the random variable x has mean 8 and standard deviation 2. the random variable w is defined as w=7 4x . what are the mean and standard deviation of w ?

Answer:

$27.35

Step-by-step explanation:

To solve this, we just set up an equation based on the situation given:

2 candles for 5.95 each would be (2 x 5.95)

3 cans of candy for 2.50 each would be (3 x 2.50)

1 ornament for 7.95 would just be 7.95

(2 x 5.95) + (3 x 2.50) + 7.95 = total cost

   11.90     +     7.50     + 7.95 = total cost

                $27.35 = total cost

The percentage change of the first quantity with reference to the second quantity: 480 units, 560 units is: -14.29%.

First step is to find the difference between the two numbers

Difference = New Number - Original Number

Difference =  480 -560

Decrease  = -80

Now let find the percentage change

Percentage change = Decrease  / Original Number × 100

Percentage change = -80 /560 × 100

Percentage change = -14.29%

Therefore we can conclude that the percentage change is -14.29%.

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All of the above options a) implement an expansion strategy b)attract capital c)reduce tax burdens d)easy entry into an industry e)take advantage of limited liability ,are correct.

A corporation is generally set up to take advantage of limited liability. This means that the owners of the corporation (the shareholders) are not personally responsible for the debts and obligations of the corporation. The other options you have listed are also potential reasons for setting up a corporation, but they are not the primary purpose of a corporation.

An expansion strategy refers to a company's plan for growth and expansion, and setting up a corporation can be one way to implement this strategy. Attracting capital refers to the process of raising funds for a business, and a corporation may be able to attract more capital because it is a separate legal entity that can issue stocks and bonds. Reducing tax burdens refers to the process of minimizing the amount of taxes a business has to pay, and a corporation may be able to do this because it is taxed as a separate entity. Finally, setting up a corporation can also make it easier for a business to enter an industry because it provides a legal framework for the business and can make it easier to raise capital.

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Answer:

B

Step-by-step explanation:

The function is increasing anywhere the slope is positive.  This corresponds to the intervals -4<x<-2 and 0<x<2.  So, answer B is correct.

Answer: n = 4

9 = x

y = 2

Step-by-step explanation:

2 ( x + 5 ) = 3x + 1

2x +10 = 3x + 1

10 = 1x + 1

- 1       -1

9 = 1x

9 = x

3y - 4 = 6 - 2y

5y -4 =6

5y = 10

y = 2

3 (n + 2) = 9 ( 6-n)

3n + 6 = 54 -9n

3n +9n = 54 - 6

12n =54 -6

12n =48

n = 4

Using Pythagoras theorem, the length of the pole is 57 feet

Pythagoras theorem states that “In a right-angled triangle,  the square of the hypotenuse side is equal to the sum of squares of the other two sides“. The sides of this triangle have been named Perpendicular, Base and Hypotenuse. Here, the hypotenuse is the longest side, as it is opposite to the angle 90°.

In this problem, assuming the pole runs down to the ground.

We can apply Pythagoras's theorem to find the height of the the conical roof.

Taking half the length of the the wall, i.e it's diameter = 72 /2 = 36ft

Using Pythagoras theorem;

45² = 36² + x²

x² = 45² - 36²

x² = 729

x = √729

x = 27 feet

The height of the conical roof is 27

The length of the pole = height of the conical roof + height of cylindrical wall

Length of pole = 27 + 30 = 57 ft

The length of the pole is 57ft

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From the given options, Option A and Option D will represent the proportionality relation between x and y.

Equivalence between two variables that are related to one another and preserve a particular amount is referred to as a proportional relationship.

It is a mathematical concept that describes how two variables are related when they do so in equivalency and is also known as the "Relation of Proportionality."

