how to calculate calculate mean and standard deviation after transforming a random variable combining random variables

A:  y = 2x³, is a non-linear function.

B: y = x + 5, is a linear function.

C: y = x² − 3, is a non-linear function.

D: 5x + 5y = 25 and y = x² / 2, is a linear and non-linear function.

What is a function?

A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.

If the degree of the function is one. Then the function will be a linear function.

If the degree of the function is not one. Then the function will be a non-linear function.

Hence,

A:  y = 2x³, is a non-linear function.

B: y = x + 5, is a linear function.

C: y = x² − 3, is a non-linear function.

D: 5x + 5y = 25 and y = x² / 2, is a linear and non-linear function.

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A:  y = 2x³, is a non-linear function.

B: y = x + 5, is a linear function.

C: y = x² − 3, is a non-linear function.

D: 5x + 5y = 25 and y = x² / 2, is a linear and non-linear function.

A statement, idea, or rule that creates a link between two variables is known as a function. Mathematics has functions, which are necessary for the creation of meaningful connections.

if the function has a degree of one. The function will thereafter be linear in nature.

if the function's degree is not one. The function will then be non-linear in that case.

As a result, the function A: y = 2x3 is not linear.

B: The linear function y = x + 5 is given.

C: The non-linear function y = x2 3 is.

D: The equation 5x + 5y = 25 has a linear and nonlinear component, y = x2 / 2.

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Answer:

hope this helps you to understand.

The volume of the given shape would be = 410cm³

A rectangle is defined as the type of quadrilateral that has two pairs of equal sides that are parallel to each other with angles equal to 90°.

From the shapes given above,

it is made up of three rectangles combine together with different lengths, width and height.

The volume of a rectangle = l×w×h

Rectangle A = 10×3×8 = 240

Rectangle B = 6×5×3 = 90

Rectangle C = 2×5×8 = 80

Therefore the volume of the shape = 240+90+80= 410cm³.

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The supplied differential equation by variable separation is y(x) = sin(x²/2+c), as stated in the statement.

Any equation containing one or more terms and first or more derivatives of the dependent variable with respect to the independent variable is referred to as a differential equation (i.e., independent variable) dy/dx = f (x) In this case, the variables "x" and "y" are isolated and dependent, respectively. For illustration, dy/dx = 5x. Common differential equations are used in everyday life to compute the flow of electricity, the motion of an item back and forth like a pendulum, and to illustrate the principles of thermodynamics. Additionally, in medical terminology, they are employed to graphically monitor the progression of illnesses.

With respect to that differential equation [tex]\frac{d y}{d x}=x \sqrt{1-y^2}[/tex]

[tex]\frac{d y}{\sqrt{1-y^2}}=x d x[/tex]

By implementing integration across both sides,

[tex]\begin{aligned}& \int \frac{d y}{\sqrt{1-y^2}}=\int x d x \\& \sin ^{-1}(y)=\frac{x^2}{2}+c \quad\left[\int \frac{d y}{\sqrt{a^2-y^2}}=\sin ^{-1}\left(\frac{y}{a}\right)\right]\end{aligned}[/tex]

[tex]y(x)=\sin \left[\frac{x^2}{2}+c\right][/tex]

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Answer:

Since 21 and 22 are vertical angles, they are congruent. Therefore, m/1 = m22.

Using the equation m/1 = (17x + 1) we can find the measure of the angle m22.

m22 = (17x + 1)

Since ZK and ZL are complementary angles, the sum of their measures is 90 degrees.

mZK + mL = 90

Using the equations mZK = (3x + 3) and mL = (10x-4) and substituting them in the equation, we can find the measure of each angle.

3x + 3 + 10x - 4 = 90

13x - 1 = 90

13x = 91

x = 7

Therefore, mZK = (3x + 3) = (3(7) + 3) = 24 and mL = (10x-4) = (10(7) - 4) = 66

Step-by-step explanation:

A 1-U, 1-V graph is a special type of graph that has only one vertex of degree 1 (U) and one vertex of degree 2 (V). The edge connecting the two vertices is called the "bridge" of the graph.

Because the graph has only one vertex of degree 2, it forms a simple path (a straight line) between the two vertices. The vertex of degree 1 is a leaf, which means it is only connected to one vertex, and the vertex of degree 2 is the other end of the path. The path is a simple one, meaning it has no loops or multiple edges between the two vertices.

