2x^{3}+30xx^{2} +72x=0 solve using zero product property

The primary reason that the standard deviation is preferred to the variance is because the standard deviation is the most widely used measure of center.

Standard deviation and variance are two fundamental mathematical concepts that play an important role in everything from accounting to economics to investing in finance. Both use the average of a set of numbers to measure the variability of numbers in a data set. They are important to help determine volatility and return distributions. But there are inherent differences between the two. The standard deviation measures the square root of the variance, which is the average of each point from the mean.

(1) Standard deviation measures the distance between numbers in a set of data. The variance, on the other hand, gives the true value of the difference between the numbers in the data set and the mean.

(2) The standard deviation is the square root of the variance, expressed in the same units as the data set. Variance can be expressed as a square unit or as a percentage (especially in financial terms).

(3) The standard deviation can be greater than the variance because when the variance is less than one (1.0 or 100%).

(4) When the deviation is greater than 1 (such as 1, 2, or 120%), the standard deviation is less than the deviation.

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To determine if a function crosses the horizontal asymptote, analyse the behavior of the function as it approaches the asymptote and on either side of it.

1. Identify the horizontal asymptote of the function. The horizontal asymptote is a horizontal line that the function approaches as the independent variable (usually denoted as x) goes to positive or negative infinity. It is often denoted by a horizontal line y = a, where "a" is a constant.

2. Examine the behavior of the function as x approaches positive infinity. Evaluate the limit of the function as x goes to positive infinity. If the limit is equal to the value of the horizontal asymptote, then the function does not cross the asymptote. However, if the limit does not equal the asymptote, move to the next step.

3. Examine the behavior of the function as x approaches negative infinity. Evaluate the limit of the function as x goes to negative infinity. If the limit is equal to the value of the horizontal asymptote, then the function does not cross the asymptote. If the limit does not equal the asymptote, proceed to the next step.

4. Investigate the behavior of the function around critical points or points where the function changes its behavior. These points may include the x-intercepts or vertical asymptotes. Determine if the function crosses the asymptote around these points by analyzing the behavior of the function in their vicinity.

If, at any point in this process, the function crosses the horizontal asymptote, then it does not have a true horizontal asymptote. However, if the function approaches the asymptote and does not cross it at any point, then it has a horizontal asymptote.

It's important to note that some functions may have multiple horizontal asymptotes or no horizontal asymptote at all. The steps outlined above are a general guideline, but the specific behavior of the function needs to be analyzed to make a conclusive determination.

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The standard form of the expression  3√-16 +2√-64 is 28i

The square root of minus one √(−1) is the "unit" Imaginary Number, the equivalent of 1 for Real Numbers. In mathematics the symbol for √(−1) is i for imaginary.

We need to write the expression is  3√-16 +2√-64 in standard form

The value of √-1 is i

3√-16 + 2 √-64

3√-1 √16 + 2√-1 √64

3 i 4 + 2 i 8

12 i + 16 i

= 28 i

Therefore, the standard form. of the expression  3√-16 +2√-64 is 28i

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The equation of the line that passes through the points (-8, 9) and (2, -6) is y = (-3 / 2)x - 3.Given two points (-8, 9) and (2, -6). We are supposed to find the equation of the line that passes through these two points.

We can find the equation of a line that passes through two given points, using the slope-intercept form of the equation of a line. The slope-intercept form of the equation of a line is given by, y = mx + b,Where m is the slope of the line and b is the y-intercept.To find the slope of the line passing through the given points, we can use the slope formula: m = (y2 - y1) / (x2 - x1).Here, x1 = -8, y1 = 9, x2 = 2 and y2 = -6.

Hence, we can substitute these values to find the slope.m = (-6 - 9) / (2 - (-8))m = (-6 - 9) / (2 + 8)m = -15 / 10m = -3 / 2Hence, the slope of the line passing through the points (-8, 9) and (2, -6) is -3 / 2.

Now, using the point-slope form of the equation of a line, we can find the equation of the line that passes through the point (-8, 9) and has a slope of -3 / 2.

