if the owner decides to increase the living room dimensions by 20%, what is the new length and width of the living room floor?

Answer:

The radius can be shown in 2 different forms

Fraction Form

[tex]r=\sqrt[3]{\frac{27}{\pi}}[/tex]

Decimal Form

[tex]r=2.05[/tex]

Step-by-step explanation:

The formula for the volume of the sphere is

[tex]V=\frac{4}{3}\pi r^3[/tex]

We are given the volume and we are asked to find the radius.

We can solve for [tex]r[/tex] in the equation for volume to evaluate the radius.

[tex]\frac{4}{3}\pi r^3=V[/tex]

Move [tex]\pi[/tex] and [tex]r^3[/tex] into the numerator.

[tex]\frac{4\pi r^3}{3}=V[/tex]

Divide both sides of the equation by 3.

[tex]4\pi r^3=3V[/tex]

Divide both sides of the equation by [tex]4\pi[/tex].

[tex]r^3=\frac{3V}{4\pi }[/tex]

Take the cube root of both sides to eliminate the exponent.

[tex]r=\sqrt[3]{\frac{3V}{4\pi }}[/tex]

Numerical Evaluation

Now we have an equation to evaluate [tex]r[/tex].

Given [tex]V=36[/tex]

Insert 36 in for [tex]V[/tex].

[tex]r=\sqrt[3]{\frac{3*36}{4\pi }}[/tex]

Factor 4 out of [tex]3*36[/tex] and add parenthesis.

[tex]r=\sqrt[3]{\frac{4(3*9)}{4(\pi) }}[/tex]

Cancel the common factor of 4.

[tex]r=\sqrt[3]{\frac{3*9}{\pi}}[/tex]

Multiply [tex]3*9[/tex].

[tex]r=\sqrt[3]{\frac{27}{\pi}}[/tex]

The answer can be shown in multiple forms.

Fraction Form

[tex]r=\sqrt[3]{\frac{27}{\pi}}[/tex]

Decimal Form

[tex]r=2.05[/tex]

The trigonometric form of the complex number is,  

-6+ i (-6) = 6√2( cos5pi/4 + i sin 5pi/4)

In mathematics, a complex number is an element of a number system that extends the real numbers with a specific element denoted i, called the imaginary unit and satisfying the equation {\displaystyle i^{2}=-1}; every complex number can be expressed in the form a + bi, where a and b are real numbers.

here, we have,

the complex number which we get from the given graph is,

-6+ i (-6)

so, a = -6

    b = -6

i.e. z = √a^2+b^2

        =6√2

so, we know,

The trigonometric form of a complex number:

z = |z| (cosα +i sinα)

now, cosα = a/|z|

                 = -1/√2

and, sinα = b/|z|

              = -1/√2

so, solving we get,

α = 5pi/4

i.e. -6+ i (-6) = 6√2( cos5pi/4 + i sin 5pi/4)

Hence, The trigonometric form of the complex number is,  

-6+ i (-6) = 6√2( cos5pi/4 + i sin 5pi/4)

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Answer:

n = 10

Step-by-step explanation:

2x = y

2(n)=20

n = 20/2

n = 10

After 15 hours there will be 1.875 grams of the radioactive tellurium.

We know that the half-life of a radioactive kind of tellurium is 3 hours.

This means that for any quantity A of that radioinuclei, after 3 hours we will have half of that amount.

Then we can write the exponential equation:

M(x) = A*(1/2)^(x/3h)

Here we start with A= 60 grams, and after 15 hours we will have:

M(15h) = 60g*(1/2)^(15h/3h)

M(15h) = 60g*(1/2)^(5) = 1.875 g

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An outlier in a data set can significantly affect the value of the mean but not the median because the mean is calculated by adding up all the values and dividing by the total number of values, while the median is the middle value of a set of data when it is arranged in numerical order. Outliers can greatly influence the mean because they can greatly increase or decrease the sum of all the values, which changes the average. However, outliers do not significantly affect the median because the median only depends on the middle value of the data set, and not the total sum of all the values.

The largest possible number of red socks in the drawer that is consistent with this data is 990.

