The diameter of a vase is now 4 cm. If the diameter increases by a factor of 7/3, what will be the diameter then?

The real eigenvalues of the given matrix, once it has been diagonalized, are presented to its right as D = (7 0 0, 0 11 0, 0 0 11).

Learn about the dimensions and components of matrices by starting your first introduction. A rectangular grid of numbers organized into rows and columns is known as a matrix. Matrix A, as an illustration, has two rows and three columns. matrix, a collection of numbers lined up in rows and columns to create a rectangular array.  In addition to many other areas of mathematics, matrices have extensive applications in the fields of engineering, physics, economics, and statistics. It is so named because there is just one row, and a row matrix has the order 1 n as a result.

given

Eigen values ( λ )

| A - λI | = 0

=  ( 7 - λ ) ( 11 - λ ) ( 11 - λ ) =0

= λ = 7 , 11 , 11

eigen vector for λ = 7

( A - IB ) X = 0

= Let y = 1 , n1 = ( -1  1  0 )

eigen vector for λ = 11

( A - λI ) X = 0

n2 = ( 0 1 0 ) let n3= ( -2 0 1 )

D = ( 7 0 0 ,  0 11 0 , 0 0 11 )

The real eigenvalues of the given matrix, once it has been diagonalized, are presented to its right as D = (7 0 0, 0 11 0, 0 0 11).

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An equation of the tangent line to the given curve at the specified point will be y = e(x - 1) + e.

Given the equation y = e^x /x and the point (1, e), the goal is to find an equation of the tangent line at this point.

To do this, we need to find the derivative of the equation at the point (1, e). Taking the derivative with respect to x gives us:

y' = (e^x * (1 - 1/x) - e^x/x^2) / x^2

Since we are looking for the derivative at the point (1, e), we can plug in x = 1 to get the derivative at this point:

y' = (e - e/1) / 1^2

y' = e

Therefore, the equation of the tangent line at the point (1, e) is y = e(x - 1) + e.

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The table which shows the input and output values of g (x) is,

f (x)              g(x)

  2                 4

  1                  2

  0                 0

  1                  2

  2                 4

A relation between a set of inputs having one output each is called a function.

Given that;

The input and output values of a function f (x) are shown in the table.

     X                          f (x)

     -4                           2

     -3                           1

     -2                           0

     -1                            1

     0                            2

Here, We have;

⇒ g (x) = 2f (x),

Hence, The table which shows the input and output values of g (x) is,

f (x)              g(x)

  2                2×2 = 4

  1                 1×2 = 2

  0               0×2 = 0

  1                 2×1 = 2

  2                2×2 = 4

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My forecast is that you will either enter the next market or, more likely, keep your existing position. These are the theories we have.

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The ratio of the number of tickets sold by Jake to the number of tickets sold by Jeanne in the simplest form, will be 4:3

The ratio of the number of tickets sold by Jake to the number of tickets sold by Jeanne is 28:21.

To simplify this ratio, we can divide both numbers by their greatest common factor (GCF). The GCF of 28 and 21 is 7.

So, the simplified ratio is 28/7: 21/7 = 4:3

So the ratio of the number of tickets sold by Jake to the number of tickets sold by Jeanne is 4:3 in simplest form.

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If length of a rectangle is 4 inches shorter than its width and perimeter of  rectangle is 80 inches , then the length of rectangle is 18 in and width of rectangle is 22 in .

The Perimeter of rectangle can be calculated by using formula : [tex]2(l+w)[/tex] ;

let the width of rectangle be = w ,

it is given that the length is 4 inches shorter than width , that means ;

the width of rectangle is ⇒ [tex]w-4[/tex] ;

So , the perimeter becomes ⇒ [tex]80=2(l+w)[/tex]

⇒ [tex]80=2(w-4+w)[/tex]

⇒ [tex]40=2w-4[/tex] ;

⇒ [tex]2w=44[/tex] ;

⇒ [tex]w=22[/tex] ;

and substituting [tex]w=22[/tex] , we get [tex]l=22-4 = 18[/tex] in

Therefore , the length of rectangle is 18 in and width is 22 in .

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Answer:

25:6

Step-by-step explanation:

1/0.24

100/24

50/12

25/6

The rate in cups of ketchup per cup of mustard is given as 6 cups of ketchup per cup of mustard.

The expression model is defined as the model of the given situation in the form of an expression using variables and constants.