Let the variables x and y are proportional to each other

=> x ∝ y

=> x = ky

=> x/y = k  [ where k is proportionality constant ]  

Here we will use the formula x/y = k to check the given variables' proportionality

Now check given options given below

Option A

x  0    1/5    2/5    3/5

y  0   1/10  2/10     3/10  

For  x = 1/5 and y = 1/10

=>  [tex]\frac{x}{y} = \frac{1}{5} \times \frac{10}{1}[/tex]  = 2

For  x = 2/5 and  y= 2/10

=>  [tex]\frac{x}{y} = \frac{2}{5} \times \frac{10}{2}[/tex]  = 2

Therefore, Table A represents the proportionality relation

Option B:

x -   0     1/2   1/3   1/4

y -   0     1/3   1/4   1/5

For  x = 1/2 and y = 1/3

=>  [tex]\frac{x}{y} = \frac{1}{2} \times \frac{3}{1}[/tex]  = 3/2

For  x = 1/3 and y = 1/4

=>  [tex]\frac{x}{y} = \frac{1}{3} \times \frac{4}{1}[/tex]  =  4/3  

Therefore, Table B doesn't represent the proportionality relation

Option C:

x -  0    1    3     5  

y -  0    1    9    25

For  x = 1 and y = 1

=>  [tex]\frac{x}{y} = \frac{1}{1} = 1[/tex]    

For  x = 3 and 9

=>  [tex]\frac{x}{y} = \frac{9}{3} = 3[/tex]  

Therefore, Table C doesn't represent the proportionality relation

Option D:

x -   0    1      3      4

y -   0    5    15    20

For  x = 1 and y = 5

=>  [tex]\frac{x}{y} = \frac{1}{5} = 1/5[/tex]    

For  x = 3 and y = 15

=>  [tex]\frac{x}{y} = \frac{3}{15} = \frac{1}{5}[/tex]  

Therefore, Table D will represent the proportionality relation

Therefore,

From the given options, Option A and Option D will represent the proportionality relation between x and y.

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Answer:

D

Step-by-step explanation:

A Hyperbola looks like a Parabola and its reflection, each Parabola curving opposite directions.

Answer:

D.  Hyperbola

Step-by-step explanation:

A conic is the intersection of a plane and a right circular cone.

Formed when a cone is intersected by a plane so that the plane is parallel to the circular base.

Formed when a cone is intersected by a plane so that the plane is at an angle with respect to the circular base.

Formed when a cone is intersected by a plane so that the plane is parallel to an edge.

Formed when a double-cone is intersected by a plane so that the plane is perpendicular to the circular bases.

Answer:

6. X, Y and Z are different numbers. X is a factor of Y. Z is a multiple of Y. Which of the following is DEFINITELY true?

7. The following graph shows Vinit's journey as he cycled from his home to a park, 4 kilometers away in 800 seconds. Which of these can be said based on this graph?

8. How many TENS must be added to 7 000 to make it 70 000.

Step-by-step explanation:

There are 6 probability  5 card poker hands with at least 3 Aces that can be dealt from a standard deck of 52 cards.

A standard deck of 52 cards contains 4 Aces, so the maximum number of Aces that can be dealt in a 5 card hand is 3. To determine the number of possible 5 card poker hands with at least 3 Aces, we must first consider the different combinations of 3 Aces in a 5 card hand. There are 6 possible combinations: AAAxx, AAxxA, AxxAA, xAAAX, xAxxA, and xxAAA. This means that there are 6 possible 5 card poker hands with at least 3 Aces that can be dealt from a standard deck of 52 cards. To calculate this, we first counted the number of Aces in the deck and then calculated the number of possible combinations of 3 Aces in a 5 card hand. Finally, we multiplied this number by the number of remaining cards in the deck (48) to get the total number of possible hands.

