suppose that a will be randomly selected from the set {-3, -2, -1, 0, 1} and that b will be randomly selected from the set {-2, -1, 0, 1}. what is the probability that a*b>0

Answer:

See Below.

Step-by-step explanation:

To find the perimeter of a trapezoid, you simply add up the lengths of all four sides.

In this case, the trapezoid has sides of 8 cm, 10 cm, 16 cm, and 10 cm.

Perimeter = 8 cm + 10 cm + 16 cm + 10 cm

Perimeter = 44 cm

Therefore, the perimeter of the trapezoid is 44 cm.

Construct a triangle PQR with sides PQ=8cm, PR=5cm, and QR=6cm, then draw a circle passing through P, Q, and R. This circle is called the circumcircle of triangle PQR.

We draw a line segment PQ = 8 cm long. From point P, we draw a line segment PR = 5 cm long at an angle of 60 degrees to PQ. Then, we draw a line segment QR = 6 cm long joining points Q and R to complete the triangle. Next, we use a compass to draw a circle passing through points P, Q, and R. This circle is called the circumcircle or circumscribed circle of the triangle, which is the unique circle that passes through all three vertices of the triangle. The circumcircle has a special property that its center is equidistant from the three vertices of the triangle.

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In calculus, integration is the process of finding the integral of a function. The integral is a mathematical concept that represents the area under a curve or the net accumulation of a quantity over a given interval.

(a) The pressure, p, at point (x, y) on the plate is proportional to the square of the distance of that point from the origin, so we have:

p(x,y) = k(x^2 + y^2)

where k is the constant of proportionality.

(b) To find the total force on the plate, we need to integrate the pressure over the entire surface of the plate. The surface area of the plate is given by A = ab, so the total force on the plate is:

F = ∬p(x,y) dA

where the double integral is taken over the surface of the plate.

(c) We can evaluate the integral by expressing the pressure as a function of either x or y and integrating it over the other variable. Since the pressure is symmetric in x and y, we can integrate over an either variable. Let's integrate over x first:

F = ∫[0,b] ∫[0, a] k(x^2 + y^2) dx dy

= k ∫[0,b] (a^3/3 + ab^2/2) dy

= kab^2/2 + k(a^3/3) ∫[0,b] dy

= kab^2/2 + k(a^3/3) b

= (kab^2/2 + ka^3b/3)

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Answer:

x = 8

Hope this helps!

Step-by-step explanation:

( 2x + 42 )° + ( 4x )° = 90°  ( right angle )

6x + 42 = 90

6x = 90 - 42

6x = 48

x = 8

30 is the value of x in parallelogram .

What is a parallelogram?

With sides that are parallel to one another, a parallelogram is a two-dimensional geometric shape. The pair of parallel sides in this sort of polygon with four sides, also known as a quadrilateral, are of equal length. In a parallelogram, the sum of the adjacent angles equals 180 degrees.

4x+68 = 6x + 8

 6x - 4x = 68 - 8

     2x = 60

        x = 30

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Step-by-step explanation:

Volume of a cube = s x s x s      (all of the sides are the same length)

s^3 = 8 / 729

s = 2 / 9  in

Answer:

Step-by-step explanation:

Choose three values for

x and substitute in to find the corresponding y values.(0,−3),(1,0),(2,3)

You can choose any of these three pairs or the equation y=3x-3

The maximum area of the surfboard correct to 2 places is 0.67 m².

Given that a surfboard is in the shape of a rectangle and a semicircle, and its perimeter is to be 4m. We need to find the maximum area of the surfboard, correct to 2 decimal places.

Let the radius of the semicircle be 'r' and the length and breadth of the rectangle be 'l' and 'b' respectively. Perimeter of the surfboard = [tex]4m => l + 2r + b + 2r = 4 => l + b = 4 - 4r[/tex] -----(1)

Area of surfboard = Area of rectangle + Area of semicircle Area of rectangle = l × b Area of semicircle = πr²/2 + 2r²/2 = (π + 2)r²/2Area of surfboard = l × b + (π + 2)r²/2 -----(2)

We have to maximize the area of the surfboard. So, we have to find the value of 'l', 'b', and 'r' such that the area of the surfboard is maximum .From equation (1), we have l + b = 4 - 4r => l = 4 - 4r - bWe will substitute this value of 'l' in equation (2)

Area of surfboard = l × b + (π + 2)r²/2 = (4 - 4r - b) × b + (π + 2)r²/2 = -2b² + (4 - 4r) b + (π + 2)r²/2Now, we have to maximize the area of the surfboard, that is, we need to find the maximum value of the above equation.