Here,
The recipe calls for 3 cups of ketchup for every 1/2 of mustard.
Now,
The rate in cups of ketchup per cup of mustard = ketchup/mustard
                                                                                = 3 / [1/2]
                                                                                = 3 × 2 = 6 / 1

Thus, the rate in cups of ketchup per cup of mustard is given as 6 cups of ketchup per cup of mustard.

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Answer: P(rolling a sum of 4 or rolling a sum of 5)

Step-by-step explanation: edge2023

The scenario that uses the addition rule for mutually exclusive events is:

p(rolling a sum of 4 or rolling a sum of 5) = p(rolling a sum of 4) + p(rolling a sum of 5)

This is because the events "rolling a sum of 4" and "rolling a sum of 5" are mutually exclusive, meaning that they cannot occur at the same time. Therefore, the probability of either event occurring is the sum of their individual probabilities.

The probability of rolling a sum of 4 is 3/36, and the probability of rolling a sum of 5 is 4/36. The addition rule states that the probability of rolling a sum of 4 or 5 is the sum of their individual probabilities: 3/36 + 4/36 = 7/36

The other scenarios do not use the addition rule for mutually exclusive events:

p(rolling a sum of 4) is a single event and does not involve a second event.

p(rolling a sum of 12 or rolling a double 6) although the two events are mutually exclusive, it's not the sum of their individual probabilities.

p(rolling a sum of 11 and rolling a sum of 12) these events are not mutually exclusive, they can happen at the same time, so it's not the sum of their individual probabilities.

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The equation that models how many parts p each machine can manufacture in any number of minutes m is m = 1.5p

The term equation in math is defined as a mathematical sentence that has two equal sides separated by an equal sign

Here we have given that a machine manufactures a part in 11 minutes and here we have also know that a newer machine can manufacture the same part 1.5 minutes faster.

Let us consider that p refers the number of parts for old machine and m refers the time taken for manufacturing.

Then the equation can be written as,

=>  m = 1.5p

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The graph to represent this data is pie chart.

In math, a graph can be defined as a pictorial representation or a diagram that represents data or values in an organized manner.  

The points on the graph often represent the relationship between two or more things.

For a solution to be solution to a system, it must satisfy all the equations of that system, and as all points satisfying an equation are in their graphs, so solution to a system is the intersection of all its equation at single point(as we need common point, which is going to be intersection of course)(this can be one or many, or sometimes none)

The graph used to represent the data is shown in the figure;

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The quantity of units that the company needs to sell in order for the net income to equal $0 would be = 8.

The net income of the company in thousands of dollars is represented with the function;

f(x) = 9x2 – 54x – 144,

It can be simplified as follows:

f(x) = 9(x² - 6x - 16)

Then:

f(x) = 9[(x + 2)(x - 8)]

It has a net income equals to 0 when:

f(x) = 0, hence:

x + 2 = 0 -> x = -2.

x - 8 = 0 -> x = 8.

The positive value and not a negative shows that there are amount of products sold which should be = 8.

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Answer:

To the nearest tenth of an inch, the length of the arc is 54.0 inches

Step-by-step explanation:

To determine the length of the arc, x, we need to use the formula for arc length, which is:

arc length = radius * angle (in radians)

Therefore,

arc length = 30 inches * 1.8 radians = 54 inches

Answer: I'm pretty sure there was suppose to be a 4th option that is not included here, none of these are correct, Lorraine can fill 8 jars.

Step-by-step explanation: First, we need to convert the 2.5 gallons of tomatoes to quarts. Since 1 gallon is equal to 4 quarts, 2.5 gallons is equal to 2.5 x 4 = 10 quarts.

Then we divide the number of quarts by the number of quarts per jar: 10 quarts / 1.25 quarts/jar = 8 jars.

⚠️Please verify inthe comments if there was indeed a 4th option⚠️

Answer:

8

Step-by-step explanation:

convert the 2.5 gallons of tomatoes to quarts. Since 1 gallon is equal to 4 quarts, 2.5 gallons is equal to 2.5 x 4 = 10 quarts.

Then divide the number of quarts by the number of quarts per jar: 10 quarts / 1.25 quarts/jar = 8 jars.

Answer:

96% of the houses were up for sale.

Step-by-step explanation:

Total number of houses

888 = 37 = 925

888 / 925 = .96

You change a decimal into a percent by multiplying by 100%

.96 x 100% = 96%

There are three main types of solutions found in mathematics for a given problem or equation: No solution, Unique solution, and Infinitely many solutions.

Solutions in mathematics are a set of values that can be assigned to the variables of an equation or a system of equations so that it holds true. In other words, it is a set of values that satisfies the equation or system of equations.