The point-slope form of the equation of a line is given by,y - y1 = m(x - x1)Here, x1 = -8, y1 = 9 and m = -3 / 2.

Hence, we can substitute these values to find the equation of the line.y - 9 = (-3 / 2)(x - (-8))y - 9 = (-3 / 2)(x + 8)y - 9 = (-3 / 2)x - 12y = (-3 / 2)x - 12 + 9y = (-3 / 2)x - 3.

Therefore, the equation of the line that passes through the points (-8, 9) and (2, -6) is y = (-3 / 2)x - 3. Thus, the answer is (-3/2)x - 3.

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Answer:

Why is | 7 | the absolute value of the number 7?

The absolute value of a number is how far away the number is from zero. The absolute value is ALWAYS positive.

What is the absolute value of -7?

The negative version of the number is also | 7 |

Step-by-step explanation:

Answer:

7 and -7

Step-by-step explanation:

Absolute value is the distance a number is from 0 on a number line. If you go back 7 spaces from positive 7 you will land at 0, and if you go up 7 spaces from -7 you will land at 0.

Answer:

Use colon method

Step-by-step explanation:

So it is more easy

A pencil consists of a cylindrical body (10 cm long, radius 0.3 cm) with a cone-shaped eraser (1 cm slant height) and a hemisphere-shaped eraser.

A pencil consists of three main parts: a cylindrical body, a cone-shaped eraser, and a hemisphere-shaped eraser. Let's break down the dimensions of each part:

Cylindrical Body:

Length: 10 cm

Radius: 0.3 cm

Cone-shaped Eraser:

Slant height: 1 cm (assumed height of the cone)

Hemisphere-shaped Eraser:

Since the dimensions of the hemisphere-shaped eraser are not specified in detail, we'll assume a few things:

Let's assume that the hemisphere is attached to the cone in such a way that the flat surface of the hemisphere is aligned with the circular base of the cone.

We'll assume that the radius of the hemisphere is the same as the radius of the cylindrical body, which is 0.3 cm.

Please note that the actual dimensions of a pencil can vary, and these assumptions are made for the purpose of explanation.

It's worth mentioning that the cylindrical body of the pencil is the main part used for writing, while the cone-shaped and hemisphere-shaped erasers are located at the opposite end of the pencil, typically used for erasing mistakes.

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Answer:

ED = 6

Step-by-step explanation:

Since the triangles are similar then the ratios of corresponding sides are equal, that is

\(\frac{ED}{BA}\) = \(\frac{EF}{BC}\) , substitute values

\(\frac{ED}{9}\) = \(\frac{12}{18}\) ( cross- multiply )

18 ED = 108 ( divide both sides by 18 )

ED = 6

The value of the given and completed expression in this problem is

-1

Combined operations are defined as a set of operations applied to the same problem, for example addition, subtraction, multiplication, are frequently used in arithmetic polynomials.

In this case we have an arithmetic polynomial.

We complete the expression as follows:

1 + 2 - 3 + 4 - 5

We group the positive terms on one side and negative terms on the other:

The value of the expression (1 + 2 - 3 + 4 - 5) is -1

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Answer:

\(y = 3 \div 4x + 10\)

Answer:

\(9a^{2}\)+6\(ab\)+\(b^{2}\)

Step-by-step explanation:

It is called the y-coordinate

The point itself is called a coordinate, vertically, the vertical component of the coordinate is called the y-coordinate, while horizontally, the horizontal component of the coordinate is called the x-coordinate.

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Hamlet opened a credit card at a department store with an APR of 17. 85% compounded quarterly. The APY on this credit card is 19.77%, which is closest to option C) 19.08%. Hence, the correct option is (C) 19.08%.

The APY on a credit card is determined by the credit card issuer and is usually stated in the credit card agreement. The APY can also be calculated using the formula APY = (1 + r/n)ⁿ⁻¹, where r is the APR and n is the number of times interest is compounded per year.