To find the maximum value of the equation, we can differentiate the above equation with respect to 'b' and equate it to zero. d(Area of surfboard)/db = -4b + 4 - 4r = 0 => b = 1 - r Substitute the value of 'b' in equation (1),

we get l = 3r - 3Now, we can substitute the values of 'l' and 'b' in the equation for the area of the surfboard.

Area of surfboard =

[tex]l × b + (π + 2)r²/2 = (3r - 3)(1 - r) + (π + 2)r²/2 = -r³ + (π/2 - 1)r² + 3r - 3[/tex]

[tex]-r³ + (π/2 - 1)r² + 3r - 3 = -0.6685 m² \\[/tex]

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Answer:

Step-by-step explanation:

To find the probability of choosing a random number that starts with 2, we need to find two things:

1. The total number of valid four-digit numbers that can be created from the digits 0-9 where the first and last digits are even and no digit can repeat.

2. The number of valid four-digit numbers that start with 2 and meet the other criteria.

Let's begin by calculating the total number of valid four-digit numbers.

There are 5 even digits (0, 2, 4, 6, 8) to choose from for the first and last digits. For the second digit, there are 9 digits to choose from (since 0 cannot be repeated), for the third digit there are 8 digits to choose from (since we used one digit already and neither the first nor last digit can be repeated), and for the last digit there are only 4 choices left (since we used 5 for the first digit, and one more can’t be repeated). Therefore, the total number of valid four-digit numbers is:

5 * 9 * 8 * 4 = 1,440

Now we need to calculate the number of valid four-digit numbers that start with 2.

We already determined that there are 5 even digits to choose from for the last digit, leaving 8 digits for the second and 7 for the third digit (since the first digit is fixed). So the number of valid four-digit numbers that start with 2 is:

5 * 8 * 7 * 1 = 280

Therefore, the probability of choosing a random number that starts with 2 is:

280 / 1,440 = 0.1944 rounded to 4 decimal places.

So the answer to the problem is 97/500, which simplifies to 0.1940 when rounded to 4 decimal places.

Answer:

Step-by-step explanation:

m∠O = 90° - 34° = 56°

cos M = [tex]\frac{MN}{MO}[/tex]  ⇒  MO = [tex]\frac{12}{cos34}[/tex] ≈ 14.5 cm

tan M = [tex]\frac{ON}{MN}[/tex]  ⇒  ON = 12 × tan 34° ≈ 8.1 cm  

The nearest hundredth, we get:

C ≈ 12.56 feet.

Circle circumference (or perimeter) = 2R

where R denotes the circle's radius. 3.14 is the approximate (up to two decimal points) value of the mathematical constant. Again, Pi () is a special mathematical constant that represents the circumference to diameter ratio of any circle.

The circumference of a circle is calculated as follows:

C = 2πr

where C is the circumference, (pi) is a constant close to 3.14, and r is the radius of the circle.

When the given values are substituted, the following results are obtained:

C = 2(3.14)(2) \s= 12.56

We get the following when we round to the nearest hundredth:

C ≈ 12.56 feet.

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The new enlarged triangle has vertices at P4, P5, and P6, and is three times larger than the original triangle, with the blue dot as its center of enlargement.

What is a triangle?

A triangle is a geometric shape that consists of three straight sides and three angles. It is one of the most basic and fundamental shapes in geometry, and it is formed when three non-collinear points are connected by straight lines.

To enlarge a triangle by a scale factor of 3 using the blue dot as the center of enlargement, follow these steps:

Draw a line connecting the blue dot and each vertex of the triangle.

Mark a point on each line that is 3 times the distance from the blue dot as the corresponding vertex of the original triangle.

Connect the points on each line to form the new enlarged triangle.

Here is a step-by-step visual guide:

1. Draw lines connecting the blue dot to each vertex of the original triangle.

           B

           /\

          /  \

         /    \

    P1  /      \  P2

       /        \

      /          \

     /____________\

    A      P3      C

2. Mark a point on each line that is 3 times the distance from the blue dot as the corresponding vertex of the original triangle.

