Simplify by combining like terms

2/3b - 2 3/4

Answer:

x = 28

Step-by-step explanation:

We can write a proportion to solve

50 dollars       175 dollars

--------------- = --------------------

8 hours                  x hours

Using cross products

50x = 8 * 175

Divide each side by 50

x = 8 * 175 / 50

x = 28

Answer:

[tex]\huge\boxed{\sf 28 \ hours}[/tex]

Step-by-step explanation:

Given that,

$50 = 8 hours

Divide both sides by 50

$1 = 8/50 hours

$1 = 0.16 hours

Multiply 175 to both sides

$175 = 0.16*175 hours

[tex]\rule[225]{225}{2}[/tex]

Answer:

Area is calculated by multiplying the length of a shape by its width.

Step-by-step explanation:

Area is defined as the total space taken up by a flat (2-D) surface or shape of an object. Take a pencil and draw a square on a piece of paper. It is a 2-D figure. The space the shape takes up on the paper is called its Area.

Answer:

I guess this is the answer

Answer:

Step-by-step explanation:

(x+8)(x-4) = 0

x = -8

x = 4

The type of function that describes function f(x) is given as follows:

Rational function.

The four types of functions are given as follows:

These functions are identified as follows from their graphs:

From the graph given by the image at the end of the answer, the features are given as follows:

Hence the function is a rational function.

The graph of the function is given by the image shown at the end of the answer.

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In the right angle triangle UVW and with help of Pythagoras Theorem, the value of tan W, rounded to the closest hundredth, is 4.55.

According to Pythagoras's Theorem, the square of a right angle triangle's hypotenuse side is equal to the sum of the squares of its other two legs.

The opposite side is the 40 units, while the hypotenuse side is 41 units long in the right angle triangle. Thus, the value of base side W is,

[tex]VW^{2} + 40^{2}=41^2\\VW=\sqrt{41^2-40^2}\\VW= 9 units[/tex]

Now tan W=[tex]\frac{UV}{VW}[/tex]=[tex]\frac{41}{9}[/tex]=4.55;

In the right angle triangle UVW and with help of Pythagoras Theorem, the value of tan W, rounded to the closest hundredth, is 4.55.

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The range of the graph is [-4, 11).

A graph is a diagram that depicts the relationship between two variables, usually measured along opposite axes in a pair, is used.

In the given graph,

The value of the x coordinate varies from -8 to 11.

And the values of x shows the domain,

Therefore, domain is (-8, 11).

The y coordinate varies from -4 to 11.

And the values of y coordinate shows the range.

The value of y at 11 is open circle, So it shows open interval.

And at -4 it shows close interval.

So the range of the graph will be [-4, 11)

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Answer:

All sum of Traingle Angle is 180°

180= 87+31+ Angle C

Angle C = 180 - (31+87)

Angle C = 62

The sequence's average difference is 12.5.

According to the given information

The sum of an arithmetic sequence's second and third terms is 27.

The combination of the fourth and fifth terms is 77.

We must ascertain,

Let d represent the sequence's common difference.

The arithmetic series' second term is,

Second term = a + d

The arithmetic series' third term is as follows:

Third term = a + 2d

The second and third terms in the sequence add up to 27, thus.

Second term + third term = 27

a + d  + a + 2d  = 27

2a + 3d = 27

The arithmetic series' fourth term is,

Fourth term = a + 3d

The fifth term in the mathematical series is as follows:

Fifth term = a + 4d

The sequence's fourth and fifth terms add up to 77

Fourth term + fifth term = 77

a + 3d + a + 4d = 77

2a + 7d = 77

After resolving the two equations,

2a + 3d = 27

2a + 7d = 77

Subtracting both the equations

2a + 3d - ( 2a + 7d ) = 27 - 77

2a + 3d - 2a - 7d = -50

-4d = -50

d = 12.5

The sequence's average difference is 12.5

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The probability that the mean number of lightning strikes per square kilometer is less than 5 is 0.0016, when  open ground in a year has mean 6 and standard deviation 2.4.

It imply a quantity that falls somewhere between the values of the extreme members of a set in mathematics. There are different types of means, and how they are calculated relies on the relationship that is known about or is regarded as governing the other members.

Given,

Mean = 6

Standard deviation = 2.4

The value that has been reduced by the population mean and divided by the standard deviation is called the z-value.

z = x - mean/ standard deviation/√n

z = 5 - 6/2.4/√50

z = - 2.95

Using table A, calculate the corresponding probability;

= P(x <5)

= P( z < -2.95)

= 0.0016

The probability that the mean number of lightning strikes per square kilometer is less than 5 is 0.0016.