An APR of 17.85% compounded quarterly, Let's calculate APY using the formula,

APY = (1 + r/n)ⁿ - 1

Where r = 17.85% and n = 4 (quarterly)

APY = (1 + 17.85%/4)⁴ - 1= (1 + 0.044625)⁴ - 1= (1.044625)⁴ - 1= 1.197732 - 1= 0.197732 = 19.77%

The correct option is C. 19.08% as it is the closest one.

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The c d f is (  1     : x≥4), b) mean is 2, c) the variance of x is 4/3 d) the value of f is 0.35 e) value of p is 0.375 and value of k is 1.4

a) F(x)=P(x ≤ x)=(  1     : x≥4

b) E(x)=∫^ (x)dx=2

c) ∫^4^0 x^ 2f(x)dx=4/3

d) f(x)=x/4,0<x<4)=0.35

e)P(1/2<X<2)=0.375

f)(p(x ≤ k)=F(K)=1.4

The pdf of x is
F(X)=1/4: 0<X<4
0 : otherwise


A) The c d f of x is
F(x)=P(x ≤ x)

=∫^ x f(t) αt
= ∫^ x1/4 αt
=1/4(t)^ x
=x/4,0<x<4
F(x)=(0: x≤0)        
      ( x/4:0<x<4)
     (  1     : x≥4)


B) We need, mean(x)
=E(x)=∫^ (x)dx

=1/4  ∫^4^ x dx
=1/4 (x^ 2/2)^ 4
=16/8
=2    

C) Here, E(X^2)          
=∫^4^0 x^ 2f(x)dx

=1/2∫^4^0 x^2 dx        
=1/4(x^ 3/3)^ 4^0
=16/3
Var(x)+E(X^2)-E^2(X)
=16/3-(2)^2
=4/3
       
d) F(1.4)=1.4/4   ∵   f(x)=(x/4,0<x<4)

=0.35


e)P(1/2<X<2)
=F(2)-F(1/2)

=2/4-1/2/4
=1/2-1/8=3/8              
=0.375

F) let R=35th percentile

so, we must have,
p(x ≤ K)=0.35           ∵  (p(x ≤ k)=F(K)
=K/4=0.35                    =k/4
k=1.4

Complete Question is given below

1. let x be a random variable with pdf . a) find the c d f f(x). b) find the mean of x. c) find the variance of x. d) find f (1.4). round to 3 decimal places. e) find P(1/2<X<2). f) find THE 35TH PERCENTILE.

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Answer:

YES

Step-by-step explanation:

Answer:

Yes

Step-by-step explanation:

Distributive Property:

3(3x+1)

9x+3

Answer:

R60 is the answer to your question

The instance in question was chosen at random assignment.

Given statement;

Participants should be selected by chance for an experimental or control group so each has an equal probability of being assigned to any of the groups.

The given case is done by Random assignment.

In Mathematical experiments, random assignment refers to the use of chance processes to ensure that each participant has an equal chance of being assigned to any particular group. Participants in studies are divided into several groups at random, such as the experimental group or the treatment group.

It is known as random assignment.

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Answer:

141.37167in³

Step-by-step explanation:

V=

π

d

2

2

h

=

π

6

2

2

5

≈

141.37167in³

Answer:

exact: V = 45pi in.^3

approximate: V = 141.4 in.^3

Step-by-step explanation:

V = (pi)r^2h

r = d/2 = 6 in./2 = 3 in.

V = (pi) * (3 in.)^2 * 5 in.