           B

           /\

          /  \

         /    \

    P1  /      \  P2

       /        \

      /    P4    \

     /____________\

    A      P3      C

Note that P4 is located 3 times the distance from the blue dot to vertex A along the line connecting them. Similarly, P5 and P6 are located 3 times the distance from the blue dot to vertices B and C respectively along their respective lines.

3. Connect the points on each line to form the new enlarged triangle.

       P5

        /\

       /  \

      /    \

 P1 /      \ P2

    /        \

   /    P4    \

  /____________\

 P3      P6      P7

Therefore, the new enlarged triangle has vertices at P4, P5, and P6, and is three times larger than the original triangle, with the blue dot as its center of enlargement.

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It would make it easier for the cafe to adjust prices if necessary, as they would only need to modify the cost per ounce for each size.

Cost is the amount of money or resources required to purchase or produce something. It can be the total expenditure on a product, service, or activity. It can also refer to the amount of money or resources consumed in order to maintain or achieve something. Cost can also be the value of a resource lost or sacrificed in order to obtain something.

To make the price of smoothies a function of the size, the sign should be modified to include the following additional information:

8 ounce       $2.29/ounce
12 ounce      $2.79/ounce
12 ounce.     $3.09/ounce
16 ounce       $3.69/ounce
20 ounce        $4.09/ounce
22 ounce
( Bonus size).  $4.09/ounce

This change would make the price of smoothies a function of the size, as each smoothie size would then have its own associated cost per ounce. This would make it easier for customers to compare the cost of different sizes and make an informed decision. Furthermore, it would make it easier for the cafe to adjust prices if necessary, as they would only need to modify the cost per ounce for each size.

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Answer:

Evaluating the impact of the 16 Days of Activism campaign on Gender Based Violence (GBV) in South Africa requires a high-order analysis that considers various factors and perspectives. The campaign, which runs annually from November 25th (International Day for the Elimination of Violence against Women) to December 10th (International Human Rights Day), aims to raise awareness and mobilize action to prevent and respond to GBV.

The impact of the 16 Days of Activism campaign on GBV in South Africa can be evaluated through different lenses, including quantitative data, policy and legal changes, societal attitudes, and lived experiences of survivors.

Quantitatively, South Africa has one of the highest rates of GBV in the world, with statistics showing that one in five women in the country is a survivor of GBV. While there has been a slight decrease in the incidence of GBV in recent years, the numbers remain alarmingly high. It is difficult to attribute the reduction to the 16 Days of Activism campaign alone, as there are several other factors at play.

However, the campaign has contributed to policy and legal changes aimed at addressing GBV in South Africa. For instance, the Domestic Violence Act was amended in 2018 to include broader definitions of domestic violence and harsher penalties for perpetrators. In addition, the government has established various institutions and initiatives, such as the National Council Against Gender-Based Violence and the GBV Command Centre, to respond to GBV and provide support to survivors.

The 16 Days of Activism campaign has also had an impact on societal attitudes towards GBV in South Africa. Through awareness-raising activities, community dialogues, and media campaigns, the campaign has helped to break the silence and stigma around GBV, and encouraged more people to speak out and seek help. However, entrenched patriarchal norms and gender inequalities continue to fuel GBV in the country, and changing these attitudes requires sustained efforts beyond the 16 Days of Activism campaign.

Lastly, the impact of the 16 Days of Activism campaign on GBV in South Africa can be evaluated through the lived experiences of survivors. While the campaign has provided a platform for survivors to share their stories and advocate for change, many still face significant barriers in accessing justice and support. This includes systemic issues such as under-resourced police and healthcare systems, as well as cultural and social norms that blame and stigmatize survivors.

In conclusion, while the 16 Days of Activism campaign has had some impact on GBV in South Africa, it is clear that much more needs to be done to effectively address the root causes of this pervasive issue. The campaign serves as an important reminder of the urgent need for sustained and collaborative efforts from all sectors of society to prevent and respond to GBV.

Step-by-step explanation:

The area of the circle will decrease by 51% if the diameter increases by 40%. Then the new diameter will be 1.4 times the original diameter.

Let's assume the original diameter is d and the original area of the circle is A.