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The answer to this Question based on Length is Yes he can easily make a bow with that

What is Length?

Length is a measurement of distance or size. It is the greatest of the three linear dimensions and is often denoted by the letter “L”. Length is commonly used to measure the size of objects, the distance between two points, or the magnitude of a displacement. Length can be measured in a variety of units such as inches, feet, meters, kilometers, or miles. Length is also used to determine the area of a two-dimensional shape, the volume of a three-dimensional shape, and the circumference of a circle. Length is an important concept in mathematics, physics, engineering, and other scientific disciplines. Length can also be used to describe how long something lasts, such as the length of a movie or a song.

we can see that length of henry ribbon that is available is 6 1/4 feet long ribbon which means 25/4 feet ribbon
= 6.25 feet of ribbon
whereas length of ribbon he needs is 1 1/12 feet ribbon to make a bow which is equal to

13/12 = 1.08 feet ribbon and he has 6.25 feet available hence he can easily make a bow with that

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The slope of the line which is perpendicular to the given line is (-6/5).

Describe the negative reciprocal.

The negative reciprocal of a number, let's say "n," is "- (1/n).

We are aware of a line's equation in slope intercept form, y = mx + b, as well as the fact that perpendicular lines have slopes that are reciprocal to each other's negative values.

The slope intercept form of the line 15x - 18y = -486 can be expressed as,

-18y = -15x - 486.

- y = (-15/18)x - (486/18).

- y = (-5/6)x - 27.

y = (5/6)x + 27.

The slope of the supplied line is (5/6), making the perpendicular line's slope (-6/5).

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Answer: 15 is a 25% increase of 12.

Step-by-step explanation: Difference of 12 and 15 = |12 - 15|/((12 + 15)/2) = 3/13.5 = 0.22222222222222 = 22.222222222222%

The inequality expression given by 4x + 6 + 2x < -2(3 + 3y) can be simplified and written as : x + y < - 2.

We have the following inequality -

4x + 6 + 2x < -2(3 + 3y)

We have -

4x + 6 + 2x < -2(3 + 3y)

4x + 6 + 2x < - 6 - 6y

6x + 6 + 6y + 6 < 0

x + y < - 2

Therefore, the inequality 4x + 6 + 2x < -2(3 + 3y) is equivalent to -

x + y < - 2.

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After solving we can conclude that (c) f(x) = -x is an odd function.

If -f(x) = f(-x), then a function f is said to be odd for all values of x.

When taking into account additive inverses, the functions even and odd are those that satisfy particular symmetry relations.

They are crucial to understanding power, the Fourier series, and mathematical analysis.

So, (a) f(x) = x³ + 5x² + x:

f(-x) = (-x)³ + 5(-x)² + (-x)

      = -x³ + 5x² - x

      = -(x³ - 5x² + x)

Neither even nor odd describe the function.

(b) f(x) = x² + x

f(-x) = (-x)² + (-x)

       = -(-x² + x)

Neither even nor odd describe the function.

(c) f(x) = -x

f(-x) = -(-x)

      = x

      = -f(x)

f(-x) = -f(x) makes the function odd.

Therefore, after solving we can conclude that (c) f(x) = -x is an odd function.

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Complete question:
Which of the following is an odd function?

(a) f(x) = x³ + 5x² + x

(b) f(x) = x² + x

(c) f(x) = -x

The balance sheet that correctly represents the engineer's income, expenses and balance is illustrated below.

We should know that a balance sheet is a summary of assets and liabilities and income and expenses of a  legal person. We are told that the balance sheet shows a bi-weekly net pay.

This implies that a month has two bi-weeks, therefore every income and expense is multiplied by 2 to get the following figures.

Income                                             Amount

Bi-weekly income                          $2,175.25

Total Monthly Income                   $4,350.50

Expenses                 Percent                              Amount

Housing                        35%                                $1,522.68

Food/Household          10%                               $435.05

Savings                         10%                                $435.05

Transportation              15%                                $652.58

Debt                              5%                                   $217.53

Entertainment               6%                                   $261.03

Medical/Personal Care 5%                                  $217.53

Giving                             5%                                 $217.53

Clothing                         4%                                  $174.02

Miscellaneous               5%                                 $217.53

                                                                          $4,350.50

Balance

Income $4,350.50

Expenses $4,350.50

Balance $0

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Answer:

Step-by-step explanation:

114048

Answer:

114048

Step-by-step explanation:

Answer:

To find the asymptotes and the end behavior of the function f(x) = 4x / (x-16), we can first divide both the numerator and denominator by the highest common factor of 4x and (x-16). This gives us:

f(x) = (4x / 4x) / ((x-16) / 4x)

= 1 / ((x-16) / 4x)

Next, we can find the horizontal asymptotes by looking at the values of the function as x approaches positive and negative infinity. When x approaches positive infinity, the denominator of the function approaches 0, so the function approaches 1 / 0, which is undefined. Therefore, the function does not have a horizontal asymptote as x approaches positive infinity.