V = 45pi in.^3

V = 141.4 in.^3

Answer:

\(\large\boxed{\tt x=2}\)

Step-by-step explanation:

\(\textsf{We are asked to solve for the value of x.}\)

\(\textsf{We are given an equation where x is on both sides of the equation.}\)

\(\large\underline{\textsf{Solving;}}\)

\(\textsf{Begin solving by adding x to both sides of the equation to cancel out -x on the right}\)

\(\textsf{side of the equation. Afterwards, simplify the left side of the equation to evaluate}\)

\(\textsf{x.}\)

\(\large\underline{\textsf{Evaluating x;}}\)

\(\tt -2 + x= -x + 2\)

\(\textsf{Remove the -x on the right side by adding x to both sides of the equation.}\)

\(\tt -2 + x +\boxed{\tt x} = -x + \boxed{\tt x}+ 2\)

\(\tt -2 + 2x = 2\)

\(\textsf{Now, we should simplify the left side of the equation as there's only a whole number}\)

\(\textsf{on the right side of the equation.}\)

\(\textsf{Remove the -2 on the left side of the equation by adding 2 to both sides of the equation.}\)

\(\tt -2 + \boxed{\tt 2}+ 2x = 2 + \boxed{\tt 2}\)

\(\tt 2x = 4\)

\(\textsf{Lastly, divide both sides of the equation by 2 to find the value of x.}\)

\(\tt \frac{2x}{2} = \frac{4}{2}\)

\(\large\boxed{\tt x=2}\)

Answer:

\( \sf \: x = 2\)

Step-by-step explanation:

Now we have to,

→ Find the required value of x.

The equation is,

→ -2 + x = -x + 2

Then the value of x will be,

→ -2 + x = -x + 2

→ x + x = 2 + 2

→ 2x = 4

→ x = 4 ÷ 2

→ [ x = 2 ]

Hence, the value of x is 2.

Answer:

can't see an image

Step-by-step explanation:

The functions y = 2 (1/5)^x - 5 and y = 4^x are compared as follows

                                  y = 2 (1/5)^x - 5             y = 4^x

Initial value:               2                                    1

base function:        1/5 = decay function       4 = growth function

Translation:             5 units down                    no transformation

A decay function is a mathematical function used in various fields such as physics, engineering, economics, and machine learning, to model the reduction or decline of a value over time.

It is a type of function that decreases at a rate proportional to its current value, so that it approaches zero as time progresses.

Decay function are exponential functions with the base function as

This is the opposite of growth function which has values greater than 1

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Answer:

3

Step-by-step explanation:

Answer: 31

Step-by-step explanation: 1. Since you need to find the distance between the Y coordinates, find the absolute value of both Y coordinates. (7, 19) = (7, 19) and (7, -12) = (7, 12).

2. Add both Y coordinates. 19 + 12.

3. 19 + 12 = 31. There are 31 units between (7, 19) and (7, -12).

The probability that a student who drives to campus in the city drives a luxury car or has comprehensive auto insurance is approximately 0.5668.

To find the probability that a student who drives to campus in the city drives a luxury car or has comprehensive auto insurance, we can use the principle of inclusion-exclusion.

Let's denote:

A = Event that a student drives a luxury car

B = Event that a student has comprehensive auto insurance

We are given:

P(A) = 0.24 (probability of driving a luxury car)

P(B) = 0.43 (probability of having comprehensive auto insurance)

Since A and B are independent events, we can calculate the probability of their intersection as the product of their individual probabilities:

P(A ∩ B) = P(A) * P(B) = 0.24 * 0.43 = 0.1032

Now, to calculate the probability of a student driving a luxury car or having comprehensive auto insurance, we can use the formula for the union of two events:

P(A U B) = P(A) + P(B) - P(A ∩ B)

Plugging in the values:

P(A U B) = P(A) + P(B) - P(A ∩ B)

         = 0.24 + 0.43 - 0.1032

         = 0.5668

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The dimensions of the poster be so that the least amount of poster is used are 10 and 20 inches.

Print area of the rectangular poster =128 in²

Let  "x"  and  "y" be the  dimensions for the print area of the poster .