Let r be the number of socks that are red, and t be the total number of socks. We get:

2(r(r-1)+(t − r)(t − r − 1)) = t(t − 1)

Expanding the left hand side and the right hand side,

we get: 4r²-4rt+2t²- 2t = t²- t

And, moving terms, we will get that:

47r²-4rt + t² = t

We notice that the left side is a perfect square.

(2r-t)² = t

Thus t is a perfect square. And, the higher t is, the higher r will be. So, we should set t =44²= 1936

And, we see, 2r- 1936 (+-)44

We will use the positive root, to get that 2r -1936 = 44, 2r =1980, and r = 990

Thoughts about probability began with a question from a French nobleman named Chevalier de Mere to Pascal (1623-1662). He wants to know how the pattern of distributing betting money in a gambling game is if the game has to be stopped before it is finished. This question then became the subject of discussion between Pascal and Fermat (1601-1665), based on this discussion came the theory of probability.

Although the basics of probability initially appeared to explain problems in gambling, in its development, the concept of probability can be applied to various problems such as social problems, engineering, health, biology, industry, transportation, management, accounting, education etc.

Probability is the amount of chance (likely) that an event will occur. The amount of opportunity can be written in the form of a decimal number, fraction or percent.

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A graph of the system of linear inequalities is shown in the image attached below.

In Mathematics, an inequality simply refers to a mathematical relation that is typically used for comparing two or more numerical data and variables in an algebraic equation based on any of the following inequality symbols:

In this exercise, we would use an online graphing calculator to plot the given system of linear inequalities y > -x + 5 and y ≤ 3x -4 as shown on the graph attached below. Based on the graph (see attachment), we can logically deduce that the solution to the given inequality is the shaded region, with a point of intersection at the ordered pair (2.25, 2.75) in quadrant I.

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From the graph of the system of equations y = 3x - 8 and 6x - 2y = 10, there is no solution

An equation is an expression that uses mathematical operations to show the relationship between numbers and variables. Types of equations are linear, quadratic, cubic and so on.

The standard form of a linear equation is:

Ax + By = C

Where A, B and C are constants

The slope intercept form of a linear equation is:

y = mx + b

Where m is the slope and b is the y intercept

The slope of the line passing through points (x₁, y₁) and (x₂, y₂) is:

m = (y₂ - y₁) / (x₂ - x₁)

Given the system of equations:

y = 3x - 8        (1)

and:

6x - 2y = 10     (2)

From the graph of the equations, there is no solution

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The points will  meet x when it is folded are C or E

A point is a location of an object by taking reference of origin, In general case we consider it at (0,0), At the origin value of both the coordinate position is considered as Zero, In simple words point indicates how much it is above or below from the coordinate axes.

Vertical distance from the x axis is known as y coordinate and horizontal distance from the y axis is known as x coordinate.

Given that,

A green colored Net,

After folding x point will  meet the points = ?

When we start folding,

First step,

Side ABCD and DEFG will be folded,

C and E will meet with each other

Second Step,

Side ABCD and AGHI will be folded,

B and I will meet with each other

Third step,

Side DEFG and AGHI will be folded,

F and H will meet each other

Fourth step,

Upper portion AHI will cover the upper portion BCF of the box

X will at position of C or E

Hence, the X will meet C or E

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Check the picture below.

If it is assumed that all 52 5 poker hands are equally likely, the probability of being dealt a flush is 0.001981

Flush means all 5 cards are of the same suit.

Now, we need to select one suit out of 4 which can be done in ⁴C₁ ways.

Now, when the suit is selected, we have to select 5 cards from that specific suit. This can be done in ¹³C₅ ways

In the game of poker, there are ⁵²C₅ possible hands.

