h

Dividing both sides by 2w², we get:

4/w² = h

Therefore, the height of the box can be expressed as a function of the width, h = 4/w².

The domain of the height function is determined by the width. Since the width of a rectangular box cannot be zero or negative (as it represents a physical dimension), the domain of the height function is the set of positive real numbers, excluding zero. In interval notation, the domain can be expressed as (0, +∞).

In conclusion, the height of the box can be represented as a function of the width, h = 4/w², where the domain of the function is (0, +∞).

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Answer:

a or c

Step-by-step explanation:

I don’t know ask for help sorry don’t blam this on me

Answer:

below

Step-by-step explanation:

Domain is the set of all x values a function can have

 this one goes from    - inf to the asymtope at x = 2

(-∞, 2)     domain

range is the y values the function can have

   looks like 0   to - inf

(- ∞, 0]       ( but it COULD be  ( -∞, 0)    <===cannot tell from graph)

The answer to this question is 0.16666666666

Step-by-step explanation:

convert equation to y = mx+c:

3x-2y= - 6

3x+6=2y

y=3/2x+6/2

y=3/2x+3

gradient/slope=3/2

y intercept = 3

Please mark as brainliest :))))0

Answer:

Step-by-step explanation:

y = mx + b , where "m" is a slope and "b" is a y-intercept

~~~~~~~~~~~~~~

3x - 2y = - 6

3x - 3x - 2y = - 3x - 6

- 2y = - 3x - 6

\(\frac{-2}{-2}\) y = \(\frac{-3}{-2}\) x + \(\frac{-6}{-2}\)

y = \(\frac{3}{2}\) x + 3

Slope: \(\frac{3}{2}\)

y-intercept: 3

The easiest way to solve this problem is to substract 2π from the angle until we get an angle that is less than 2π.

13/3π is not less than 2π, so we have to substract 2π once more:

7/3π is still not less than 2π, substract 2π once more:

1/3π is less than 2π. It means that the positive angle less than 2π that is coterminal with 19/3π is 1/3π.

The correct answer to this open question is the following.

Although the question does not include references, under that context we can say that if Canada experiences rapid and prolonged economic growth, instead of México, this would affect Canada's economic growth for the better and it will have a direct impact in various US states, basically, the border states to Canada.

This would mean more trade relations and people border crossing activity due to the increase of trade and businesses.

However, let's have in mind that México, Canada, and the United States have signed a new trade agreement that substitutes the North American Free Trade Agreement (former NAFTA). The new agreement is called USMCA, the United States, México, and Canada Agreement, and creates tight trade bonds between the three countries.

Answer:

grow quickly: michigan minnesota new york

not impacted: texas n. carolina

Step-by-step explanation: states that border canada are expected to gain from trade easier.

Answer:

62

Step-by-step explanation:

∠2 + ∠1 = 180

as they lie on the same line

∠2 = 180 - 118

= 62

Answer: Its 62

Step-by-step explanation: Since a triangle is 180 degree angel you subtracted 180 from 118 so its 180-118=62