Then, the new diameter will be 1.4d and the new area of the circle can be calculated as follows:

New area = pi * (New diameter/2)²= pi * (1.4d/2)² = pi * (0.7d)² = 0.49 * pi * d²

Therefore, the new area is 0.49 times the original area.

To calculate the percentage increase in area, we can use the following formula:

Percentage increase = (New value - Old value) / Old value * 100%

In this case, the old value is the original area A and the new value is the new area, which is 0.49*A. Therefore,

Percentage increase = (0.49A - A) / A * 100%

= -0.51A / A * 100%

= -51%

Therefore, the area of the circle will decrease by 51% if the diameter increases by 40%.

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45.53 ,fencing is needed to build the fence.

A solid object's surface area is a measurement of the total area that the surface of the object takes up.

The definition polyhedra of arc length for one-dimensional curves and the definition of surface area for (i.e., objects with flat polygonal faces), where the surface area is the sum of the areas of its faces, are both much simpler mathematical concepts than the definition of surface area when there are curved surfaces.

A smooth surface's surface area is determined using its representation as a parametric surface, such as a sphere.

This definition of surface area uses partial derivatives and double much simpler mathematical concepts than the definition of surface area integration and is based on techniques used in infinitesimal calculus.sought a general definition of surface area.



Henri Lebesgue and Hermann Minkowski at the turn of the century sought a general definition of surface area.

2*3.14*14.5/2

45.53ft

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The transformation of energy from eating the nutritious meal to the five-mile run involves the conversion of the nutrients from the meal into usable energy in the body. This energy is then converted into the kinetic energy necessary to move the student's body while running. The energy produced from the meal is broken down and used to fuel the muscles and other body systems necessary for the run.

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Simplifying Mrs. Perez's class donated 11 units of vegetables, 66 units of pasta, and 22 units of soup.

The process of solving a math problem is simply known as simplifying an expression. An expression is simplified when it is written in the most straightforward way feasible

vegetables = (1/9) x 99

Simplifying this expression, we get:

vegetables = 11

So the class donated 11 units of vegetables.

Next, we can figure out how much of the donation was pasta. We know that 2/3 of the donation was pasta, so we can set up the equation:

pasta = (2/3) x 99

Simplifying 66 units homemade pasta, 22 units of soup, and 11 units of veggies were all provided by Mrs. Perez's students.

Which expression should I simplify?

A math difficulty is simply solved by simplifying the expression. When you simplify a phrase, your goal is essentially to make it as simple as you can. There shouldn't be any more multiplication, dividing, adding, or removing to be done at the conclusion.

veggies = 1/9 times 99

When we condense this statement, we get:

eleven vegetables

We can then determine what proportion of the contribution was pasta. Given that we know that pasta made up 2/3 of the donation, we can construct the following equation:

spaghetti equals (2/3) x 99

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A typical water bed weighs around 1797.6 pounds. It depends upon the volume of water bed and the unit conversion of the weight and volume units.

A typical water bed holds 28 cubic feet of water.

The volume of the typical water bed and its weight can be calculated with the help of the quantities:

Identify the volume of water held by the water bed, which is 28 cubic feet.
Multiply the volume by the weight of 1 cubic foot of water, which is 64.2 pounds.
Perform the calculation: 28 cubic feet × 64.2 pounds per cubic foot = 1797.6 pounds.

Therefore, a typical water bed weighs approximately 1797.6 pounds when filled with water.

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The statement "the equations of motion of a two-degree-of-freedom system can be expressed in terms of the displacement of either of the two masses" is TRUE.

The equations of motion refer to a set of mathematical equations that describe the behavior of a physical system over time. These equations define how the position, velocity, and acceleration of an object are related. The equations of motion are applicable to both single and multi-degree-of-freedom systems.

A two-degree-of-freedom system is a physical system with two independent modes of motion or two degrees of freedom. It is defined by two generalized coordinates that completely define the system's state.

A two-degree-of-freedom system can be either linear or nonlinear, depending on the nature of the force. It is used in the study of structural dynamics, mechanical vibrations, and control engineering.

In a two-degree-of-freedom system, the equations of motion can be expressed in terms of the displacement of either of the two masses. The equations of motion are usually derived using Lagrange's equations, which are a set of equations that describe the dynamics of a mechanical system in terms of its energy. They are given as follows:

Where q₁ and q₂ are the generalized coordinates, m₁ and m₂ are the masses, k₁ and k₂ are the spring constants, and c₁ and c₂ are the damping coefficients.

