Solve by using Cramer's Rule: \[ \begin{array}{l} -3 x-4 y-4 z=-8 \\ x-3 y-3 z=-19 \\ -x+y-2 z=3 \end{array} \]

According to the properties of quadrilaterals:

If a shape is a Parallelogram than it is a Square: False.

If a shape is a Square than it is a Rectangle: True.

If a shape is a Rhombus than it is a Quadrilateral: True.

If a shape is a Trapezoid than it is a Parallelogram: False.

If a shape is a Quadrilateral than it is a Rectangle: False.

Explain about quadrilaterals ?

Quadrilaterals are closed two-dimensional shapes with four straight sides and four angles. The word "quadrilateral" comes from the Latin words "quadric" which means "four" and "latus" which means "side". Some common examples of quadrilaterals include squares, rectangles, parallelograms, rhombuses, and trapezoids.

Each type of quadrilateral has its own unique set of properties and characteristics. For example, a rectangle has four right angles and opposite sides that are parallel and congruent. A parallelogram has opposite sides that are parallel and congruent, and opposite angles that are congruent. A rhombus has four congruent sides and opposite angles that are congruent.

According to the question:
Here are the answers to the true or false questions:

1. If a shape is a Parallelogram than it is a Square.

False. A parallelogram can have any angle measure as long as the opposite sides are parallel. A square is a specific type of parallelogram with four congruent sides and four right angles.

2. If a shape is a Square than it is a Rectangle.

True. A square is a special type of rectangle where all four sides are congruent.

3. If a shape is a Rhombus than it is a Quadrilateral.

True. A rhombus is a type of quadrilateral with four congruent sides.

4. If a shape is a Trapezoid than it is a Parallelogram.

False. A trapezoid has only one pair of parallel sides, while a parallelogram has two pairs of parallel sides.

5. If a shape is a Quadrilateral than it is a Rectangle.

False. A quadrilateral is a broad category of four-sided shapes that includes rectangles, but it also includes many other types of shapes, such as trapezoids, parallelograms, rhombuses, and kites.

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The Euclidean inner product of the given vectors is 25.

The Euclidean inner product of two vectors u and v is defined as the sum of the products of the corresponding entries of the vectors. In mathematical terms, it is given by:

Euclidean inner product = u[1]*v[1] + u[2]*v[2] + u[3]*v[3]

Given the vectors u=[[5],[3],[-4]] and v=[[1],[0],[-5]], we can find the Euclidean inner product by substituting the values into the formula:

Euclidean inner product = (5)*(1) + (3)*(0) + (-4)*(-5)
= 5 + 0 + 20
= 25

Therefore, the Euclidean inner product of the given vectors is 25.

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The solutions to the quadratic equation (u-3)^(2)-20=0 are u=3+2√5 and u=3-2√5.

To solve the quadratic equation (u-3)^(2)-20=0, we will use the following steps:

1. Add 20 to both sides of the equation to isolate the squared term: (u-3)^(2)=20

2. Take the square root of both sides of the equation: u-3=±√20

3. Simplify the radical on the right side of the equation: u-3=±2√5

4. Add 3 to both sides of the equation to isolate the variable: u=3±2√5

5. Write the two solutions separately: u=3+2√5 or u=3-2√5

Therefore, the solutions to the quadratic equation (u-3)^(2)-20=0 are u=3+2√5 and u=3-2√5.

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The solution to the equation tan²(x) = sec(x) − 1 in the interval [0, 2π) is x = 0

Consider equation tan²(x) = sec(x) − 1

We know that tan(x) = sin(x)/cos(x) and sec(x) = 1/cos(x)

so the equation becomes,

[tex]\frac{sin^2(x)}{cos^2(x)}-\frac{1}{cos(x)}+1=0[/tex]

sin²(x) - cos(x) + cos²(x) = 0

We know that the trignometric identity sin²(x) + cos²(x) = 1

(1 - cos²(x)) - cos(x) + cos²(x) = 0

1 - cos²(x) - cos(x) + cos²(x) = 0

1 - cos(x) = 0

cos(x) = 1

We know that for x = 0 and 2π, the value of cos(x) is 1

In the interval [0, 2π), the solution for equation would be x = 0

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The complete question is:

Find all solutions of the equation in the interval [0, 2π). (Enter your answers as a comma-separated list. If there is no solution, enter NO SOLUTION.) tan²(x) = sec(x) − 1

Answer:

Solve for the first variable in one of the equations, then substitute the result into the other equation.