In a 1-U, 1-V graph, the vertex of degree 1 (U) can be thought of as the start of the path and the vertex of degree 2 (V) as the end of the path. Because there are no other edges or vertices in the graph, the path is the only structure in the graph and it's a straight line.

It's important to note that a 1-U, 1-V graph is a special case of a graph and it's not a general representation of all possible graphs. Most graphs have more than one vertex and multiple edges, making them more complex than a simple straight line.

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The particle's total d2 distance for the course of the time period indicated above, in accordance with the supplied assertion, was -3/2 m.

An example of a utility rule is one that generates a single output from a single input. The picture was obtained from Alex Federspiel. The equation y=x2 serves as an example of this. There is only one output for y for every input for x. We may assert that y appears to be a time variable given that x remain the source value. A function, according to a technical definition, is a relationship between a set of inputs and a set of potential outputs, where each input is connected to precisely one output.

dx(t)/dt = 5t-8

[tex]\int_0^{x(t)} \mathrm{dx}(t)=\int_0^3 5 t-8 \mathrm{~d} t[/tex]

[tex]x(t)=\left.\left[\frac{5}{2} t^2-8 t\right]\right|_0 ^3[/tex]

f(0) = 0

[tex]f(3)=\frac{5}{2} * 3^2-8 * 3=-\frac{3}{2} m[/tex]

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The complete question is-

The velocity function v(t) (in meters per second) is given for a particle moving along a line.

V(t)= 5t-8, 0 <equal to 't' <equal to 3

Find the Total distance d2 traveled by the particle during the time interval given above?

I need help solving this problem, i know how to solve it but i keep getting the wrong answer. My answer is 457/10.. how do you solve this problem

The absolute value or modulus |x| of a real number x is the non-negative value of x without regard to its sign.

The absolute value is always a positive value and not a negative number. so those numbers are called absolute values.

It is represented as |a|, which defines the magnitude of any integer ‘a’.

It defines removing any negative sign in front of a number and thinking of all numbers as positive.

Absolute value is a term used in mathematics to indicate the distance of a point or number from the origin (zero point) of a number line or coordinate system.

When x itself is negative (x<0), then its absolute value is necessarily positive

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This is a condition known as ankylosis, and it describes a situation in which two bones lose their contact with each other.

Ankylosis can result from a variety of causes, including trauma, infection, or degenerative joint diseases. In cases of trauma, the articulating surfaces of the bones can be damaged, leading to a complete absence of contact between the two bones. Similarly, if an infection is present, the cartilage and ligaments of the joint can be destroyed, leading to ankylosis.

Finally, in cases of degenerative joint diseases, such as arthritis, the joint's articulating surfaces can be damaged, leading to a complete loss of contact between the two bones.

The symptoms of ankylosis vary depending on the severity of the condition. In mild cases, the patient may experience stiffness, pain, and reduced range of motion in the joint. In more severe cases, the joint may become completely immobile, and the patient may have difficulty walking or performing other activities.

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The Scale On A Map Is 1 Inch = 60 Miles. If Two Cities Are 2 3/4 Inches Apart On The Map,  the number of miles they are apart is, 165  Miles

So, Option B is correct.

Scale factor is a mathematical term, which we use to scale 2-dimensional and 3-dimensional shapes. Scale factor is a measure of similar figures. Those figures who look the same but are in different sizes.

For example, Two spheres look similar but could have different radii.

Given that,

The Scale On A Map Is 1 Inch = 60 Miles

Two Cities Are 2 3/4 Inches Apart On The Map

The number of miles they are apart =?

1 Inch = 60 Miles

11/4 Inch = 60 × 11/4 Miles

              = 165  Miles

So, The actual distance is 165  Miles

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The amount of food eaten was the dependent variable in this experiment.

Everything that track in the study and what is impacted by it are both considered dependent variables. Depending on the independent variable, the dependent variable will change. Because it "depends" on the independent variable, it is known as a dependent variable. The dependent variable on other measurable variables As a result of an experimental modification of the independent variable or variables, these variables should change.

The amount of study one did, how much sleep one got the night before the test, or even how hungry he or she were can all affect your test result, which makes it a dependent variable. As an example, the test score might be a dependent variable.