4 Aces x 6 combinations = 24

24 x 48 remaining cards = 1,152

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By completing squares in the quadratic equation, we can see that the values of p and q are:

p = -10

q = 40

Here we want to complete squares for the following quadratic equation:

x^2+20x+60=0

Remember that the perfect square trinomial is:

(a + b)^2 = a^2 + 2ab + b^2

So we can rewrite our equation as:

x^2 + 2*10*x + 60 = 0

If we add and subtract 10^2 = 100 we will get:

x^2 + 2*10*x + 10^2 - 10^2 + 60 = 0

(x^2 + 2*10*x + 100) - 100 + 60 = 0

(x + 10)^2 - 40 = 0

(x + 10)^2 = 40

So the value of p is p = -10 (the negative sign comes because in the given equation p is being subtracted) adnt he value of q is q = 40.

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Answer:

1.   d = 40; 2 irrational

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{7.6 cm}\underline{Discriminant}\\\\$b^2-4ac$ \quad when $ax^2+bx+c=0$\\\\when $b^2-4ac > 0 \implies$ two real solutions.\\when $b^2-4ac=0 \implies$ one real solution.\\when $b^2-4ac < 0 \implies$ no real solutions.\\\end{minipage}}[/tex]

Given quadratic equation:

[tex]3x^2+4x-2=0[/tex]

Therefore:

Substitute the values of a, b and c into the discriminant formula:

[tex]\begin{aligned}\implies b^2-4ac&=(4)^2-4(3)(-2)\\&=16-12(-2)\\&=16+24\\&=40\end{aligned}[/tex]

Therefore, as d = 40 and 40 > 0:

[tex]\implies b^2 - 4ac > 0 \implies \text{two real solutions}.[/tex]

To determine if the solutions are irrational or rational, simply square root the discriminant.

[tex]\implies \sqrt{d}=\sqrt{40}=2 \sqrt{10}[/tex]

As the discriminant is not a perfect square, then its square root is irrational and so the solutions of the quadratic equation are irrational.

A ∝ 1/M

A = K/M

A is the acceleration and M is the mass of the object.

The object's acceleration for an object of mass 13 kg is 4 m/s²

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 4 = 8 is an equation.

We have,

When a constant force acts upon an object, the acceleration of the object varies inversely with its mass.

This means,

A ∝ 1/M

A is the acceleration and M is the mass of the object.

Now,

A = K/M

26 = K / 2

K = 26 x 2

k = 52

Now,

M = 13

A = K/M

A = 52/13

A = 4 m/s²

Thus,

The object's acceleration for an object of mass 13 kg is 4 m/s²

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Under coverage of the population will be the most noticeable bias in distributing the survey at his point in time.

Undercoverage bias happens when segments of the target population are entirely executed or loses represented in the sample than they are in the population. This means that these segments are executes from the sampling process. Non response bias occurs when parts of the sampled population are unable or refuse to respond.

Undercoverage occurs when an element of the target population is not represented on the survey frame and therefore not given any chance of selection in the survey sample; that is the element has zero probability of selection into the sample. It refers to a type of sampling bias that occurs when a piece of information from your sample responses goes missing or uncovered in the results. This significant entity goes unselected or has zero chance of getting in your representing sample.

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The smallest rational number among -5/16, -13/24, -3/4, and -7/12 is -3/4.

We have,

To determine the smallest rational number among -5/16, -13/24, -3/4, and -7/12, we need to compare their values.

Let's convert all the given rational numbers to have a common denominator of 48:

-5/16 = -15/48

-13/24 = -26/48

-3/4 = -36/48

-7/12 = -28/48

Now, the values of these rational numbers, when expressed with a common denominator, are:

-15/48, -26/48, -36/48, -28/48

Among these values, the smallest one is -36/48, which is equivalent to -3/4.

Therefore,

The smallest rational number among -5/16, -13/24, -3/4, and -7/12 is -3/4.

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Answer:

2.4 would be the answer i took this before

Step-by-step explanation:

The rate at which the diameter decreases is  -0.16cm/min

Diameter:

In geometry, diameter refers the straight line that goes from one side to the other side of a circle, passing through the center.

Given,

Here we need to find if a snowball melts so that its surface area decreases at a rate of 1cm^2/min, find the rate at which the diameter decreases when the diameter is 10 cm. Finish solving the problem. Write an equation that relates the quantities.