Point Form:

(

0

,

−

3

)

Equation Form:

x

=

0

,

y

=

−

3

Step-by-step explanation:

Answer:

x=0 y=3

Step-by-step explanation:

3(0) + 5(3) = 15

0 + 15 = 15

15=15

The variance of the error term is equal to the expected value of the squared error term, which is equal to the variance of Xi.

The asymptotic distribution of the coefficient β from bivariate OLS is given by √N(β – β) + d(0,σ2), where σ2 is the variance of the error term and is given by Var((Xi - E[X])) / Var(xi)2. If the error term is homoskedastic, then the variance of the error term does not depend on the value of Xi and is constant for all values of Xi. This implies that the variance of Y given X and r does not depend on r, as shown below:

Var(Y|X, r) = Var(βX + ε|X, r) = Var(ε|X, r) = σ2

Since the variance of the error term is constant and does not depend on the value of X or r, the variance of Y given X and r is also constant and does not depend on r.

If Yi is earnings and Xi is an indicator for whether someone has gone to college, homoskedasticity would imply that the variance of earnings for college and non-college workers is the same. This is unlikely to hold in practice, as there are likely to be other factors that affect earnings, such as occupation, experience, and location, that may differ between college and non-college workers and lead to different variances in earnings.

If the error term is homoskedastic and E[εi|Xi] = 0, then the variance of the error term is equal to the variance of Xi, as shown below:

Var(εi) = E[εi2] - (E[εi])2 = E[εi2] = E[(Xi - E[Xi])2] = Var(Xi)

This is because the error term is uncorrelated with Xi and has a mean of zero

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One possible set of values that would make the inequality true is:

g = 5

g = 0

g = -1

When we substitute these values into the inequality, we get:

4 + 5 ≥ 9 (true)

4 + 0 ≥ 9 (false)

4 + (-1) ≥ 9 (false)

Therefore, the values that make the inequality true are g = 5, g = 0, and g = -1.

The variables to use in a model depend on the type of model being developed and the problem being addressed. In general, variables are the inputs to a model that are used to predict the outputs or dependent variables.

In statistical models, the independent variables, also known as predictors or features, are chosen based on their ability to explain the variability in the dependent variable. For example, in a linear regression model, the independent variables may include factors such as age, income, education, and gender, which are thought to be related to the dependent variable, such as the likelihood of purchasing a product.

In machine learning models, the variables may include a wide range of features, such as text, images, or sensor data, that are used to make predictions or classifications. The process of selecting the most relevant features, also known as feature selection, is an important step in developing effective models that can generalize well to new data.

Ultimately, the choice of variables depends on the specific problem being addressed, and may involve a combination of domain expertise, statistical analysis, and machine learning techniques to identify the most important predictors or features.

P.S: An overview was given as your information is incomplete.

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Step-by-step explanation:

12(5x - 4.5) = 36

if that is really correct, then we solve this first by dividing both sides by 12

5x - 4.5 = 3

then we add 4.5 to both sides

5x = 7.5

and finally we divide both sides by 5

x = 1.5

The tοtal area οf the cοmpοsite figure is 358.38 mm² (rοunded tο twο decimal places).

Area is the measurement οf the size οf a surface οr a regiοn in a 2D plane, typically measured in square units. It is calculated by multiplying the length and width οf a surface οr regiοn fοr simple shapes like rectangles, οr by using fοrmulas specific tο each shape fοr mοre cοmplex shapes.

The area οf a semicircle with radius r is given by (π/2)r², and the area οf a trapezium with height h and parallel sides a and b is given by (h/2)(a+b).