And A[p] = print area of poster

⇒A(p)  = Print area of the poster = xy

⇒128 = xy    

⇒ y  = 128/x

Total area of the poster is:

A( t ) = ( y + 4 )( x + 2 )

A( t ) = yx +2y +4x + 8    And as  y = 128/x

Poster 's area as function of x is -

A(x)  =( 128 /x)x + 2 (128/x) + 4x + 8

⇒ A(x)  = 128 x² + 256/x + 4x + 8    ⇒  A(x)  = 128 + 256 /x + 4*x

On taking the derivatives on both sides of the equation :

A´(x)  =  - 256/x² + 4

A´(x)  = 0        

⇒ - 256 /x²  = -4    

⇒  4x² = 256

⇒ x² = 256/4     ⇒  x²  = 64

x = 8inches

And   y  =  128/x    

⇒y = 128/8   ⇒ y = 16 inches

After finding out the values of x and y the dimensions of the poster are:

w = x + 2    ⇒  w  = 8+ 2    w  = 10 in

Y  = y + 4   ⇒  Y  = 16+ 4   Y  =  20 in

Hence, the dimensions of the poster be so that the least amount of poster is used are 10 and 20 inches.

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Therefore , the solution of the given problem of triangle comes out to be  the equilateral triangle are is 62.28 cm².

In geometry, triangular polygons are ones that have three vertices and a right side. This object in two dimensions has three straight sides. Triangles are examples of three-sided polygons. The sum of a triangle's three angles is 180 degrees. The triangle lies on one plane.

Here,

Given : side = 12cm

Area of an equilateral triangle

=> √3/4 * side²

Side of triangle =12 cm

Area of an equilateral triangle

= >  √3/4 * 12²

=>√3/4 * 12*12

=> 62.28 cm²

Therefore , the solution of the given problem of triangle comes out to be  the equilateral triangle are is 62.28 cm².

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The total surface area of the composite solid is equal to 28π square centimeters.

In this problem we need to determine the surface area of a composite solid, that is, a solid formed by a cone and a hemisphere. The volume formula for the composite solid is equal to:

V = (2π / 3) · R³ + (π / 3) · R² · h

Where:

And formula for the surface area (A), in square centimeters, is:

A = 2π · R² + 2π · √(R² + h²)

First, determine the height of the cone:

h = [V - (2π / 3) · R³] / [(π / 3) · R²]

h = [30π - (2π / 3) · 3³] / [(π / 3) · 3²]

h = 4 cm

Second, determine the surface area of the composite solid:

A = 2π · 3² + 2π · √(3² + 4²)

A = 28π cm²

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The graph for the solution set of the absolute value inequality is given at the end of the answer.

The absolute value function is given by:

It measures the distance of a point x to the origin, which is given to x = 0.

In this problem, the inequality is given by:

3|x-3| ≥9

|x-3| ≥ 3

Which means that the distance of x - 3 to the origin is of at least 3 units, hence x - 3 can be:

Hence:

x - 3 ≤ -3

x ≤ 0

x - 3 ≥ 3

x ≥ 6.

The graph of the inequality is given at the end of the answer.

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(27d^(2))/(8c^(2)) contains the C term with the same exponent and the d term with a different exponent as compared to the given expression.  The correct is option (C).

The given expression is ((3C^(4)d^(4))/(2d^(9)))^(3).

We need to find the expression that is equivalent to the given expression. Here, we will use the properties of exponents to simplify the given expression, and then we will compare it with the expressions .

Let us simplify the given expression.

((3C^(4)d^(4))/(2d^(9)))^(3) = (3C^(4)d^(4)/2d^(9))^(3) = (3/2)(C^(4)d^(4-9))^(3) = (3/2)(C^(4)d^(-5))^(3) = (3/2)C^(4*3)d^(-5*3) = (3/2)C^(12)/d^(15)

Now, we need to compare this expression with the expressions given in the answer choices.

Option (A) (3d^(4))/(2c^(2)) cannot be the equivalent expression because it does not contain C and d terms with the same exponents.

Option (B) (81d^(6))/(8C^(6)) cannot be the equivalent expression because it contains the C term with a different exponent as compared to the given expression.

Option (C) (27d^(2))/(8c^(2)) contains the C term with the same exponent and the d term with a different exponent as compared to the given expression. Hence, this expression is equivalent to the given expression.

Hence, this expression is equivalent to the given expression .Therefore, the correct is option (C) (27d^(2))/(8c^(2)).

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