Here  we obtained the equation that relates the surface area S and the diameter D of a sphere given by

=> S = πD²

Now, we have differentiate the equation as,

=> dS/dt = d/dt (πD²)

=> dS/dt = π d/dt (D²)

​=> dS/dt = 2πD dD/dt

Now, Solving for dD/dt, which is the unknown for this problem, we have

=> dD/dt ​= 1/2πD​ x dS​/dt

Now, substituting the given values, the rate of change of the diameter when D=10 cm and dS/dt as (-1) is

=> dD/dt = 1/2 x π x 10 (-1)

=> dD/dt = -1/20π

=> dD/dt = -0.16cm/min

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The equation that can be used to determine the pounds of laundry the customer brought in to be washed and folded that month is;

D. 0.53x + 26.00 = 37.66

We are given that;

Monthly service fee for Lundromat = $26

They wash and fold clothes at $0.53 per pound  for those customers with a laundry service.

Now, we are told that a customer paid $37.66 total for the month.

If the number of pounds of clothes is denoted as x, then it means that the equation for this will be;

0.53x + 26.00 = 37.66

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The standardized distribution known as the T distribution is a member of the one-parameter family. The degrees of freedom are the only input for the t distribution.

A measure of the distribution of a set of data points is called population variance. It measures the mean squared departure from the mean, specifically. As a result, the variance will be minimal if all of the data points are very near to the mean. The variation will be high if the data points are dispersed throughout a wide range.

The standardized distribution known as the T distribution is a member of the one-parameter family. The degrees of freedom are the only input for the t distribution. Because sample size is used to assess this degree of freedom, degrees of freedom are dependent on sample size.

The t distribution tends to follow a normal distribution as sample size rises. The degree of freedom is ultimately determined by the sample size, so as the degree of freedom rises, the t distribution tends to be a normal distribution.

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Base (cube): [tex]V=s^3[/tex]

   [tex]V=9\cdot9\cdot9=729[/tex]

Top (triangular prism): [tex]V=\frac{1}{2}bhl[/tex]

   [tex]V = \frac{1}{2}(9\cdot7)\cdot9=283.5[/tex]

Together:

   [tex]V = 729+283.5 =1012.5[/tex]

C.

1012.5 cubic units.

In the Algebra prompt above, If f(1) = 8 and f(n)=1/2f(n-1) + 2 then  the value of f(3) is 5.

Algebra is the branch of mathematics that aids in the representation of problems or situations using mathematical expressions.

We are given the following:

f(n)=1/2f(n-1) + 2; and

f(1) = 8

Thus,

f(2) = 1/2 x 8 + 2

= 4 + 2

f(2 )=  6

Hence,

f(3) = 1/2 x 6 + 2

= 3 + 2; thus,

f(3) = 5

Therefore,  it is correct to state that if f(1) = 8 and f(n)=1/2f(n-1) + 2 then  the value of f(3) is 5.

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Answer:

I have solved this on Paper and attached an image in the explanation part!

Step-by-step explanation:

All rectangles are square is a false statement

The given statement is false statement.

What is a rectangle and square?

A rectangle is a quadrilateral with opposite sides parallel and equal and each angle is a right angle, where as a square is quadrilateral with opposite sides parallel and each side is equal. and every angle is a right angle.

We are given a statement All rectangle are squares.

As every side of a square is of equal length And only opposite sides are of equal length in rectangle

All rectangles are not square

Hence the statement is not true

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the original price was "x", which oddly enough is the 100%.

now, we know the TV is 75% off, that means the sale price is 100% - 75% = 25%, and we know that's 24 bucks.

