Find the LU-factorization of the matrix. (Your L matrix must be unit diagonal.) [ 1 0 -2 1]
LU =

The mean of the total sum of the balls remaining is (n-k)(n+1)/2 and the variance of the total sum of the balls remaining is  k(n-k)(n+1)/6

The mean of the total sum of the balls remaining in the urn is calculated by finding the average of each number of the remaining balls and summing them up. To find the variance, we use the formula for the variance of a discrete uniform distribution, which states that the variance is equal to the range of the distribution squared divided by 12. In this case, the range is n-k, since we have removed k balls, and the number of remaining balls will range from 1 to n-k.

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The expression that would find the percent error is:

(38 - 28) / 38 x 100 = 26%

The percentage is calculated by dividing the required value by the total value and multiplying by 100.

Example:

Required percentage value = a

total value = b

Percentage = a/b x 100

Example:

50% = 50/100 = 1/2

25% = 25/100 = 1/4

20% = 20/100 = 1/5

10% = 10/100 = 1/10

We have,

Sameera predicted that she would sell 38 blankets.

Actual sold 28 blankets.

Now,

Percentage error.

= (38 - 28) / 38 x 100

= 10/38 x 100

= 26%

Thus,

The percentage error is 26%.

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Answer:

20 Aussies

Step-by-step explanation:

20% times 5 = 100%

4 times 5 = 20 Aussies

So, there are 20 Aussies in a group.

Answer:

20

Step-by-step explanation:

4/20%

4/[tex]\frac{2}{10}[/tex]

4 x [tex]\frac{10}{2}[/tex] = [tex]\frac{40}{2}[/tex] = 20

There are 27 chocolate bars and 17 Pretzels in the vending machine

An equation is an expression showing the relationship between two or more numbers and variables. An equation can either be linear, quadratic, cubic and so on depending on the degree.

Let x represent the number of chocolate bars and y represent the number of pretzels

The vending machine has a total of 41 chocolate bars and bags of pretzels, hence:

x + y = 41      (1)

The number of chocolate bars is one less than twice the number of bags of pretzels, hence:

x = 2y - 1

x - 2y = -1     (2)

From both equations:

x = 27, y = 14

There are 27 chocolate bars in the vending machine

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0.003 is  the expected value and the standard deviation of the distribution.

What does a probability simple definition entail?

A probability is a number that expresses the possibility or likelihood that a specific event will take place.

                          Both proportions between 0 and 1 and percentages between 0% and 100% can be used to describe probabilities.

Let X shows the random variable corresponding to binomial distribution in the question.

 (a)

      Expected value of the binomial distribution is

       μ = E(X) = ηp =  20 . 040  = 8

and

   σ = √np( 1 - p )  = √20 .04.( 1 - 0.40 )  = √4.8  = 2.19

(b)

For a binomial distribution it is unusal to obtain the sucesses the less than μ - 2.5σ  and greater than μ + 2.5σ

here r = μ - 2.5σ  = 8 - 2.5 . 219 = 2.525

That is for the given binomial distribution it is unusal to obtain the number of successes less than 2.5 or approximately less than 3.

Probability of less than 3 sucesses is

  P( X < 3 ) = P( X≤ 2 ) = P(X=0) + P( X = 1 ) + P( X = 2 )

                  = 2∑k=0 (k²⁰) [tex]( 20 )^{k} ( 1 - 0.4)^{20 - k}[/tex]

                   = 0.003

It is very low probability.

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The exponent that makes the equation 3^x = e true is x = log(e) / log(3).

A mathematical function called an exponential function is applied in numerous instances in the real world. It is mostly used to calculate investments, model populations, and do other tasks like determining exponential growth or decay.

x = log(e) / log(3) is the exponent that ensures the truth of the equation 3^x = e, where log is the natural logarithm.

In general, if y = logb(x) then x = b^y. The natural logarithm (base e) is a special logarithm that helps us solve exponential equations.

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its 0

because zero to four down to the floor and five to nine climb the vine

Speed of the slower plane = 350 miles/hour

Relative speed is the speed of a moving body in relation to another. When two bodies are moving in the same direction, their difference is used to calculate their relative speed. When two bodies are moving in opposite directions, however, the relative speed is derived by summing their speeds.

Given,

Two planes heading opposite directions

After 2 hours the planes are 1500 miles apart.