Types of solutions:

No solution: In this situation, there is no set of values that can be assigned to the variables of an equation or system of equations so that it holds true.

Unique solution: In this situation, there is only one set of values that can be assigned to the variables of an equation or system of equations so that it holds true.

Infinitely many solutions: In this situation, there are infinitely many sets of values that can be assigned to the variables of an equation or system of equations so that it holds true. This situation arises when the given equation is not independent.

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Answer:

4

Step-by-step explanation:

(H,H) (T,T)(T,H)(H,T)

Answer: x = 23

Step-by-step explanation:

Move all terms that don't contain

x

to the right side and solve.

Hope this helps :)

According to the area of rectangle, the maximum area is given by a 300 × 500 ft rectangle that is being half of a square

The formula to calculate the area of square is written as

A = l x b

where l refers the length and b refers the breadth in rectangle.

Here we have know that if there were no river then the maximum area would be given by a square configuration since increasing the length and decreasing the width of a square by the same value t  will decrease the area by a square with sides of length t.

Here we have to add the river on one side.

As we all know that we need to fence in a rectangle on one side of the river and then here we have imagine an identical rectangle on the other side of the river.

Then the maximum area is given when the two rectangles form a square that is when we have a rectangle twice as long as wide is written as

=> 1500 feet of fence then the rectangle has fenced sides written as 500feet and 300feet.

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It is possible for this statement to be true for a vending machine that occasionally dispenses more or less than 6 oz of coffee per cup.

The term "on average" or "on the average" refers to the mean or expected value of a distribution. The vending machine may have some variations in the amount of coffee it dispenses, but on average it dispenses 6 oz of coffee per cup.

It is possible that the vending machine may dispense more or less than 6 oz of coffee per cup due to machine variations, incorrect calibration, or maintenance issues. However, as long as the mean or average amount of coffee dispensed over a certain period of time is 6 oz per cup, the statement is considered true.

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The difference between the 51st term of a and the 51st term of b is 1000.

the nth term of an arithmetic series is given by [tex]a_{n}= a_{0}+(n-1)*d[/tex]

where [tex]a_{0}[/tex] is the first term of the arithmetic series, [tex]a_{n}[/tex] is the nth term of the series and d is the common difference

Given that,

[tex]a_{0}=b_{0}=30[/tex]

Common difference of both series that have absolute value = 10

common difference of series a is 10 as this series is increasing

similarly, the common difference of series b is -10 as it is decreasing

Putting the values in the above equation we get:

[tex]a_{51}= a_{0}+(n-1)*d\\[/tex]

=> 30 + (51-1)*10

=> 30 + 500 = 530

Thus, the value of [tex]a_{51}[/tex] is 530.

[tex]b_{51}= b_{0}+(n-1)*d\\[/tex]

=> 30 + (51-1)*-10

=> 30 -500 = -470

Thus, the value of [tex]b_{51}[/tex] is -470.

so we have to find the value of [tex]a_{51}-b_{51}[/tex] which is 530 - (-470) =530 +470 =1000

Therefore, The difference between the 51st term of a and the 51st term of b is 1000.

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Answer:

48

Step-by-step explanation:

First you should subtract 43 and 19

then you get a answer 24

Multiply it by 2

you get 48

Answer:

no. of books =48 books

Step-by-step explanation:

lets say that he started with

x

books so,

(X÷2)-19=43

X÷2=24

X=48

The total Number of ways to select five students out of 11 boys and 18 girls will be=104642

We have, total number of boys = 11, while the total number of girls = 18

Let us assume that,

X = total number of boys chosen

As it is given,

P(X>=4)=1

-P(X<=3)

Where, P(at most 3 boys are chosen) needs to be found out

As we know,

Here, the total number of ways to get at most 3 boys= Number of ways to get three boys and two girls + number of ways to get one boy and four girls + Number of ways to get two boys and three girls + Number of ways to get zero boys and five girls

Making the combination as per above arrangements:

We will get it as:

=11C3*18C2+11C1*18C4+11C2*18C3+11C0*18C5

As we know,

The formula of combination is:

[tex]$${ }_n C_r=\frac{n !}{r !(n-r) !}$$[/tex]

[tex]${ }_n C_r=$[/tex] number of combinations

n= total number of objects in the set

r= number of choosing objects from the set

So, applying the concept of combination in the above,

=11C3*18C2+11C1*18C4+11C2*18C3+11C0*18C5

[tex]= \frac{11!}{8! \times 3!} \times \frac{18!}{16! \times 2!}+\frac{11!}{9! \times 2!} \times \frac{18!}{15! \times 3!}+\frac{11!}{10! \times 1!} \times \frac{18!}{14! \times 4!}+\frac{11!}{11! \times 0!} \times \frac{18!}{13! \times 5!}[/tex]