Substituting the given values, we get

Area οf semicircle = (π/2)(9mm)² = 81π/2 mm²

Area οf trapezium = (13mm/2)(7mm+18mm) = 227.5 mm²

Therefοre, the tοtal area οf the semicircle and trapezium is:

81π/2 + 227.5 ≈ 358.38 mm²(rοunded tο twο decimal places).

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1 and 3

Step-by-step explanation:

pick one from the junior side and 3 from seniors because the senior is more that the junoir

Answer:

990 different combinations

Step-by-step explanation:

There are 6 juniors and 12 seniors for a total of 16 students

Out of 6 juniors we have to pick 2 juniors

Out of 12 seniors we have to pick 2 seniors

The number of items r that we can pick from a larger set of n items is given by C(n, r) pronounced n choose r.. This is sometimes written as nCr

The formula forC(n, r) is

[tex]\boxed{C(n,r) = \dfrac{n!}{r! (n - r)! }}[/tex]

where n! = n factorial = n x (n-1) x (n-2) x .... x 3 x 2 x 1

We can choose 2 juniors out of 6 juniors in C(6, 2) ways
and
2 seniors out of 12 seniors in C(12, 2) ways

[tex]C(6, 2) = = \dfrac{6!}{ 2! (6 - 2)! }\\\\= \dfrac{6!}{2! \times 4! }\\\\= 15[/tex]

[tex]C(12, 2) = \dfrac{12!}{ 2! (12 - 2)! }\\\\ = \dfrac{12!}{2! \times 10! }\\\\= 66[/tex]

Therefore the total number of ways you can select 2 juniors and 2 seniors from a pool of 6 juniors and 12 juniors

= 15 x 66 = 990

Answer:

AC is about 33 inches.

Step-by-step explanation:

Set your calculator to degree measure.

[tex] \tan(35) = \frac{x}{47} [/tex]

[tex]x = 47 \tan(35) = 32.91[/tex]

The numbers in the intersection of sets P and Q are 0, 1, 2, 3, and 4.

The integers in Set P are {-7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4}.

The absolute values of these integers are {7, 6, 5, 4, 3, 2, 1, 0, 1, 2, 3, 4}, which make up Set Q. The intersection of Set P and Set Q are the integers that are in both sets, which are {0, 1, 2, 3, 4}.

Therefore, the numbers in the intersection of sets P and Q are 0, 1, 2, 3, and 4.

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Answer: C

8x+6/-x^2+1

Step-by-step explanation:

we can graph the solution on the number line. The solution will be the intersection of the two inequalities, which is u >= 5. The solution to the compound inequality is u >= 5.

To solve the compound inequality, we need to isolate the variable on one side of the inequality.

For the first inequality, 4u + 5 > 13, we can subtract 5 from both sides to get:
4u > 8

Then, we can divide both sides by 4 to get:
u > 2

For the second inequality, 2u + 6 >= 16, we can subtract 6 from both sides to get:
2u >= 10

Then, we can divide both sides by 2 to get:
u >= 5

Now, we can graph the solution on the number line. The solution will be the intersection of the two inequalities, which is u >= 5.

On the number line, we can draw a closed circle at 5 and shade to the right to indicate that the solution includes 5 and all numbers greater than 5.

The solution to the compound inequality is u >= 5.

Here is the graph of the solution on the number line:

    0  1  2  3  4  5  6  7  8  9  10

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Answer:

The students would be paying a low amount of $5.60. The 30% discount takes off $2.40 of the original price, so the discount is worth $2.40

For the given function f(x) = (x - 4)² - 3, the following statements are correct -

B: relative minimum at (4,-3).

C: decreasing interval from (-∞, 4).

E: increasing interval is (4, ∞).

What is a function?

In mathematics, a function is a unique arrangement of the inputs (also referred to as the domain) and their outputs (sometimes referred to as the codomain), where each input has exactly one output and the output can be linked to its input.

