show that if a basis i is not optimal, then there is an improving swap, which means thtat there is a pair of indices

Answer:4 individuals

Step-by-step explanation:

Two pairs refers to 2 sets of two things. In general terms, a pair refers to two items and when you have two of them, it would be two sets of two things, or simply "four items".

For example, two pairs of socks would be four socks.

The values of x and y that are solutions to the system of simultaneous equations are; y = 573/25 and x = 17.1

We are given the simultaneous equations;

²/₃x + ³/₅y = 12    -----(eq A)

⁵/₂y - 3x = 6       ------(eq B)

Multiply eq A by 9 and eq B by 2 to get;

6x + ²⁷/₅y = 108    -----(eq C)

5y - 6x = 12       ------(eq D)

Add eq C to eq D to get;

5y + ²⁷/₅y = 120

Multiply through by 5 to get;

25y + 27 = 600

25y = 600 - 27

25y = 573

y = 573/25

Thus;

5(573/25) - 6x = 12

6x = 5(573/25) - 12

6x = 102.6

x = 17.1

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There is a linear relationship between exercise intensity and cardiac output. Therefore, when one rises, the other rises as well.

Cardiac output quantifies the volume of blood that your heart can pump in a minute. The phrase "exercise intensity" refers to how hard your body is working throughout a workout. These two are directly related to one another in some way.

The increase in cardiac output is linearly associated with exercise intensity up until the point of exhaustion. This happens as a direct result of the interaction between the heart rate and stroke volume reactions to the intensity of activity. Therefore, cardiac output will increase as exercise intensity does.

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Answer:

Using Words: The total area of the house and deck is given by the sum: 40x20 + x(13x) .

Using Symbols: The total area of the house and deck is given by the sum: 800 + 13x^2 ft².

Step-by-step explanation:

Answer:

I think of bills/notes.

Step-by-step explanation:

Money is the mode or medium of exchange for goods and services.

Currency is a type of money that is used as a medium of exchange in a specific country or region. It is a standardized unit of value that is accepted as payment for goods and services within the jurisdiction where it is used. Currency can take the form of physical banknotes and coins, or digital representations of money that can be used for online transactions.

Here,

Money is medium of exchange or a unit of account that is used to purchase goods and services. It is a tangible or intangible asset that represents value and is accepted by individuals, businesses, and governments in exchange for goods or services. Money is a fundamental component of modern economies, and its importance cannot be overstated.

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f(x) = x⁵ – 8x⁴ + 16x³ at x = 4, does not cross the x-axis. at x = 0, crosses the x-axis. This relates to the x-axis end behavior of a graph of a function.

Let's now find the roots of this function;

f(x) = x⁵ - 8x⁴ + 16x³

Let's factorize it first to get;

f(x) = x³(x² – 8x + 16)(x² – 8x + 16) is a perfect square trinomial and can be expressed as (x – 4)(x - 4).

Thus; f(x) = x³ (x – 4)(x - 4)

C) Since we have found the factorized form to be;

f(x) = x³ (x – 4)(x - 4)

The roots are at f(x) = 0;

The roots are; x³ = 0; (x – 4) = 0 ; (x - 4) = 0

This indicates that x=0 and x=4 are f(xroots. )'s x = 4

As a result, the graph will touch the x-axis but not the repeated root of 4, which indicates that the graph has a repeated root.

D) The graph will cross at x = 0 because it is a root and does not cross at x = 4.

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The equation that represents circles that have a diameter of 12 units and a center that lies on the y-axis is,

⇒ x²+ (y - 6)² = 36

The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.

Now, We know that;

The standard form for finding the equation of a circle is expressed as;

⇒(x - a)² + (y - b)² = r²

where; (a, b) is the center of the circle and r is the radius of the circle.

Here, we have;

⇒ Diameter = 12 units

⇒ Radius = 12/2 = 6 units

Since, The center lies on the y-axis,

Hence, the center will be at (0, 6).

Substituting into the formula, we will have;

⇒ (x - 0) + (y - 6)² = 6²

⇒ x² + (y - 6)² = 36

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If XV =27-2x and VZ =3x+2, then the diagonal of parallelogram XZ = 34 units and VZ = 17 units.

What is a parallelogram?

A quadrilateral with two sets of parallel sides is referred to as a parallelogram. In a parallelogram, the opposing sides are of equal length, and the opposing angles are of equal size.

The length of line XV = 27 - 2x.

The length of line VZ = 3x + 2.

According to the properties of a parallelogram the diagonals bisect each other .

Hence, XV = VZ.