These equations of motion are nonlinear and can be solved analytically or numerically using various techniques.

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Answer: 18/80 for theoretical and then 18/80=.225 = 22.5% for experimental

Step-by-step explanation: theoretical: theres 18 white marbles, and then add up 34 + 18+9+19 to get 80. to get theoretical its number of favorable outcomes over total size of sample space, therefore 18 over 80

Experimental: divide 18/80 to get .225 then move decimal over by 2 to get 22.5%

The phone is worth $128 after 2 years, which is option C.

What is exponential decay ?

Exponential decay is a decrease in a quantity over time where the rate of decay is proportional to the current value. In this case, the value of the phone decreases by 3/5 each year after it is released. This means that the value after one year is 2/5 of the original value, and the value after two years is (2/5) times (2/5) of the original value. Exponential decay is a common phenomenon in many areas of science and mathematics, including radioactive decay, population growth and decay, and financial investments.

Calculating the worth of the phone :

The phone is not worth the same amount after 2 years, as it loses 3/5 of its value each year. We need to calculate its worth after 2 years.

Let's use the formula for exponential decay: [tex]A = A_0(1 - r)^t[/tex], where A is the final amount, [tex]A_0[/tex] is the initial amount, r is the decay rate, and t is the time elapsed.

In this case, the initial amount is $800, the decay rate is 3/5, and the time elapsed is 2 years. Substituting these values into the formula, we get:

[tex]A = 800(1 - 3/5)^2[/tex]

[tex]A = 800(2/5)^2[/tex]

[tex]A = 800(4/25)[/tex]

[tex]A = 128[/tex]

Therefore, the phone is worth $128 after 2 years, which is option C.

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Answer:

5 gallons

Step-by-step explanation:

20÷3.50=5.714...

so the answer is 5 gallons

When solving arithmetic expressions, Oracle 12c resolves addition and subtraction operations first from left to right in the expression. This statement is true.

By following these rules, Oracle 12c is able to resolve arithmetic expressions accurately and efficiently. This is particularly important when dealing with large amounts of data, where the correct order of operations is critical to ensure that the correct result is obtained.

Oracle 12c is a database management system that is used to handle large amounts of data. It has a variety of features that enable it to manage and maintain data effectively.

Oracle 12c has a SQL engine that allows it to execute SQL statements and expressions to retrieve and manipulate data.

When performing arithmetic operations in Oracle 12c, the order of operations is critical. The order of operations is the set of rules that dictate the sequence in which arithmetic operations should be performed in a mathematical expression.

These rules are also known as the rules of precedence.In Oracle 12c, the rules of precedence dictate that arithmetic operations should be resolved from left to right in an expression. This means that addition and subtraction operations should be resolved before multiplication and division operations.

This is because addition and subtraction operations have a lower precedence than multiplication and division operations. As a result, Oracle 12c always resolves addition and subtraction operations first from left to right in an expression .This order of operations ensures that the correct result is obtained when performing arithmetic operations in Oracle 12c.

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Answer:

x= 2√ 7

Step-by-step explanation:

We can solve it with applying the sin of 30°

Sin 30° = opposite leg / hypotenuse

Sin 30° = √ 7 / x

Being x unknown.

Now, being 30°  a notable angle, we know that its sin is 1/2.

Sin 30° = 1/2

Replacing,

Sin 30° = √ 7 / x.           (we clear x)

1/2 = √ 7 / x

x/2 = √ 7

x= 2√ 7

Answer: The two angles are 117 degrees and 63 degrees.

Step-by-step explanation:

Supplementary angles are two angles whose sum is 180 degrees. Let the two angles be 13x and 7x, where x is a constant of proportionality.

We know that the sum of the angles is 180 degrees, so:

13x + 7x = 180

Combining like terms, we get:

20x = 180

Dividing both sides by 20, we get:

x = 9

So the measures of the angles are:

13x = 13(9) = 117 degrees

7x = 7(9) = 63 degrees

Therefore, the two angles are 117 degrees and 63 degrees.