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By the concepts of trigonometric ratios, the value of x in the right angle triangle is 1.

We know a right-angled triangle has three sides they are -: Hypotenuse,

Opposite and Adjacent.

We can remember SOH CAH TOA which is,

sin = opposite/hypotenuse, cos = adjecen/hypotenuse and

tan = opposite/adjacent.

If we take the reference angle of 60°, Then the hypotenuse is x and the adjacent is 2.

We know, cos = adjacent/hypotenuse.

Therefore,

cos60° = 2/x.

x = 2cos60°.

x = 2×1/2.

x = 1.

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To simplify the expression 3k + 9 - 2k + 11, we need to combine like terms and simplify the expression.

The first step is to combine the constants (numbers without variables)

3k + 9 - 2k + 11 = 3k - 2k + 9 + 11

The next step is to combine the variable k

3k - 2k = k

Now we have

k + 9 + 11 = k + 20

The final simplified expression is k+20

Answer:

20

Step-by-step explanation:

3k+(-2k) = 1k or just k

+9+11 = +20

= k+20

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Answer: Side SK

Step-by-step explanation:

Answer:225 m^2

Step-by-step explanation:

Answer:

A = 225 m²

Step-by-step explanation:

the sides of a square are congruent

the perimeter is the sum of the 4 congruent sides (s) , then

s = 60 ÷ 4 = 15 m

the area (A) of a square is calculated as

A = s² , then

A = 15² = 225 m²

[tex]f(t)=0.4(1.16)^{t-1}\qquad \begin{cases} x=0.4\\ y=1.16 \end{cases}\implies f(t)=xy^{t-1} \\\\[-0.35em] ~\dotfill\\\\ xy^{t-1}\implies xy^t y^{-1}\implies x\cfrac{y^t}{y}\implies \cfrac{x}{y}y^t\implies \stackrel{\textit{substituting back}}{\cfrac{0.4}{1.16} ~~ (1.16)^t} \\\\\\ \stackrel{\textit{"r" is positive, \Large Growth}}{\cfrac{0.4}{1.16} ~~ (1+0.16)^t \implies f(t)~~ \approx ~~ 0.34 ~~ (1+0.16)^t}\qquad \begin{cases} a\approx 0.34\\\\ r=0.16 \end{cases}[/tex]

Answer:

a. y = 2x - 6

To find the slope of the equation, we need to find the coefficient of x which is 2. So the slope of this equation is m=2

To find the y-intercept, we can substitute x = 0 into the equation:

y = 2(0) - 6

y = -6

So the y-intercept of this equation is b = -6

b. y = 1/2 * x + 12

To find the slope of the equation, we need to find the coefficient of x which is 1/2. So the slope of this equation is m=1/2

To find the y-intercept, we can substitute x = 0 into the equation:

y = 1/2(0) + 12

y = 12

So the y-intercept of this equation is b = 12

Therefore, the slope-intercept form of the equation is y = 2x - 6 and y = 1/2x + 12 respectively.

2.

D

Answer:

4

Step-by-step explanation:

If we fix x = 0 and z = 0 only y coordinate can change. So triple (0, y, 0) can only represent a point in y axis.

What do you mean by a plane?

In geometry, a plane is a surface made up of all the lines that are parallel to one another and connect any two locations on it. It is, in other words, a level or flat surface.

                          A plane is defined uniquely through any of the following in a Euclidean space of any number of dimensions: with the aid of three non-collinear points.

For the triple  (x,y,z ) to represent the point on the y - axis .

    x must be 0    y must be a real number

  and z must b 0

For the triple  (x,y,z ) to represent the point on the y - axis .

    x must be 0    y must be 0

  and z must be  a real number

For the triple  (x,y,z ) to represent the point on the y - axis .

    x must be real number     y must be 0

  and z must be  a real number

For the triple  (x,y,z ) to represent the point on the y - axis .

    x must be 0     y must be real number

  and z must be  a real number

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On solving the provided question, we can say that area of the ellipse equation = [tex]\pi ab[/tex] = 3.14*10*8 = 251.2 cm sq.