So, the probability of a flush is given by:

              P = (⁴C₁ × ¹³C₅)/⁵²C₅

              P = (4 × 1287)/2598960

              P = 5148/2598960

              P = 0.001981 or 1.981 × 10⁻³ or 0.1981 %

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Step-by-step explanation:

hope you can see the awful green

Answer:

13.14cm

Step-by-step explanation:

lets start by finding the length of AD

90 + 65=155...........180-155= 25

x/sin 25= 7/sin 90

xsin90=7sin 25

x= 2.96cm=AD

Now lets find DC

we shall find DB first;

x/sin65=7/sin90

xsin90=7sin65

x=6.34cm...=DB

Now lets use Pythagoras theorem to find DC

12²-6.34²=√103.80

DC=10.18cm

Add AD and DC

2.96+10.18= 13.14cm

AC=13.14cm

The  height of the pyramid is 6cm

a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.

Given that Six square-based pyramids fit exactly onto the six faces of a cube of side 4 cm.

The volume of the object formed is 256 cm³.

We need to find the  height of each of the pyramids.​

The total volume can be calculated as

Total volume= cube volume+6 one pyramid volume

cube volume=4³=64

pyramid volume=1/3.4²h=16/3h

64+6.16h/3=256

64+32h=256

Subtract 64 on both sides

32h=256-64

32h=192

Divide both sides by 32

h=6

Hence, the  height of the pyramid is 6cm

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The probability that less than four colours will be chosen when the spinner is spun once would be = 0.5. That is option D.

Probability is defined as the expression that show the possible outcome of an event which is likely or unlikely to occur.

The coloured spinner is divided into = 8 colour sections

The number of blue section = 3

The number of red = 1

The number of purple section = 2

The number yellow section = 2

Therefore the probability to select 4 colour when spun once = 4/8 = 1/2 = 0.5

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Answers:

#6: (6,32)

#7: total cost for kites R fun   Total cost for windy kites

                    4                                              42

                     7                                               62

                     10                                             82

The student that has the half piece of paper with the greater area is blake.

Find the area that its outer surfaces possess. Sum of all those surfaces' area is the surface area of the considered object.

Given;

Tyler and Blake have rectangular pieces of paper with the same length and same width

Tyler cuts his paper horizontally through the middle

Blake cuts his paper along a diagonal

Now,

Let the length and breadth be y

Tylers half area= y*y/2=y^2/2

Blakes half area=1/2* [tex]\sqrt{3}[/tex]y*[tex]\sqrt{3}[/tex]y/2

=3y^2/4

Therefore, blakes piece of paper has more area.

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Option A is a correct representation of the graph of the function,

g(x) = -1/3f(x).

When two parallel lines intersect, a two-dimensional coordinate plane called the cartesian plane is created. The horizontal line is the X-axis, while the vertical line is the Y-axis. If the sign of x is positive, the coordinate point (x, y) in the Cartesian plane indicates that the point is on the right of the origin; otherwise, it indicates that the position is on the left of the origin.

Given the graph of the function,

f(x) is the shape of a parabola so the graph is of a quadratic function.

and given g(x) = -1/3f(x)

graph of f(x) is on coordinates (0, 0), (1, 1), and (-1, 1)

so the function is f(x) = x²

so g(x) should lie in coordinates (0, 0), (1/3, -1/3), and (-1/3, -1/3)

the shape of g(x) will be the same as f(x), but due to the negative sign, the shape will be in opposite quadrants.

and g(x) is 1/3 time f(x) so the shape will evolve more as compared to g(x),

so the graph of Option A only follows the required condition.

Hence option A is correct.

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There are 120 possible ways for two tables and 90 ways for 3 tables.

If we split the six people into 4/1/1, there will be (6 4) ways to select the 4 people sitting together, and 3! ways to arrange them at their table, so this gives (6 4)(3!)=15(6)=90 possibilities.

If we split the six people into 3/2/1, we will get (6 3) ways to select the 3 people sitting together, 2! ways to arrange them at their table, and (3 2) ways to select the 2 people sitting together, so this gives (6 3)⋅2⋅(3 2)=20(2)(3)=120 possibilities.

Finally, there are 120 possible ways for two tables and 90 ways for 3 tables.

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The x-intercepts or roots of the parabola are the locations where a parabola contacts the x-axis. These are the solutions to the parabola equation where the y-value is equal to zero.