Equating the expressions -

27 - 2x = 3x + 2

-2x - 3x = 2 - 27

-5x = -25

x = 5

The value of line XV = 27 - 2x

27 - 2(5)

27 - 10

17 units

The value of line VZ = 3x + 2

3(5) + 2

15 + 2

17 units

The value of line XZ = XV + VZ

17 + 17

34 units

Therefore, the value of VZ = 17 units and value of XZ = 34 units.

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If a certain store is selling packages of 10 pencils and 4 pens for back to school . The number of pencils that are in the larger package is 25 pencils.

First step is to find the  number of pencils per pen

Number of pencils per pen = 10 / 4

Number of pencils per pen = 2. 5

Now let find the number of pencils  that are in the larger package

Number of pencils = Number of pens x Pencils per pen

Number of pencils  = 10 x 2.5

Number of pencils = 25 pencils

Therefore we can conclude that the number of pencils is 25 pencils.

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A triangle whose any one of the angles is an obtuse angle or more than 90°, then it is called an obtuse-angled triangle or obtuse triangle.

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Answer:

Step-by-step explanation:

Karine De Marchand is 54 years

The relationship between data items is displayed using tables of values. In science class, you might utilize a table of values. Some  methods are explained.

Tables of values are used by scientists and researchers to record their data, which is then examined for patterns. Then, they can use this pattern to make predictions.

Some steps to prepare the table are-

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Answer:

12.375 hours

Step-by-step explanation:

We know that car travel

400 miles = 5.5 hours

900 miles = ?

We take 900 times 5.5, then divide by 400 and get 12.375 hours

So, the car take 12.375 hours to travel 900 miles

Answer:

12.375

Step-by-step explanation:

400+400+100=900miles

5.5+5.5=11

5.5÷4=1.375

11+1.375=12.375

Answer:(b)7m^4

Step-by-step explanation:
56m^8/8m^4
is can be said as

(7m^4 )(8m^4)/8m^4

8m^4 from both numerator and as well as denominator cancels so the final answer is 7m^4(7 m to the power 4)

Answer:

x=10 guests and $250

Step-by-step explanation:

Cater A=15x+100

Cater B=20x+50

2x+50=15x+100

5x=50

x=10

Answer:

121

Step-by-step explanation:

3x + 94 + x + 36 + 2x - 4 = 180

6x + 126 = 180

6x = 54

x = 9

m<AOC = 3x + 94

m<AOC = 3(9) + 94

m<AOC = 121

50%

because a coin only has 2 sides, resulting with a 50/50 chance of either option

Answer:

$11.90

Step-by-step explanation:

.85(9.86 + 2.15 + 1.99)

.85(14)

11.90

If we take off 15% from 100%, that leaves 85%.  85% as a decimal is .85

Answer:

$11.90 total bill after discount.

Step-by-step explanation:

the original amount is $14.00 with 15% discount it will come down to $11.90. Your discount was $2.10.

Out of 50 people, there are 50C5 = 50!/(5!*45!) ways to select 5 of them.

A probability is a numerical representation of the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to express probabilities.

How many of those methods involve picking a particular person (you)? If you are selected, there are only 4 more options left out of the remaining 49. There are thus 49C4 = 49!/(5!*44!) ways to select both you and the other 4 individuals.

Therefore, (49C4)/(50C5) = 1/10 is the probability.

The probability that you are one of the five individuals chosen from 50 is 5/50, or 1/10, as a second check.

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Three-dimensional space is a geometric concept that involves three values, known as coordinates, to determine the position of an object. These three coordinates are known as length, width, and height. It can also be referred to as x, y, and z coordinates.

1. Understand the concept of three-dimensional (3D) space. Three-dimensional space is a geometric concept that involves three values, known as coordinates, to determine the position of an object.

2. Identify the three coordinates. These three coordinates are known as length, width, and height. They can also be referred to as x, y, and z coordinates.

3. Determine the coordinates of a specific point. To find the exact coordinates of a point in 3D space, you must determine the length, width, and height of that point.

4. Use the coordinates to calculate the distance between two points. To calculate the distance between two points in 3D space, you must use the Pythagorean Theorem to determine the length of the hypotenuse.

5. Visualize the 3D space. To better understand 3D space, you can use tools such as 3D modeling software to create a virtual representation of the space.

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The value 255 in pixels means the code for the image is white. Therefore, any image with 255 pixels means it is white color.

Pixel values are the numerical values that make up the matrix in which images are stored in computers. The byte image, the most popular pixel format, stores this number as an 8-bit integer with a possible value range of 0 to 255.

Normally, zero and 255 are considered to be black and white, respectively. The many colors of gray are composed of values in between. This has the tremendous benefit of allowing computers to operate with color values that can be stored in a tidy number of bytes.

It is represented in 8 bits because 2⁸ equals 256 (from 0 to 255).

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Answer:

Should be right and scalene

The y-intercept of Y = - 10 is -10.