A mathematical equation is a formula that joins two statements and uses the equal symbol (=) to indicate equality. A mathematical statement that establishes the equality of two mathematical expressions is known as an equation in algebra. For instance, in the equation 3x + 5 = 14, the equal sign places the variables 3x + 5 and 14 apart. The relationship between the two sentences on either side of a letter is described by a mathematical formula. Often, there is only one variable, which also serves as the symbol. for instance, 2x – 4 = 2.

area of an ellipse with equation  = [tex]x^2/100 + y^2/64 = 1\\[/tex]

here, a = 10 and b = 8

area of the ellipse equation = [tex]\pi ab[/tex] = 3.14*10*8 = 251.2 cm sq.

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So, the equation to determine the number of months is 200 + 10x = 0 + 60x.

Let x be the number of months you can belong to each gym for it to cost the same at both places.

The equation to determine the number of months is:

200 + 10x = 0 + 60x

To solve for x, we can subtract 200 from both sides of the equation:

10x = -200

And finally, we divide both sides by 10:

x = -20

Therefore, you can belong to each gym for -20 months for it to cost the same at both places. But since month are positive numbers, x=-20 is not a solution. Therefore, the statement is not true, the cost will never be the same for both gyms.

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Answer:

The amount of phones that were not defective is 98% or 49/50 as a fraction in simplest form

Step-by-step explanation:

Steps to solve "what percent is 100 of 5000?"

100 of 5000 can be written as:

100/5000

To find percentage, we need to find an equivalent fraction with denominator 100. Multiply both numerator & denominator by 100

100

5000

×

100

100

= (

100 × 100

5000

) ×

1

100

=

2

100

Therefore, the answer is 2%

If you are using a calculator, simply enter 100÷5000×100 which will give you 2 as the answer. That lets you know how many were defective

If only 2% were defective, then 98% were not

The area of inscribed regular hexagon is 6[tex]\sqrt{3\\[/tex] unit square using the properties of equilateral triangles which combined, form the hexagon.

In a circle, a regular hexagon can be inscribed with all the six vertices of hexagon touching the circumference of the circle. The center of the circle is the center of the hexagon itself.

Now, if we join the center with all the vertices of the hexagon, we see six equilateral triangles are formed. The other two sides of each triangle apart from the ones joining the vertices of hexagon, are radii of the circle and all the sides are equal in length. The attached image can be referred for better understanding.

To find the area of the hexagon, we need to find the area of single equilateral triangle and multiply it by 6, as six triangles make a regular hexagon.

Radius of the circle ([tex]r[/tex]) = 2 units

Area of a single equilateral triangle = [tex]\sqrt{3} /4[/tex] [tex]r^{2}[/tex]

                                                           =( [tex]\sqrt{3} /4[/tex] ) × [tex]2^{2}[/tex]

                                                           = [tex]\sqrt{3}[/tex]

Area of hexagon = Area of 6 equilateral triangles = 6 × [tex]\sqrt{3}[/tex]

Area of hexagon = [tex]6\sqrt{3}[/tex] [tex]units^{2}[/tex]

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Answer:

Step-by-step explanation:

The idea is, for each triangle, sort all of its sides and then store it in a map, if all those three sides are already present in the map then increase the frequency by 1, else its frequency will be 1. The count of elements of the map which have frequency 1 in the end will be the answer.

The top 15 Excel functions are SUM, AVERAGE, COUNT, MAX, MIN, IF, VLOOKUP, CONCATENATE, INDEX, MATCH, ROUND, TEXT, OFFSET, TODAY, and RAND.

1. SUM: Add up the values in a range of cells

2. AVERAGE: Calculate the mean of a range of cells

3. COUNT: Count the total number of cells in a range

4. MAX: Find the maximum value in a range of cells

5. MIN: Find the minimum value in a range of cells

6. IF: Perform different actions based on whether a condition is met

7. VLOOKUP: Look up the value of a cell in another table

8. CONCATENATE: Join two or more cells together

9. INDEX: Return a value from a given range of cells

10. MATCH: Find the position of a value in a range of cells

11. ROUND: Round a number to a specified number of decimal places

12. TEXT: Format a number or value as text

13. OFFSET: Return a range of cells at a given offset from another cell

14. TODAY: Return the current date

15. RAND: Generate a random number

The top 15 Excel functions are SUM, AVERAGE, COUNT, MAX, MIN, IF, VLOOKUP, CONCATENATE, INDEX, MATCH, ROUND, TEXT, OFFSET, TODAY, and RAND, which are used for various tasks such as adding up values, calculating the mean, counting cells, finding maximum/minimum values, looking up values in another table, joining cells together, returning a value from a given range, finding the position of a value, rounding numbers, formatting values as text, generating a random number, and returning the current date.