When x approaches negative infinity, the denominator of the function approaches -16 / -infinity, which is 0. Therefore, the function approaches 1 / 0, which is undefined. Therefore, the function does not have a horizontal asymptote as x approaches negative infinity.

Next, we can find the vertical asymptotes by setting the denominator of the function equal to 0 and solving for x. In this case, the denominator is (x-16) / 4x, so we can set each factor equal to 0 and solve for x:

x-16 = 0

x = 16

4x = 0

x = 0

Therefore, the function has two vertical asymptotes at x = 0 and x = 16.

Step-by-step explanation:

Answer:

A)18in.

Step-by-step explanation:

Given,

A trapezoid Area= 216 sq

The length of its longer base=2x

The length of its shorter base= x

Height of Trapezoid = 8in

Area of Trapezoid= 1/2h(a+b)

216=1/2 x 8(2x+x)

216=4(2x+x)

216/4=3x

54=3x

54/3=x

18=x

Length of shorter base=18

Length of longer base=2x18=36

Hence, the length of the shorter base is 18in

Option A) is correct

To find the actual size of an item, multiply the scale factor by the size of the item in the drawing

The scale factor is the ratio of the measurement of the new figure to the measurement of the original figure

Here, we are drawing an item on the paper, the size of the object on the paper maybe less than or greater than of original item

The dimensions of the actual item will be equal to the product of scale factor and the dimensions of the item on drawing.

If the scale factor is greater than 1, then the actual size will be greater than drawing, if the scale factor is between 0 to 1, then actual size will be less than drawing

Therefore, to find the actual size multiply the scale factor and size of drawing

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The statement which is true about Data Visualization is:

a) Data presented in charts, graphs, and maps provides an accessible way to see and understand trends, patterns, and outliers.

Data Visualization:

Data visualization is the representation of data using common graphics such as charts, diagrams, infographics, and even animations. The visual representation of this information can communicate complex data relationships and data-driven insights in an easy-to-understand manner.

Data visualization can be used for many purposes, but it's important to note that it's not just for data teams. Executives also use it to teach organizational structure and hierarchy, and data analysts and data scientists use it to discover and explain patterns and trends. Harvard Business Review (link is outside IBM) categorizes data visualization into his four main objectives: idea generation, idea expression, visual discovery, and everyday data visibility.

Importance:

Data visualization provides a quick and effective way to communicate information in a universal way using visual information. Practice also helps businesses understand the factors that influence customer behavior. Identify areas that need improvement or need more attention. Make data more memorable for stakeholders. Understand when and where to place specific products. Then, Predict sales volume.

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Answer: 15,600 different choices for initials

Step-by-step explanation:

26 choices for the first, 25 for the second, and 24 for the third. When multipled, this is 15600.

We can use polynomial division concept for the given question. The quotient for the polynomial division is (2x^2+11x+32).

Divide the first term of the dividend by the first term of the divisor to divide polynomials using long division. The quotient's initial term is this. Dividend is calculated by multiplying the new term by the divisor. The new dividend is this difference. A polynomial is divided by another polynomial in an arithmetic operation called division, usually with a lower degree than the dividend. A polynomial may or may not be produced when two polynomials are divided.

Take Dividend as (2x^3 + 5x^2 - x + 6)

Take Divisor denominator as (x-3)

By using long hand division technique,

    (2x^3+5x^2-x+6)/(x-3)

  ⇒(x-3)(2x^2+11x+32)/(x-3)

 ∴ The quotient for the given polynomial division is 2x^2+11x+32 and the    

   Remainder for the polynomial division is 90.

We can use polynomial division concept for the given question. The quotient for the polynomial division is (2x^2+11x+32).

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Plot the Graph with time on X-axis and Cost on Y-axis.

It costs 12$ for 8,10,12 hours.

A graph is a diagram that shows the fluctuation of one variable in relation to one or more other variables (as a series of one or more points, lines, line segments, curves, or regions). In other words, depending on what you are attempting to prove or establish, values may be represented on a Cartesian coordinate system in a variety of ways. Discrete data would be shown on the graph as single points, such as the average price of vehicles from year to year. Since the calculation is only performed once each year, the data is discrete. The y axis would show the average price of cars for each year, while the x axis would indicate each year.

Given;

5$ for first hour;

10$ for up to 2 hours;

12$ for entire day.