By using CDF  [tex]P(X \le 1)[/tex],  [tex]P(0.5 \le X \le 1)=0.1875[/tex] , [tex]\mu= 1.4142[/tex],  density function f(x) is [tex]0[/tex]  [tex], E(X)=1 , V(X) = 1,[/tex]    the expected charge  [tex]E[h(X)]=2.[/tex]

(a) To obtain CDF

[tex]P(X \le 1)[/tex]

We have:

[tex]P(X \le 1) = F(1) = (1^2)/4 = 0.25[/tex]

(b)  [tex]P(0.5 \le X \le1)[/tex]

We have:

[tex]P(0.5 \leX \le 1) \\ =F(1) - F(0.5) \\= (1^2)/4 - (0.5^2)/4 \\ =0.1875[/tex]

(c)  [tex]P(X > 1.5)[/tex]

We have:

[tex]P(X > 1.5) \\= 1 - F(1.5) \\= 1 - (1.5^2)/4 \\= 0.1094[/tex]

(d) The median checkout duration [solve 0.5 = F(μ)]

To find the median, we need to solve the equation 0.5 = F(μ) for μ. This means we need to solve:

[tex]0.5 = (\mu^2)/4[/tex]

[tex]\mu^2= 2[/tex]

[tex]mu = \sqrt(2) \approx 1.4142[/tex]

(e) Use F'(x) to obtain the density function f(x)

We have:

[tex]f(x) = F'(x) \\= d/dx [(x^2)/4]\\ = x/2, 0 \le x \le 2[/tex]

[tex]f(x) = 0[/tex], otherwise

(f) Calculate  [tex]E(X)[/tex]

We have:

[tex]E(X) = \int\ x f(x)dx[/tex]   from 0 to 2

[tex]E(X) = \int\ x(x/2)dx[/tex] from 0 to 2

[tex]E(X) = [x^3/6][/tex] from 0 to 2

[tex]E(X) = (2^3/6)[/tex]

[tex]E(X) = 1[/tex]

(g) Calculate V(X) and σx

We have:

[tex]V(X) = E(X^2) - [E(X)]^2[/tex]

[tex]V(X) = \int\x^2f(x)dx[/tex] from 0 to 2 - [E(X)]²

[tex]V(X) = \int\x^2 (x/2)dx[/tex] from 0 to 2 - 1²

[tex]V(X) = [x^4/8][/tex] from 0 to 2 - 1

[tex]V(X) = (2^4/8) - (0^4/8) - 1[/tex]

[tex]V(X) = 1[/tex]

Therefore, [tex]\sigma x = \sqrt{(V(X))} = \sqrt{(1)} = 1.[/tex]

(h) If the borrower is charged an amount  [tex]h(X) = X^2[/tex]  when checkout duration is X, compute the expected charge E[h(X)]

We have:

[tex]E[h(X)] = \int\ h(x)f(x)dx[/tex] from 0 to 2

[tex]E[h(X)] = \int\x^2(x/2)dx[/tex] from 0 to 2

[tex]E[h(X)] = [x^4/8][/tex] from 0 to 2

[tex]E[h(X)] = (2^4/8) - (0^4/8)[/tex]

[tex]E[h(X)] = 2[/tex]

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Answer:

Step-by-step explanation:

kernel composition rules 2 1 point possible (graded) let and be two vectors of the same dimension. use the the definition of kernels and the kernel composition rules from the video above to decide which of the following are kernels. (note that you can use feature vectors that are not polynomial.) (choose all those apply. )

The both vectors' components are independent of each other, and they do not interfere with each other.

1. A nonzero vector that has a component of zero is a vector with one of its component set to zero. An example of such a vector is a two-dimensional vector (x,0). For instance, a vector of (5,0) has a component of zero in the y-axis.

2. A vector cannot have a component greater than its own magnitude because the magnitude is the total length of the vector, which represents its total strength. The components of the vector are directional pieces that define the vector. Thus, if the component is more significant than the total length, it means the vector's direction has been multiplied in that component, and the vector's magnitude cannot handle the force. Therefore, the component cannot be more significant than the vector's magnitude.

3. If the vectors A and B are perpendicular, the component of A along the direction of B is zero, and the component of B along the direction of A is zero. When two vectors are perpendicular, it means they meet at a 90-degree angle, and their dot product is zero, implying that the product of the magnitude of one vector and the magnitude of the other vector multiplied by the cosine of the angle between them is zero. Therefore, both vectors' components are independent of each other, and they do not interfere with each other.

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