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Answer:

15/16

Step-by-step explanation:

In a dice, there are 3 even and 3 odd numbers.

So, to calculate the required probability, we will have to calculate the probability of getting an odd number in all of them.

Probability of getting odd number in 1 dice = 3/6 = 1/2

Probability of getting odd number in 4 dice =

1/2 x 1/2 x 1/2 x 1/2 = 1/16

Therefore, probability of getting atleast one even number is 1 - 1/16 = 15/16

15/16 is the answer.

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Answer:

Step-by-step explanation:There are a total of 20 sweets in the bag (5 red + 6 blue + 9 yellow).

To find the probability that Sarah takes two sweets of the same color, we need to find the probability of her choosing a sweet of a specific color on her first pick and then the probability of her choosing another sweet of that same color on her second pick.

For example, if she chooses a red sweet on her first pick, the probability of that happening is 5/20, or 1/4. Then the probability of her choosing another red sweet on her second pick, given that she already picked one, is 4/20, or 2/10. Therefore the probability of her choosing two red sweets in a row is (1/4) * (2/10) = 1/20.

Similarly, the probability of her choosing two blue sweets in a row is (6/20) * (5/20) = 3/50.

The probability of her choosing two yellow sweets in a row is (9/20) * (8/20) = 9/100.

The probability of her choosing two sweets of the same color is the sum of the probability of her choosing two red sweets, two blue sweets, or two yellow sweets in a row.

P(Two same color) = 1/20 + 3/50 + 9/100 = 11/50

So, the probability of her choosing two sweets of the same color is 11/50.

Answer: Simon can use the function P(z) = -125z^2 + 25000 to determine the total profit he will make at different retail prices for his board game. The function shows that his profit will be maximum at 25000 dollars and it will decrease as the price increases or decreases from that point. Simon can use this function to determine the optimal price to sell his game at in order to maximize his profit.

Step-by-step explanation:

The indicated probability P(x >43) of the random variable x normally distributed is 0.8414.

Abraham de Moivre, a Frenchman, was the first to recognize the normal distribution (1667-1754). The curve was later developed further and its equation was developed by Carl Friedrich Gauss (1777–1855); for this reason, it is also more generally referred to as the "Gauss bell" or "Gaussian distribution."

Any point (x) from a normal distribution can be converted to the standard normal distribution using the formula z = (x-mean) / standard deviation (z).

Given:

Mean u = 50

Standard Deviation o = 7

To find the probability P(x>43),

= [tex]P(\frac{x - 50}{7} > \frac{43 - 50}{7} )[/tex]

= [tex]P(z > -1) = 0.8414[/tex]

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Answer:

9 km

Step-by-step explanation:

By making use of the tangent function, we can calculate the angle inside the right triangle formed with the Lake and the 6km as two of the sides. See the attached worksheet for the detailed steps.

The value of upper quartile is, 300.

The value of 7th decile is, 250.2.

The value of 35th percentile is, 100.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

The donations are as follows,

⇒ 50, 50, 50, 100, 100, 100, 150, 150, 200, 250, 250, 300, 300, 400, 500.

Now, We find the values as;

a) The upper quartile is,

⇒ Qₐ = a/4 (n + 1)

Here, n = 15

So, We get;

⇒ Q₃ = 3/4 (15 + 1)

        = 3/4 × 16

        = 12

So, Q₃ is in 12th position.

So, The value of Q₃ = 300

The value of 7th decile is,

⇒ D₇ = 7/10 (15 + 1)

        = 7/10 × 16

        = 11.2

Here, 11.2 is between the position 11th and 12th position which are 250 and 300 respectively.

Then, We get;

⇒ 300 - 250 = 50

Hence, The value of D₇ = 250 + 0.2

                                     = 250.2

Now, The value of 35th percentile is,

⇒ Pₐ = a/100 (n + 1)

⇒ P₃₅ = 35/100 (15 + 1)

         = 35/100 × 16

         = 5.6

Here, 5.6 is between the 5th and 6th position which are 100 and 200 respectively.

Hence,  P₃₅ = 100

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