Speeds of the planes differ by 50 mph

Let the speed of slower plane be x

then speed of faster plane = x + 50

Since, plane are moving in opposite directions

Relative speed = x + x + 50

Speed = distance /time

x + x + 50 = 1500/2

2x + 50 = 750

2x = 750 - 50

x = 700/2

x = 350 miles/hour

Hence, 350 miles/hour is the speed of slower plane.

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Curved surface area of a cone is 308 cm² and it slant height is 14 cm. So the cone volume is 343√3/3 π cm³.

These are the specified parameters:

Curved surface area of a cone (A) = 308 cm²

Slant height (s) = 14 cm

The length of the radius of the base of the cone

A = π r s

308 = 22/7 × r × 14

308 = 44 r

  r = 308/44

  r = 7 cm

The cone height

h² = s² - r²

    = 14² - 7²

    = 196 - 49

    = 147

h = √147

h = 7√3 cm

Cone volume

V = 1/3 π r² h

   = 1/3 × π × 7 × 7 × 7√3 cm³

   = 343√3/3 π cm³

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Scatterplots are best for showing the relationship between two interval/ratio variables and indirect or negative relationship between two ratio variables.

Scatterplots are best for showing:

⇒the relationship between two interval/ratio variables

⇒indirect or negative relationship between two ratio variables

Scatterplots display points on a coordinate plane, with one variable plotted on the x-axis and the other variable plotted on the y-axis. This allows us to see the pattern of relationship between the two variables. If there is a positive or negative relationship, we can see if the points tend to increase or decrease as we move from left to right or from bottom to top. If the relationship is indirect, we can see if the points tend to curve in one direction or another.

Scatterplots are not the best visualisation for showing: correlation

frequency of two nominal variables

For showing correlation, a line of best fit (regression line) can be added to a scatterplot, but other visualizations such as a correlation matrix or a heat map are more commonly used.

For showing frequency of two nominal variables, a two-way table or a mosaic plot are better suited, as they can display the count or proportion of cases for each combination of the two nominal variables.

Therefore, Scatterplots are best for showing the relationship between two interval/ratio variables and indirect or negative relationship between two ratio variables.

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Scatterplots are best for showing:

⇒the relationship between two interval/ratio variables

⇒indirect or negative relationship between two ratio variables

Scatterplots display points on a coordinate plane, with one variable plotted on the x-axis and the other variable plotted on the y-axis. This allows us to see the pattern of relationship between the two variables. If there is a positive or negative relationship, we can see if the points tend to increase or decrease as we move from left to right or from bottom to top. If the relationship is indirect, we can see if the points tend to curve in one direction or another.

Scatterplots are not the best visualisation for showing: correlation

frequency of two nominal variables

For showing correlation, a line of best fit (regression line) can be added to a scatterplot, but other visualizations such as a correlation matrix or a heat map are more commonly used.

For showing frequency of two nominal variables, a two-way table or a mosaic plot are better suited, as they can display the count or proportion of cases for each combination of the two nominal variables.

Therefore, Scatterplots are best for showing the relationship between two interval/ratio variables and indirect or negative relationship between two ratio variables.

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The Domain for the function g(x) = (x² - 3x - 18)/(x² − 4) is , all Real vales except x = 2 and x = -2 .

The Domain of a function is the set of all possible input values (values of x) for which the function is defined and produces a valid output (value of y).

For the function g(x) = (x² - 3x - 18)/(x² − 4), the only restriction on the domain is the denominator (x² − 4) cannot be equal to 0. This is because division by zero is undefined.

So, the domain of the function g(x) is all real numbers except x = ±2, because if we substitute x = 2 or -2 , the denominator becomes 0 and hence undefined .

Therefore , the domain of the function g(x) is {x | x ≠ ±2}.

The given question is incomplete , the complete question is

Consider the following : g(x) = (x² - 3x - 18)/(x² − 4) .  state the domain of the function .

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Answer: It should be you lost 2.8 million dollars

Step-by-step explanation:

The number of each type of coin in the jar is 76 quarters and 83 dimes.

Given data :

Thomas collects dimes and quarters in his change jar.

If he has 7 more dimes than quarters, and the total amount of money in the jar is $27.30.

Let, x be the number of the dimes.

And y be the number of quarters.

If he has 7 more dimes than quarters,

y = x + 7

The total amount of money in the jar is $27.30.