A parabola is an open curve formed by the intersection of a right circular cone with a plane parallel to one of the cone's elements. This is known as the standard form of a quadratic function. A parabola is the graph of a quadratic function that is a U-shaped curve. A parabola is the graph of the equation y=x2 illustrated below. Parabolas are classified into three categories. There are three types of forms: vertex form, standard form, and intercept form. Each type offers a unique important characteristic for the graph. The three major forms from which we graph parabolas are known as standard form, intercept form, and vertex form. Each form will provide you with somewhat different information as well as its own set of pros and downsides.

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Answer: 14 cupcakes

Step-by-step explanation:

42 divided by 3

In total, there are 252 ways to choose five members without assigning positions, 5 ways to choose five members with assigned positions, and 56 ways to choose five members with two members assigned to a particular position.

a.) The number of ways that the five team members can be chosen without assigning them positions is 10C5 = 252. This is calculated using the formula for combinations, which is n!/(r!(n-r)!), where n is the total number of members and r is the number to choose. In this case, n=10 and r=5, so 10!/(5!(10-5)!) = 252.

b.) The number of ways that the five team members can be chosen with assigned positions is 5!. This is because there are five positions, and each team member must occupy one of the positions. The order of the positions is irrelevant, so there is only one possible combination.

c.) The number of ways that the five team members can be chosen with the two members assigned to position five is 8C5 = 56. This is calculated using the same formula as in part a, but with n=8 since two members are already assigned to position five. 8!/(5!(8-5)!) = 56.

In total, there are 252 ways to choose five members without assigning positions, 5 ways to choose five members with assigned positions, and 56 ways to choose five members with two members assigned to a particular position.

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Answer:  Elasticity

Elasticity is a measure of how responsive one variable is to a change in another variable.

A polynomial that represents the area of the soccer field is 40x² + 240x + 200

What is polynomial?

A polynomial is an expression consisting of variables (also called indeterminates) and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables.

The area (A) of the rectangular pitch is calculated as

A = lb ( l is the length and b the breadth )

  = (10x + 10)(4x + 20)

Each term in the second factor is multiplied by each term in the first factor, that is

10x(4x + 20) + 10(4x + 20) ← distribute both parenthesis

= 40x² + 200x + 40x + 200 ← collect like terms, thus

A = 40x² + 240x + 200 ← in standard form

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Complementary Angles :  ( ∠1 , ∠5 )  , ( ∠2 , ∠6 ) , ( ∠3 , ∠7 ) , ( ∠4 , ∠8 )

Supplementary Angles : ( ∠1 , ∠2 ) , ( ∠2 , ∠4 ) , ( ∠3 , ∠4 ) , ( ∠1 , ∠3 )

Congruent Angles : ( ∠1 , ∠5 )  , ( ∠2 , ∠6 ) , ( ∠3 , ∠7 ) , ( ∠4 , ∠8 )

Straight, equally spaced lines that never cross each other and are on the same plane are called parallel lines. The angles that are created when any two parallel lines are intersected by a line (referred to as the transversal) have a relationship. Corresponding angles, Alternate Interior Angles, Alternate Exterior Angles, and Consecutive Interior Angles are some of the several pairs of angles that are created at this intersection.

Corresponding angles

When two parallel lines are intersected by a transversal, the corresponding angles have the same relative position

Alternate Interior Angles

Alternate interior angles are formed on the inside of two parallel lines which are intersected by a transversal.

Alternate Exterior Angles

The pairs of angles formed on either side of a transversal that divides two parallel lines are known as alternate exterior angles.

Consecutive Interior Angles

When two parallel lines are cut by a transversal, the pairs of angles formed on the inside of one side of the transversal are called consecutive interior angles or co-interior angles.

Given data ,

Let the parallel lines be represented as m and n

Now , the lines m and n are cut by the transversal line t

So , the angles are

The corresponding angles are ( ∠1 , ∠5 )  , ( ∠2 , ∠6 ) , ( ∠3 , ∠7 ) , ( ∠4 , ∠8 )

The supplementary angles are having a sum = 180°

The supplementary angles are angles in a straight line

So , ( ∠1 , ∠2 ) , ( ∠2 , ∠4 ) , ( ∠3 , ∠4 ) , ( ∠1 , ∠3 ) are supplementary angles

And , ( ∠5 , ∠6 ) , ( ∠6 , ∠8 ) , ( ∠7 , ∠8 ) , ( ∠5 , ∠7 ) are supplementary angles

The congruent angles are having the same measure

So , corresponding angles and alternate interior angles are also congruent angles

Hence , the angles are solved

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The solution for the given expression b = √ -1 -2b is b = -1.