[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} x & 100\\ 24& 25 \end{array} \implies \cfrac{x}{24}~~=~~\cfrac{100}{25} \implies \cfrac{ x }{ 24 } ~~=~~ 4\implies x=96[/tex]

The system of equations is:

28cm = 2*(W + L)

28.8cm = 2*(0.9*L + 1.2*W)

b) Solving that we will get L = cm and W = 6cm

c) The figure becomes a square of sides of 7.2cm

First, let's define the variables:

Remember that the perimeter of a rectangle is:

P = 2*(W + L)

We know that the perimeter is 28cm, then:

28cm = 2*(W + L)

And if we decrease the length by 10% and increase the width by 20% the perimeter is 28.8cm, then

28.8cm = 2*(0.9*L + 1.2*W)

Then the system of equations is:

28cm = 2*(W + L)

28.8cm = 2*(0.9*L + 1.2*W)

We can isolate L on the first equation to get:

28cm/2 - W = L

14cm - W = L

Replacing that in the other equation we get:

28.8cm = 2*(0.9*(14cm - W) + 1.2*W)

28.8cm = 1.8*(14cm - W) + 2.4*W

28.8cm = 25.2cm + 0.6*W

28.8cm - 25.2cm =  0.6*W

3.6cm/0.6 = W = 6 cm

So the width is 6cm, then the length is:

L  = 14cm - 6cm = 8cm

c) The modified dimensions are:

0.9*L = 0.9*8cm = 7.2 cm

The new width is:

1.2*W = 1.2*6cm = 7.2 cm

So the length is equal to the width, then the figure becomes a square.

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The first and fourth quadrant of a coordinate grid should be used to display the given data .

In the question ,

it is given that ,

from the time the storm has started the temperature change is from 0° to - 20° .

we know that time cannot be in negative , and temperature can be both negative and positive .So only quadrant 1 and 4 can be used for representation .

Y = temperature

X = time

Quadrant 1 = (+x , +y) this can be used because x can only be positive and y is also positive.

Quadrant II = (-x , +y) this cannot be used because x cannot be negative

Quadrant III = (-x , -y) this cannot be used because x cannot be negative

Quadrant IV = (+x , -y) this can be used because x can only be positive and y can be negative.

Therefore , only 1 and 4 quadrants can be used .

The given question is incomplete , the complete question is

An equation is written to represent the relationship between the temperature in Alaska during a snow storm, y, as it relates to the time in hours, x, since the storm started. if the storm lasted five hours and the temperature saw a drop from 0° to - 20°, which quadrant(s) of a coordinate grid should be used to display this data ?

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Answer:

Step-by-step explanation:

Given,

No. of pens the shopkeeper has = 10

Selling price of 10 pens = Rs. 1200

Profit made by selling them = Rs 100

So,

Actual price or Cost price of 10 pens

= Rs (1200 - 100)

= Rs 1100

Now,

Cost price for each pen

= [tex]\frac{Total cost of the pens}{No. of pens}[/tex]

= [tex]Rs \frac{1100}{10}[/tex]

= Rs 110

Hence,

The cost price for each pen the shopkeeper bought is Rs. 110 (Ans)

Answer:

The following statements are true:

A) The equation |-x - 4| = 8 will have two solutions.

D) The equation |2x - 10| = -20 will have two solutions.

E) The equation |0.5x - 0.75| + 4.6 = 0.25 will have no solutions.

The other statements are not true. The equation 3.4|0.5x - 42.1| = -20.6 will not have one solution, as the absolute value of a number cannot be negative. The equation |1/2x - 3/4| = 0 will not have no solutions, as the absolute value of a number cannot be zero. The equation |1/8x - 1| = 5 will not have infinitely many solutions, as the absolute value of a number cannot be negative.

Step-by-step explanation:

The increase in the orbital period is by a factor of k^3/2. Option D

From the Kepler's laws, we know that the square of the period of the planet is directly proportional to the cube of the distance of the planet from the sun. We can see that this has been typified by the expression; T^2 =A^3 where T is the period of the planet and A is the distance between the planet and the sun.

Now, we can see that from the relationship, If planet Y is k times the mean distance from the sun as a planet X then the orbital period would be increased by a factor of about k^3/2.

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