If we draw the graph of the linear equation y = mx + c. The result is a line with m as the slope, and c as the y-intercept. This form of the linear equation y = mx + c is called the slope-intercept form, and the values of m and c are real numbers.

The slope, m, of the line represents the steepness of a line. This is also termed a gradient, sometimes. The y-intercept, b, represents the y-coordinate of the point where the graph of the line intersects the y-axis.

Now, if we equate the standard slope-intercept form of the equation with the given equation, we get

y = mx + c

y =  - 10 = 0x -10

m = 0 and c = -10

As we know the c is the y-intercept which is equal to -10.

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Answer: x=7.6

Step-by-step explanation:

x-2.6=5

Step 1: Move 2.6 to another side of the equation with addition

X-2.6+2.6=5+2.6

X=7.6

Check your answer!

7.6-2.6=5 Correct!

Answer:

Step-by-step explanation:

x - 2.6 = 5    

x = 5 + 2.6

x =  7.6

--------------------------

7.6 - 2.6 = 5        

5 = 5

Whale is 1628.87 feet far from the shoreline.

The angle of depression is the angle between the horizontal line and the observation of the object from the horizontal line. It is basically used to get the distance of the two objects where the angles and an object's distance from the ground are known to us.

Given,

Height of the tower = 200 feet

Angle of depression = 7°

Distance of whale from the shore line = x = AB = ?

In the figure

tan 7° = BC/AB = 200/AB

0.1228 = 200/AB

AB = 1628.87 feet = x

Distance of whale from the shoreline = 1628.87 feet.

Hence, Whale and shoreline are 1628.87 feet far from each other.

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Polynomial [tex]$-1+x^3-\frac{1}{3} x^3$[/tex] and its conventional form, [tex]x^5-\frac{x^2}{3}-1$$[/tex] , are both used.

[tex]$$-1+x^5-\frac{1}{3} x^2=x^5-\frac{x^2}{3}-1$$[/tex]

steps

[tex]$$-1+x^5-\frac{1}{3} x^2$$[/tex]

[tex]\begin{aligned}& \frac{1}{3} x^2=\frac{x^2}{3} \\& =-1+x^5-\frac{x^2}{3}\end{aligned}[/tex]

rephrase in proper grammar

[tex]=x^5-\frac{x^2}{3}-1$$[/tex]

The term "polynomial" refers to a mathematical statement of one or more algebraic terms in which the variables are all of non-negative integer powers. Variables, fixed values, and exponents are all present in the terms. The degree 'n' standard form polynomial is Standard form is one method of expressing a polynomial. You must consider each term's degree in order to write any polynomial in standard form.

Next, list each phrase in order of degree, left to right, highest to lowest. An expression that solely uses the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables is said to be a polynomial. Variables, which are sometimes known as indeterminates, and coefficients make up a polynomial.

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Answer:

Algebraic expressions include at least one variable and at least one operation (addition, subtraction, multiplication, division). For example, 2(x + 8y) is an algebraic expression.

Step-by-step explanation:

Recursive  equation :

Thus,

For the given question;

Common ratio or difference : 90% or 0.9.

first term  = $26,500.

Thus, Recursive equation : f(n) = f(n - 1) + 9

Explicit  equation :

Thus,

Explicit equation : f(n) = 26,500 + (n - 1)(0.9).

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A stadium brought in an average revenue of $11,000 per night for a professional sports tournament. Total receipts for the period of time the tournament took place was $132,000. This means the tournament took place throughout is 12 days

How to find the number of members ?

When the teachers joined the members of the chess club for a tournament, the number of members that Alan counted was 31 people which means that the number of members in the chess club would be this number, less the number of teachers.

A stadium brought in an average revenue of $11,000 per night for a professional sports tournament.

Total receipts for the period of time the tournament took place was $132,000.

This means the tournament took place throughout how many days?

since total divide by per night is equal to number of days

now 132000/11000= 12

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A two-step equation is an algebraic issue that can be resolved in two steps.

Two-step equations typically take the form ax b = c, where a, b, and c are real numbers.

For instance, 2 - 3x = 7 is an illustration of a two-step equation.

Use the following steps to solve 2-step equations:

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Answer:

Two step equations are algebraic equations and are the equations that can be solved in exactly two steps and gives the final value of the variable in two steps.

Step-by-step explanation:

Example 1: Solve the two step equation (x/6) - 7 = 11

Solution: To solve the given two step equation, we will follow the steps discussed above in the article.

Step 1: Add 7 to both sides of the given two step equation

(x/6) - 7 + 7 = 11 + 7

= (x/6) = 18

Step 2: Multiply both sides of the equation by 6.

6 × x/6 = 6 × 18

= x = 108

Answer: Hence the solution to the given two step equation (x/6) - 7 = 11 is x = 108.

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