To find the relative maximum and minimum of the function, we need to find its critical points by setting the derivative of the function equal to zero -

f(x) = (x - 4)² - 3

f'(x) = 2(x - 4)

2(x - 4) = 0

x = 4

So, the only critical point of the function is x = 4.

Plug in the value of x = 4 in the equation -

(4 - 4)² - 3

0 - 3

-3

Since f''(4) is positive, the critical point at x = 4 is a relative minimum.

Therefore, the function has a relative minimum at (4, -3).

To find the increasing and decreasing intervals, we can look at the sign of the first derivative -

f'(x) = 2(x - 4)

For x < 4, f'(x) is negative, meaning that f(x) is decreasing on the interval (-∞, 4).

For x > 4, f'(x) is positive, meaning that f(x) is increasing on the interval (4, ∞).

Therefore, the decreasing interval is (-∞, 4), and the increasing interval is (4, ∞).

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Answer:

Step-by-step explanation:

lets take the top part as 1 and the seconds part as 2

so for the first part

1 Area= L*B

so 8*5 =40

2 Area=L*B

so 11*4=44

44+40=84cm2

Answer:

Step-by-step explanation:

Answer:

400

Step-by-step explanation:

Answer:

Step-by-step explanation:

The answer is 400 because you have to solve from left to right because of PEMDAS. So first you mutlipy 5x8 which is 40, and then you do 40x10 which is 400.

The value of (f· g)(x) from the given functions is  -x^4 - x^2 - x.

Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.

Here,

The given functions are f(x)=x³+x+1 and g(x)=-x.

(f·g)(x)= f(x) × g(x)

= (x³+x+1) × (-x)

=  -x^4 - x^2 - x

so, e get,

(g·f)(x)= g(x) × f(x)

= (-x) × (x³+x+1)

= -x^4 - x^2 - x

Therefore, the value of (f· g)(x) from the given functions is  -x^4 - x^2 - x.

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Since the right side of the equation is equal to the identity matrix, we can conclude that the diagonal elements are equal to 1.

To find \( A \), start by multiplying both sides by \( (4A) \). Then, you will have \( (4A)^{-1}(4A)=\left[\begin{array}{ll} 5 & 2 \\ 4 & 2 \end{array}\right] \). This simplifies to \( \left[\begin{array}{ll} 5A & 2A \\ 4A & 2A \end{array}\right] \). Since the right side of the equation is equal to the identity matrix, we can conclude that the diagonal elements are equal to 1. This means that \( 5A=1 \) and \( 2A=1 \). Solving these two equations yields \( A=\frac{1}{5} \).

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Therefore , the solution of the given problem of unitary method comes out to be he only had a 19 gallon jug of petroleum, which was insufficient for both days.

To finish the job using the unitary method, multiply the subsets measures taken from this microsecond section by two. In a nutshell, when a wanted thing is present, the characterized by a variable group but also colour groups are both eliminated from the unit technique. For instance, 40 changeable-price pencils would cost Inr ($1.01). It's conceivable that one nation will have complete control over the strategy used to achieve this. Almost all living things have a unique trait.

Here,

Magnus had to fill up his skiff with 6 gallons and 3 quarts of gas on Monday. We can observe that 1 quart is equivalent to 0.25 gallons to express this in decimal form:

=> 6 gallons 3 quarts = 6 + 3/4 = 6.75 gallons

Magnus used 6.75 litres of fuel on Monday as a result.

He required twice as much petrol on Saturday as he did on Monday:

=> 13.5 gallons from

=> 2 (6.75" gallons).

So on Saturday, he consumed 13.5 litres of fuel.

Overall, he employed:

=> 6.75 gallons + 13.5 gallons = 20.25 gallons

He only had a 19 gallon jug of petroleum, which was insufficient for both days.