[tex][\frac{11 \times 10\times9\times8! }{8!\times 6} \times \frac{18\times17\times16!}{16!\times2}]+[\frac{11\times10\times9!}{9!\times2} \times \frac{18\times17\times16\times15!}{15!\times6}]+[\frac{11\times10!}{10!} \times \frac{18\times17\times16\times15\times14!}{14!\times24}]+[\frac{1}{1} \times \frac{18\times17\times16\times15\times14\times13!}{13!\times120}][/tex]

[tex]=(165 \times153)+(55\times816)+(11\times3060)+(1\times856.8)[/tex]

=25245+44880+33660+856.8

=104641.8 = 104642 (approx)

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The areaSum() method takes two Circle objects as parameters and returns the sum of the areas of both circles as a double.

Circle c1 = new Circle(5);

Circle c2 = new Circle(7);

[tex]public static double areaSum(Circle c1, Circle c2){ return c1.getArea() + c2.getArea();}[/tex]

1. Create a public static method named areaSum that takes two Circle objects as parameters.

2. The method should return a double.

3. Inside the method, use the getArea() method of the Circle class to get the area of both circles.

4. Return the sum of the areas of both circles.

5. The method should look like this:

[tex]public static double areaSum(Circle c1, Circle c2){ return c1.getArea() + c2.getArea();}[/tex]

The areaSum() method takes two Circle objects as parameters and returns the sum of the areas of both circles as a double. The method uses the getArea() method of the Circle class to get the area of both circles and returns the sum of the areas.

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This is an algebraic word problem and it evaluated to be 10 years time before the age of the man will be twice the age of the daughter.

In algebraic word problems, we can represent an unknown number using letters and then carry out basic mathematics operations to get the value of the unknown number.

We shall represent the number of years it will be before the age of the man will be twice the age of the daughter with the letter x so that;

38 + x = 2(14 + x) {open bracket}

38 + x = 28 + 2x

38 - 28 = 2x - x {collect like terms}

10 = x

also x = 10.

Therefore, the agebraic word problem have a solution of 10 years before the age of the man will be twice the age of the daughter.

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Therefore , selecting a paperback book has an odd favor of 2:5, this probability problem's solution indicates that.

Calculating the probability of an event happening or a declaration being true is the focus of the mathematical field of probability theory. A chance is just a number between 0 and 1, with 1 denoting certainty and 0 roughly indicating the likelihood of an event occurring. Probability is a mathematical expression of the likelihood or probability that because an event will take place. The percentage ranges of 0% to 100% as well as the numerals 0 and 1 can be used to describe probabilities. the percentage of times an event occurs in a perfect collection of equally likely alternatives, out of all possible outcomes.

Here,

Given The likelihood of selecting a paperback book at random from either a bookshelf is 2/5, as stated.

In order to determine whether picking a paperback book is more likely to be strange,

So, using the information provided, we observe it.

that the odd favor of picking a paperback book is 2:1.

Option D is the proper choice.

Since selecting a paperback book has an odd favor of 2:5, this probability problem's solution indicates that.

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Answer:

2:3

Step-by-step explanation:

The type of triangle that is given by the dimensions, is a Scalene triangle.

A scalene triangle has sides that are all measured differently. In such a triangle, no side will be the same length as any other side. Every interior angle in a scalene triangle is also unique.

The lengths of two of the three sides in an isosceles triangle are equal. The angles that are opposite the equal sides are therefore equal. An isosceles triangle, in other words, has two equal sides and two equal angles.

Each side of an equilateral triangle has an equal length. Each internal angle in this scenario will be 60 degrees in length. An equilateral triangle is often referred to as an equiangular triangle since its angles are equal.

The dimensions here are not the same which means that all the sides are not equal and so this is a scalene triangle.

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1 is a factor of every whole number. Every whole number can be evenly divided by 1, so 1 is a factor of every whole number.

1 is the factor of every number as one divides every number exactly, without leaving any remainder behind, and gives the quotient as the number itself.

1 is the greatest factor of itself and the smallest factor of any other number.

There are some properties of factors one:

Every whole number is the product of 1 and itself so, each number is a factor of itself.

Every number is a factor of zero and 1 is the smallest factor of every number, and multiple and the greatest factor of a multiple is the multiple itself.

Every number other than 1 has at least two factors, namely the number itself and 1.

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