0.25x + 0.10y = 27.30

Substitute the value of y in equation 2

0.25x + 0.10(x + 7) = 27.30

0.25x + 0.10x + 0.7 = 27.30

0.35x = 27.30 - 0.7

0.35x = 26.6

x = 26.6 / 0.35 = 76

Substitute the value of x in equation 1

y = x + 7

y = 76 + 7 = 83

Hence, there are 76 quarters and 83 dimes in the jar.

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Answer:

Step-by-step explanation:

all angles of a triangle equals to 180

80+40= 120

x=180-120

x=60

Answer:

can i see the question then ill solve it?

Step-by-step explanation:

In the equation value of A=[tex]\frac{-32}{5} , B= \frac{36}{5} , C= \frac{1}{10} , D= \frac{-7}{2}[/tex].

What is equation?

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

Here the given equation is [tex]\frac{3x^3+4x^2-6x}{x^2+2x+2}= \frac{(Ax+B)}{x^2+2x+2}+\frac {C}{(x-1)}+\frac{D}{x+1}[/tex]

In RHS we multiply to get common denominator. Hence

=> [tex]\frac{3x^3+4x^2-6x}{(x^2+2x+2)(x^2-1)}= \frac{(Ax+B)(x^2-1)+C(x^2+2x+1)(x+1)+D(x-1)(x^2+2x+2)}{(x^2+2x+2)(x^2-1)}[/tex]

Removing the common denominator we get

=> [tex]{3x^3+4x^2-6x}= (Ax+B)(x^2-1)+C(x^2+2x+1)(x+1)+D(x-1)(x^2+2x+2)[/tex]

=> [tex]3x^3+4x^2-6x=Ax^3-Ax+Bx^2-B+Cx^3+Cx^2 +2Cx^2 +2Cx+2Cx+2C+D(x^3 +2x^2 +2x-x ^2 -2x-2)[/tex]

=> [tex]$ 3x^3+4x^2-6x =(A+C+D)x^3+ (B+3C+D)x^2+(-A+2C+2C)x + (-B+2C-2D)[/tex]

We can compare the coefficients to get

3=A+C+D−−−−−−−−1

4=B+3C+D−−−−−−2

−6=−A+4C−−−−−3

0=−B+2C−2D−−−−−−4

Add 2 and 4  then

=> 4 = 5C-D -----------5

Add 1 and 3 then

=> -3 =5C+D--------6

Now subtract 5 from 6 then

=> -7=2D

=> D = -7/2

Now put D=-7/2 into 5 then

=> 4=5c+7/2

=> 1/2=5C

=> C= 1/10

Now put value of C into 3 then

=> -6=-A+ 4×1/10

=> -6-2/5 = -A

=> A = -32/5

Now put C and D into 2 then

=> 4=B+3C+D

=> 4 = B+3/10-7/2

=> 4 = B-32/10

=>4+32/10 = B

=> B= 36/5

Hence in the equation value of A=[tex]\frac{-32}{5} , B= \frac{36}{5} , C= \frac{1}{10} , D= \frac{-7}{2}[/tex].

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The angle x° =( y+z )° using parallel lines theorem

parallel lines are coplanar infinite straight lines that do not intersect at any point. Parallel planes are planes in the same three-dimensional space that never meet.

When a line is used to cross 2 parallel lines, angles are formed and these angles are equal based on some properties.

To prove that x° = (y+z)°

Bisect angle x° into two equal part x1 and x2

y = x1 ( alternate angles are equal)

z = x2 ( corresponding angles are equal)

x1+x2 = x

since x1 = y and x2 = z

we can therefore say x1+x2 = y+z

y+z = x

x° = (y+z)°

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The average line shows the average of the data for a particular graph by drawing a line across the chart at the mean value points on the y-axis. By default, the average line label is displayed as a combination of line value and line title. 

Graph is a collection of data from several tables that will be presented or also displayed in the form of images, such as squares, circles, tubes, triangles, beams, cones or others. Graphics are also usually also interpreted as a framework or image that will be used to create a visualization object from data in tables with the aim of being able to provide information about a data from the material presenter to the recipient of the material.

In addition, graphs are also often interpreted as a description of the ups and downs of an existing data, or depicted by lines or pictures. The data used to create graphics can be in the form of numbers, letters, symbols, pictures, symbols, sayings, or paintings.