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First step is wrong (x-2) × 3x³ should be 3x⁴ - 6x³

not 6x²

y = 3sin(πt). This function models the oscillation by representing the distance in centimeters from the equilibrium position as the sine of π multiplied by the time in seconds.

y = 3sin(πt). This function can be used to model the oscillation because it represents the distance in centimeters from the equilibrium position as the sine of π multiplied by the time in seconds. This means that for any given value of t, the value of y will be the sine of π multiplied by t, which will correspond to a certain distance from the equilibrium position. As the oscillation has a frequency of 1 cycle per second, the value of t will increase linearly, and the value of y will oscillate between a maximum and a minimum value. As the distance between the maximum and minimum points of the oscillation is 3 centimeters, the maximum and minimum values of y will be 3 when t is an integer multiple of π. Therefore, the function y = 3sin(πt) can be used to accurately model the oscillation.

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Answer:

  x = 10.1

Step-by-step explanation:

You want the value of x in the given secant-tangent geometry.

The angle between the secant ON and the tangent MN is half the measure of arc ON. The measure of arc ON is the remainder of the circle after long arc ON = 283° is subtracted:

  arc ON = 360° -283° = 77°

  (5x -12)° = 1/2(77°) . . . . . relation of angle to arc

  10x -24 = 77 . . . . . . . . divide by °, multiply by 2

  10x = 101 . . . . . . . . . . add 24

  x = 10.1 . . . . . . . . . . divide by 10

Answer:

30 baskets per minute

Step-by-step explanation:

We know

Shaq shot 420 baskets in 14 minutes.

Find his basket rate in baskets per minute.

We take

420 / 14 = 30 baskets per minute

So, the answer is 30 baskets per minute.

Epidemiology would include option (a), (c), and (d).

Epidemiology is the study of the distribution and determinants of health-related states or events in specified populations, and the application of this study to the control of health problems (JM. A Dictionary of Epidemiology, 2001). According to this definition, Epidemiology would include the following activities:

Option (a): Describing the demographic characteristics of persons with acute aflatoxin poisoning in Chittagong: This activity fits with the definition of Epidemiology because it involves studying the characteristics of a specified population, in this case the demographic characteristics of persons with acute aflatoxin poisoning in Chittagong, in order to better understand the determinants and distribution of the health-related state (acute aflatoxin poisoning).

Option (c): Comparing the family history, amount of exercise, and eating habits of those with and without newly diagnosed diabetes: This activity fits with the definition of Epidemiology because it involves studying the determinants of a health-related state, in this case newly diagnosed diabetes, in order to better understand the distribution and control of this health problem.

Option (d): Recommending that 'Kashundi restaurant' in IUB be closed after implicating it as the source of a hepatitis A outbreak: This activity fits with the definition of Epidemiology because it involves applying the study of the distribution and determinants of health-related states to the control of health problems, in this case the control of a hepatitis A outbreak.

In summary, Epidemiology would include option (a), (c), and (d).

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If h(x) = (-x + 1)2 – 5 and g(x) = -x – 2, then (hog)(x) will be B. -x2 + 2x + 2.

If h(x) = (-x + 1)2 – 5 and g(x) = -x – 2, then (hog)(x) = (h(g(x)). This means that we need to plug in the value of g(x) into the equation for h(x) and simplify. To get this result, first use the chain rule:

(hog)(x) = h(g(x)).

So, (hog)(x) = h(g(x)) = h(-x-2) = (-(x)-2+1)2 – 5 = (-x-1)2 – 5

Expanding the square, we get:

(hog)(x) = (-x-1)(-x-1) – 5 = x2 + 2x + 1 – 5 = x2 + 2x - 4

Therefore, the correct answer is B. -x2 + 2x + 2.

Answer: B. -x2 + 2x + 2

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Answer:

Let's call the total number of people who will attend the movie "x". We know that 95% of these people have yet to arrive, which means that only 5% have already arrived.

We can set up an equation to represent this situation:

5% of x = 170

To solve for x, we need to isolate it on one side of the equation. We can do this by dividing both sides of the equation by 5% (or 0.05, which is the decimal equivalent of 5%):

5% of x / 5% = 170 / 5%

Simplifying the left side of the equation gives:

x = 170 / 0.05

Evaluating the right side of the equation gives:

x = 3400

Therefore, there were 3400 tickets sold for the movie.