G(t) = 5$ up to first hour, 10$ for up to 2 hours and 12$ for more than 2 hours.(So G is a function of t)

So for 0 hours,[tex]\frac{1}{2}[/tex] hours,1 hours it takes 5$;

and 10$ for 1[tex]\frac{3}{4}[/tex]hours, 2 hours

and 12$ for 5h,8h,12h.

Plot the Graph with time on X-axis and Cost on Y-axis.

It costs 12$ for 8,10,12 hours.

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The other two roots of the polynomial are x = (7 + √33)/4 and x = (7 - √33)/4.

A polynomial is an expression of one or more algebraic terms, each of which is composed of constants and/or variables raised to non-negative integer powers. A polynomial can be written in the form of an equation, where the coefficients of the terms form a sequence of numbers. Polynomials can also be expressed using a factored form, in which each of the terms is the product of a coefficient and a single variable or factor. Polynomials are commonly used to model real-world phenomena, such as the behavior of a system or process. The degree of a polynomial, which is the highest degree of the terms, determines the number of solutions it has. For example, a polynomial of degree two has two solutions while a polynomial of degree three has three solutions. The solutions of a polynomial are determined by solving the equation formed by the polynomial's terms.

Let us first rewrite the polynomial in a standard form:

2x^3 + 7x^2 + ax + 2 = 0
We can factor this polynomial using the Factor Theorem. The Factor Theorem states that if a is a root of a polynomial, then x-a is a factor of the polynomial.
Since x=-2 is a root of the polynomial, the factor (x+2) must be a factor of the polynomial.
Therefore, we can rewrite the polynomial as:
2x^3 + 7x^2 + ax + 2 = 2(x+2)(x^2 + bx + c)
Now, we can use the coefficients of the polynomial to solve for a, b and c.
Comparing the coefficients of the polynomial on both sides:
2 = 2c
7 = b
a = -2b-4c
Substituting the values of c and b in the equation for a, we get:
a = -2(b) - 4(2)
 = -2(7) - 8
 = -16
Therefore, the value of a is -16.
To find the other roots of the polynomial, we just need to solve the remaining factor (x^2 + bx + c) = 0.
Substituting the values of b and c, we get:
x^2 + 7x + 2 = 0
We can solve this equation using the Quadratic Formula:
x = [-b ± √(b^2 - 4ac)]/2a

Substituting the values of a, b and c, we get:
x = [-7 ± √(7^2 - 4(2)(2))]/2(-2)
 = [-7 ± √(49 - 16)]/-4
 = [-7 ± √33]/-4
Therefore, the other two roots of the polynomial are x = (7 + √33)/4 and x = (7 - √33)/4.

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Answer:

3w + 2

Step-by-step explanation:

3(w + 1) - 1

(3 · w) + (3 · 1) - 1

3w + 3 - 1

3w + 2

Answer:

A. One Solution

Step-by-step explanation:

To determine if a system of equations has no solutions, infinitely many solutions, or exactly one solution, we can solve the system by any method, such as elimination or substitution.

In this case, we can solve the system by elimination. Multiplying the first equation by -2 and adding it to the second equation, we get:

0x + 4y = -3

This equation tells us that y must be equal to -3/4, but we still need to check if this value of y satisfies the original equations. Substituting -3/4 for y in the first equation, we get:

2x + (-3/4) = 7

Solving this equation for x, we get x = 5/4. Substituting this value of x and -3/4 for y in the second equation, we get:

-2(5/4) + 2(-3/4) = -5

which simplifies to:

-5/2 + (-3/2) = -5

This equation is true, so the solution of the system is x = 5/4 and y = -3/4. Since the system has a unique solution, the answer is (A) One Solution.

Fibonacci sequence is the mathematical concept which was introduce by Italian Mathematician Fibonacci.

Therefore, Fibonacci sequence is the mathematical concept that was introduce by Italian Mathematician Fibonacci.

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The amount of money each person get at the end of the summer is below;

You = $80

Kyra = $102

Paolo = $98

Total contribution = $22 + $18 + $0

= $40

Amount each person get = (Total earnings after investment - Total contribution) / 3

= ($280 - $40) / 3

= $240/3

= $80

Amount you get = Your contribution + Amount each person get

= 0 + 80

= $80

Amount Kyra get = Kyra contribution + Amount each person get

= $22 + $80

= $102

Amount Paolo get = Paolo contribution + Amount each person get

= $18 + $80

= $98

In conclusion, each person gets an equal amount including their invested money.

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Answer:

Below

Step-by-step explanation:

Statement =1425.05

    1425.05 + 1075 + 120 - 795 - 289.95 = 1535.10 should be on her register.

                  (revised statement balance)    her register does not 'balance' with what she has in her account