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The perimeter of the larger figure is equal to 20 units as the two figures have a side ratio of 4:3.

A ratio is a comparison of two or more numbers that indicates their sizes in relation to each other. It can be used to express one quantity as a fraction of the other ones.

We shall represent the perimeter of larger figure with the letter x, so that we express their ratios as fractions and solve for x as follows:

4 : 3 = x : 15

4/3 = x/15

x = (4 × 15)/3 {cross multiplication}

x = 4 × 5

x = 20 units

Therefore, the perimeter of the larger figure is equal to 20 units as the two figures have a side ratio of 4:3.

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The table for the complete data is,

Item            price before tax        sale tax         price including tax

pillow                $8                          $0.58                   $8.58

blanket              $22                        $1.59                   $23.59

trash can            $14.50                    $1.051                 $15.551

The mandatory tax imposed on the whole value of the items sold is known as the sales tax. Depending on the type of products sold, different sales tax rates apply.

The final amount of sales tax is added to the sale price of the products in the invoice because it is a charge made to the consumer.

Given the sales tax rate is 7.25%.

sales tax rate = 0.0725

to find sales tax and price including tax,

sales tax = price before tax * sales tax rate

and price including tax = sales tax + price before tax

1:  price before tax = $8.00

sales tax = 8*0.0725

sales tax = $0.58

price including tax = 8.00 + .58 = $8.58

2:  price before tax = $22.00

sales tax = 22*0.0725

sales tax = $1.59

price including tax = 22.00 + 1.595 = $23.595

3:  price before tax = $14.50

sales tax = 14.50*0.0725

sales tax = $1.051

price including tax = 14.50 + 1.051 = $15.551

Hence the table is,

Item            price before tax        sale tax         price including tax

pillow                $8                          $0.58                   $8.58

blanket              $22                        $1.59                   $23.59

trash can            $14.50                    $1.051                 $15.551

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The complete question is in image attached,

The trimming to put around the edges of the tablecloth,

A-At = 4069.44 - 2826 =  1243.44 inches square.

The area of a circle is calculated from the radius and the value of the irrational number.

The problems where the formula for calculating the area of a circle is applied are very diverse in science and engineering.

We know that 1 ft equals 12 inches, therefore 5 ft is 60 inches,

let r be the radius of the table

r=60/2=30 inches.

the area of the table is-

[tex]A_t=\pi r^2\\\\=(30)^2(3.14)\\\\=2826\ inches^2[/tex]

Let R be the radius of the tablecloth,

R=30+6=36

The area of the tablecloth is-

[tex]A=R^2\pi\\\\=4069.44\ inch^2\\[/tex]

The trimming to put around the edges of the tablecloth,

A-At= 4069.44-2826

      =  1243.44 inches square.

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No, the statements a) If she attends the meeting, she will become the secretary b) If she does not become the secretary, then she did not attend the meeting are not equivalent.

The statement "a" says that if she attends the meeting, then she will become the secretary. This is a sufficient condition for her to become the secretary.

The statement "b" says that if she does not become the secretary, then she did not attend the meeting. This is a necessary condition for her not attending the meeting.

So, while the statements are related, they don't represent the same relationship between the events of attending the meeting and becoming the secretary.

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The slope-intercept equation of the line is y= 9x + 3

The line with m as the slope, m and c as the y-intercept is the graph of the linear equation y = mx + c. The values of m and c are real integers in the slope-intercept form of the linear equation.

The slope, m, is a measure of how steep a line is. Sometimes, the gradient of a line is referred to as its slope. A line's y-intercept, ab, denotes the y-coordinate of the location where the line's graph crosses the y-axis.

Slope-intercept form of an equation: y=mx+b, where m is the slope (in this case, 9) and b is the y-intercept (in this case, the 3 from the point 0, 3)

y= 9x + 3 ( Plug in 9 for the m (slope) and 3 for the b (y-intercept))

Thus, the slope-intercept equation of the line is y= 9x + 3

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The fifth-degree polynomial in standard form is [tex]2x^5+ 5x^4+ x^3+ 3x^2+ 9x+16[/tex]. The polynomial is in the standard form because the powers of the terms are given in decreasing order.

[tex]2x^5+ 5x^4+16[/tex]  + ([tex]x^5+ 2x^4+11[/tex]) = [tex]3x^5+ 7x^4+17[/tex]

Part A:

The degree of the polynomial is the highest power of the terms of the polynomial.