An algebraic equation of the second degree in x is a quadratic equation. The quadratic equation is written as ax^2 + bx + c = 0, where x is the variable, a and b are the coefficients, and c is the constant term. First, there must be a term other than zero in the coefficient of x^2 (a not equal 0) for an equation to be a quadratic equation.

The expression is:

b = √ -1 -2b

Take square on both sides of the equation. The square negates the square root and we have the following expression:

b² = - 1 - 2b

b² + 2b + 1 = 0

The quadratic formula is given as:

x = - b ± √b² - 4ac ÷ 2a

Substituting the value of b = 2, a = 1 and c = 1:

x = -2 ± √4 - 4(1)(1) ÷ 2(1)

x = -2 ÷ 2

x = -1

Hence, the solution for the given expression b = √ -1 -2b is b = -1.

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The decimal system is a positional notation system, which means that the value of a digit in a number depends on its position in the number.

In the decimal system, each digit can take on one of ten possible values (0, 1, 2, 3, 4, 5, 6, 7, 8, or 9), and the value of a number is determined by multiplying each digit by its corresponding power of ten and then summing up the products.

For example, the number 123 can be written as [tex]1 x 10^2 + 2 x 10^1 + 3 x 10^0[/tex], where the exponent on the 10 indicates the position of the digit in the number. The left-most digit (1) is in the hundreds place, the next digit (2) is in the tens place, and the right-most digit (3) is in the ones place.

This positional notation system allows us to easily compare numbers by starting at the left-most non-zero place, because the value of each digit is determined by its position relative to the other digits in the number. The left-most digit represents the largest power of 10, and thus has the greatest impact on the overall value of the number. By comparing the left-most non-zero digits of two numbers, we can quickly determine which number is larger. If the left-most non-zero digits are the same, we can move on to the next digit to the right and continue the comparison until we find a difference.

This is why we use the left-to-right ordering of digits to compare numbers in the decimal system. It allows us to quickly determine the relative size of numbers, even when dealing with large or complex numbers.

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Answer:

Step-by-step explanation:

well then the anwser is 1.99 because the one time fee is only for downloading one movie the first, but 1.99 is the money you have to pay everytime you download a movie.

The solution is, A. m + n, must also be even .

A number that is divisible by 2 and generates a remainder of 0 is called an even number. Examples of even numbers are 2, 4, 6, 8, 10, etc. For example, assume you have ten chocolates. These chocolates may be divided into two groups, each having five chocolates. So, ten is an even number.

here, we have,

given that,

If 3(m + n) is even

so, we get,

3(m + n) is divisible by 2.

i.e. m+n is must ne divisible by 2.

Hence, The solution is,  A. m + n, must also be even .

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The probability that the pitcher will throw fewer than 4 pitches to a batter is 0.35

Probability refers to a possibility that deals with the occurrence of random events.

The probability of all the events occurring need to be 1.

P(E) = Number of favourable outcomes / total number of outcomes

This probability distribution is shown below:

Pitch                   1            2        3          4         5

Frequency         15         20      40        15        10

Probability         0.15     0.2      0.4      0.15      0.1

Thus the probability that the pitcher will throw fewer than 3 pitches to a batter = P(X < 4)

X  is the number of pitches thrown.

Therefore:

P(X < 4) = P(X = 1) or P(X = 2)

The additive rule of the probability states that if two events X and Y are dependent events, the probability of X or Y occurring is the sum of their individual probability.

P(X < 4) = P(X = 1) or

P(X = 2) = P(X = 1) + P(X = 2)

= 0.15 + 0.2

= 0.35

Hence, The probability that the pitcher will throw fewer than 4 pitches to a batter is 0.35

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