For example 3x³ + x² + 2x is a polynomial of 3rd degree because the highest power of the terms given is 3.

As we need a polynomial of 5th degree the highest power will be 5.

[tex]2x^5+ 5x^4+ x^3+ 3x^2+ 9x+16[/tex]

The above polynomial is in the standard form because the powers of the terms are given in decreasing order. The first term has the highest power and so on.

Part B:

Suppose we have 2 polynomials

[tex]2x^5+ 5x^4+16[/tex] and [tex]x^5+ 2x^4+11[/tex]

When the closure property of addition is applied

[tex]2x^5+ 5x^4+16[/tex]  + ([tex]x^5+ 2x^4+11[/tex])

= [tex]2x^5+ 5x^4+16[/tex]  + [tex]x^5+ 2x^4+11[/tex]

= [tex]3x^5+ 7x^4+17[/tex]

The coefficients are changed because of addition.

The sign will not be changed due to the addition and like terms are added to get the answer.

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Answer: When b = 4, the value of -12b is -48.

Step-by-step explanation:

When b = 4, the expression -12b can be evaluated as follows:

-12b = -12 * 4 = -48

So, when b = 4, the value of -12b is -48.

Answer:

Step-by-step explanation:

its just -12 times 4  which is -48

The expression to represent the membership cost of Platinum Gym for x

months is y  = 60 + 20x.

The expression to represent the membership cost of Super Fit for x months is y = 150 + 10x.

Yes, there is a membership period where they will pay the same amount.

The membership period will be 9 months and the cost is 240 dollars.

Tom and his best friend, Edward, are seeking to join a gym. . Tom saw on television that Platinum Gym was having a grand opening in a few months and is considering a membership there.

Platinum Gym charges a one-time registration fee of $60, and membership is $20 monthly.

Tom's best friend, Edward, says he plans to join Super Fit because it only charges $10 monthly with a one-time registration fee of $150.

a.

The expression to represent the the membership cost of Platinum Gym for x months is as follows:

y  = 60 + 20x

where

b.

The expression to represent the membership cost of Super Fit for x months is as follows:

y = 150 + 10x

c.

The membership period for them to pay the same amount can be calculated as follows:

60 + 20x = 150 + 10x

60 - 150 = 10x - 20x

-90 = -10x

x = 90 / 10

x = 9 months

Therefore, the period is 9 months

y = 150 + 10(9)

y = 150 + 90

y = 240 dollars

Therefore, at 9 month they will pay 240 dollars.

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The area of the trapezoid is A = 1,10,622 miles²

The Trapezoid is a 4 sided polygon. Two sides of the shape are parallel to each other and they are termed as the bases of the trapezoid. The non-parallel sides are known as the legs or lateral sides of a trapezoid.

There are three types of trapezoids , and those are given below:

a) Isosceles Trapezoid

b) Scalene Trapezoid

c) Right Trapezoid

The area of the Trapezoid is given by

Area of Trapezoid = ( ( a + b ) h ) / 2

where , a = shorter base of trapezium

b = longer base of trapezium

h = height of trapezium

Given data ,

Let the area of the trapezoid be represented as A

Now , the shorter base of the trapezoid a = 205 miles

The longer base of the trapezoid b = 511 miles

The height of the trapezoid h = 309 miles

Now , the Area of Trapezoid = ( ( a + b ) h ) / 2

Substituting the values in the equation , we get

Area of Trapezoid A = ( ( 205 + 511 ) x 309 ) / 2

On simplifying the equation , we get

Area of Trapezoid A = 358 x 309

Area of Trapezoid A = 1,10,622 miles²

Hence , the area of the state is 1,10,622 miles²

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The expression -x < 3 is equivalent to x > -3 because division by a negative value changes the inequality sign

From the question, we have the following parameters that can be used in our computation:

-x < 3 is equivalent to x > -3

This is so because

-x < 3 is divided by -1 to get x > -3

As a general rule

A division by a negative value changes the inequality sign

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Answer:Simon gives 5 cakes to Sali and 30 x 10% = 3 cakes to Jane, so he gives out a total of 5 + 3 = 8 cakes.

Therefore, Simon has 30 - 8 = 22 cakes left.

So, the fraction of the 30 cakes that Simon has left is 22/30

Step-by-step explanation: