An airplane flew with the wind for 2. 5 hours and returned the same distance against the wind in 3. 5 hours. If the cruising speed of the plane was a constant 360 mph in air, how fast was the wind blowing? (Hint: If the wind speed is r miles per hour, then the plane travels at (360- + r) mph with the wind and at (360 - r) mph against the wind

The first step is to describe the method to take

To solve the system of equations 4x + 2y = 11 and 3x - y = 9, the first step would be to choose a method to solve the system.

There are several methods for solving systems of equations, including:

One common method is the substitution method, which involves solving one equation for one variable and then substituting the expression for that variable into the other equation.

For example, we could solve the second equation 3x - y = 9 for y to get:

y = 3x + 9

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Answer:

there are 100 centigrams in a gram

Step-by-step explanation:

The solution to the expression is x = 1/9

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

27**** = 3³x² x 9​

Express properly

27 = 3³x² * 9​

We can start solving this equation by rearranging it to isolate the variable x:

27 = 243x

Now we divide both sides by 243 to find x

x = 27/243

Evaluate

x = 1/9

Hence, the solution is 1/9

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Answer:

Example 2:

Find m∠P  and  m∠Q

if ∠P  and  ∠Q

are supplementary, m∠P=2x+15

, and m∠Q=5x−38

.

The sum of the measures of two supplementary angles is 180°

.

So, m∠P+m∠Q=180°

Substitute 2x+15

for m∠P

and 5x−38

for m∠Q

.

2x+15+5x−38=180°

Combine the like terms. We get:

7x−23=180°

Add 23

to both the sides. We get:

7x=203°

Divide both the sides by 7

.

7x7=203°7

Simplify.

x=29°

To find m∠P

, substitute 29

for x

in 2x+15

.

2(29)+15=58+15

Simplify.

58+15=73

So, m∠P=73°

.

To find m∠Q

, substitute 29

for x

in 5x−38

.

5(29)−38=145−38

Simplify.

145−38=107

So, m∠Q=107°

.Example 2:

Find m∠P  and  m∠Q

if ∠P  and  ∠Q

are supplementary, m∠P=2x+15

, and m∠Q=5x−38

.

The sum of the measures of two supplementary angles is 180°

.

So, m∠P+m∠Q=180°

Substitute 2x+15

for m∠P

and 5x−38

for m∠Q

.

2x+15+5x−38=180°

Combine the like terms. We get:

7x−23=180°

Add 23

to both the sides. We get:

7x=203°

Divide both the sides by 7

.

7x7=203°7

Simplify.

x=29°

To find m∠P

, substitute 29

for x

in 2x+15

.

2(29)+15=58+15

Simplify.

58+15=73

So, m∠P=73°

.

To find m∠Q

, substitute 29

for x

in 5x−38

.

5(29)−38=145−38

Simplify.

145−38=107

So, m∠Q=107°

.

The height of the tower in Alex's drawing is 20.7 centimeters.

A unit of measurement is a definite magnitude of a quantity, defined and adopted by convention or by law, that is used as a standard for measurement of the same kind of quantity.

We need to find the height of the tower in Alex's drawing.

Let us multiply the actual height of the tower by the scale factor.

Scale factor = 1 : 4000

Height of the actual tower = 828 meters

Height of the tower in Alex's drawing = 828 meters x (1/4000) = 0.207 meters or 20.7 centimeters.

Therefore, the height of the tower in Alex's drawing is 20.7 centimeters.

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Answer:Y = 7x – 16,

y = 2(2x – 5)

Step-by-step explanation:

he answer to the system of equations is (2,-2)

First, we can substitute in  for y in the other equation

This will give us

Next, we distribute the 2 throughout the parenthesis

Now we can solve for x. Begin by adding 16 to each side

Now we can subtract 4x from each side

Lastly, we can divide each side by 3

Now, we need to substitute in the value that we got for x into one of the equations to find the y value.

This becomes

So

This means that the solution to the system of equations is (2,-2)

there just reflected because the shape is just refected to the other side it the same but smaller

Answer:

Its D

Step-by-step explanation:

1130 / 7 = 161

161 x 365 = 58 765

Answer: D

Step-by-step explanation:

The principal sum of the given compound interest is Rs 5000.

The total amount of money borrowed (or invested), not including any interest or dividends, also called sum.

Given that, a sum of money amounts to Rs. 6050 in 2 year and Rs. 6655 in 3 years. we are asked to find the principal amount or sum,

CI = P(1+r/100)ⁿ

P = principal amount, CI =  compound interest, r = rate, n = time

Therefore,

CI = 6050(1+r/100)²....(i)

CI = 6655(1+r/100)³....(ii)

Diving eq(ii) by eq(i)

6655 / 6050  = (1+r/100)

1+r/100 = 1.1

r/100 = 1.1-1

r/100 = 0.1

r = 10%

Put r = 10% in eq(i)

6050 = p(1.1)²

p = 5000

Hence, the principal sum of the given compound interest is Rs 5000.

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The measure of arc CDE is, 154°

The measure of arc BC is, 26°

The measure of arc AB is, 90°

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

Now, By the figure, we have;

⇒ ∠APE + ∠EPD = 180°

⇒ (25x + 15)° + (33x - 9)° = 180°

⇒ 58x + 6 = 180

⇒ 58x = 180 - 6

⇒ 58x = 174

⇒ x = 3

Hence, The measure of arc CDE is,

⇒ (20x + 4)° + (33x - 9)°

⇒ (20×3 + 4)° + (33×3 - 9)°

⇒ 64° + 90°

⇒ 154°

And, The measure of arc BC is,

⇒ 90° - (20x + 4)°

⇒ 90° - (20×3 + 4)°

⇒ 90° - 64°

⇒ 26°

The measure of arc AB is,

⇒ arc AB + 90° = 180°

⇒ arc AB = 90°

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The value of angles are,

∠ H = 20°

∠ G  = 100°

∠ I = 60°

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

Two triangles are similar.

Now, We have in triangle XYZ,

∠Y = 20°

∠Z = 100°

Hence, ∠ X = 180 - (100 + 20)

∠ X = 60°

Thus, By definition of similarity;

∠ H = ∠ Y = 20°

∠ G = ∠ Z = 100°

∠ X = ∠ I = 60°

Thus, The value of angles are,

∠ H = 20°

∠ G  = 100°

∠ I = 60°

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The method that is used to calculate the cubic units of cake batter needed to fill the mold is V equals 355 over 113 times 4 squared times 6. (third option)

A cylinder is a three-dimensional object. It is a prism with a circular base. The amount of cake batter that is needed to fill the mold is equal to the volume of the cylinder.

Volume of a cylinder = πr²h

Where:

= 355/133 x 4² x 6

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The answer is V equals 355 over 113 times 4 squared times 6, thus, option (d)

The formula for volume of a cylinder is: V= πr2h, so if pi = 355/113 then

V= (355/113)(4)2(6)

Goodluck! ~izzy~

Tables and figures area way of presenting data in an organized form or more in a presentable way to attract more audience.

With tables and figures, it arranges your data to a simplified form and also it makes the content easy to understand for the front person.

Tables and figures in scientific papers are wonderful ways of presenting data. Effective data presentation in research papers requires understanding your reader and the elements that comprise a table.

It also several elements, including the legend, column titles, and body.

With all this tables in a research paper helps the reader understand the content for the data more effectively and efficiently.

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Errors in calculations are mistakes or inaccuracies that occur when performing mathematical calculations. They can be caused by a variety of factors, including human error, equipment malfunction, incorrect assumptions or data, and flawed methodology.

There are several types of errors that can occur in calculations, including:

Transcription errors: These occur when a number or a calculation is copied down incorrectly from one place to another, such as from a calculator to a piece of paper.

Calculation errors: These occur when the wrong calculation is used, or when a mistake is made in performing a calculation, such as forgetting to carry a digit when doing long division.

Rounding errors: These occur when numbers are rounded to a certain number of decimal places, and the resulting calculation is not as precise as it could be.

Measurement errors: These occur when the instruments used to measure quantities are not accurate, or when the measurements are not taken correctly.

Conceptual errors: These occur when the underlying concepts or principles of the problem are not fully understood, leading to incorrect calculations.

It is important to identify and correct errors in calculations to ensure the accuracy and validity of the results. Checking calculations multiple times and using multiple methods of verification can help to reduce the risk of errors.

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x+6y+10

llllllllllllllllllllllllllllllllllllllllllllllllll

Answer:

Step-by-step explanation:

By using the Median Function in Excel  =Median()

The area of the left over wood is

Area of the kite

perimeter of the kite

The area of the left over wood is given by

= area of the circle - area of the pentagon

area of the circle

= pi * r^2

= pi * 5^2

= 78.54 square cm

area of the pentagon

= 5/2 * a * 5

solving for a

360 / 5 = 72

72 / 2 = 36

cos 36 = a / 5

a = 5 cos 36 = 4

area of the pentagon = 5/2 * 4 * 5 = 50 sq cm

left over wood = 78.54 - 50 = 28.54 square cm

Area and perimeter of kite

area of kite = product of the two diagonals

length of one of the diagonals = 2 * KT = 2 * 12 = 24 cm.

The second diagonal

tan 30 = KT / x

x = 12 / tan30 = 20.78

the length = 12 + 20.78 = 32.78

area of the kite = 32.78 * 24 = 786.72 square cm

perimeter of the kite

= addition of the sides = 2(shorter side + longer side)

Using Pythagoras rule

shorter side = √(12² + 12²) = 16.97

longer side =  √(20.78² + 12²) = 24

perimeter = 2 (16.97 + 24) = 81.94 cm

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If the height of a triangle is 2 cm more than base and the area of the triangle is 10 cm then the height is, 7 cm

An area is total space occupied by two-dimensional or flat surfaces. In other words we can say that it is a number of unit squares present in a closed figure. We use various units for measurement of area like, cm², m², ft², mm².

The area of a triangle is given by the formula:

Area = (base x height) / 2

We are given that the area is 10 cm² and that the height is 2 cm more than the base.

Let's call the base "b".

Then, the height is "b + 2".

We can substitute these values into the area formula:

10 = (b x (b + 2)) / 2

Expanding the right side:

10 = (b² + 2b) / 2

Multiplying both sides by 2:

20 = b² + 2b

Subtracting b² from both sides:

20 - b² = 2b

Factoring the left side:

(10 - b)^2 = b²

Taking the square root of both sides:

|10 - b| = b

Adding b to both sides:

10 = 2b

Dividing both sides by 2:

5 = b

So, the base of the triangle is 5 cm and the height is b + 2 = 5 + 2 = 7 cm.

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73 kg is equivalent to approximately 160.937 pound (lbs).

Kilogram (kg) and pound (lb) are both units of mass commonly used in different parts of the world. Kilogram is the base unit of mass in the International System of Units (SI) and is defined as the mass of the International Prototype of the Kilogram, which is a platinum-iridium cylinder kept at the International Bureau of Weights and Measures in France.

Pound, on the other hand, is a unit of mass commonly used in the United States, the United Kingdom, and other countries, which is defined as exactly 0.45359237 kilograms. This value is based on the international avoirdupois pound, which is defined as exactly 0.45359237 kg.      

To convert kilograms to pounds, you can use the conversion factor of 2.20462 lbs/kg. To convert pounds to kilograms, you can use the conversion factor of 0.45359237 kg/lb.

To convert 73 kilograms (kg) to pounds (lbs), you can use the conversion factor of 2.20462.

So,

73 kg * 2.20462 lbs/kg = 160.937 lbs (rounded to three decimal places)

Therefore, 73 kg is equivalent to approximately 160.937 lbs.

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Answer:

undefined slope

Step-by-step explanation:

The graph of the equation x = -5 is a vertical line That passes through point (-5, 0).

The slope of a vertical line is undefined.

Answer:

no solutions

Step-by-step explanation:

y = 2x → (1)

y = 2x - 3 → (2)

since both equations express y in terms of . equate the right sides to find any solutions.

2x - 3 = 2x ( add 3 to both sides )

2x = 2x + 3 ( subtract 2x from both sides )

0 = 3 ← false statement

this indicates there are no solutions

A calculus cheat sheet can be a helpful tool to assist you in studying and reviewing calculus concepts.

Here are some tips for how to use a calculus cheat sheet effectively:

1. Familiarize yourself with the content: Take the time to read through the entire cheat sheet to get a sense of what topics are covered and how the information is organized.

2. Use it as a study aid: A calculus cheat sheet can be a helpful study aid to review concepts and formulas before a test or exam. Work through practice problems and apply the concepts you have learned.

3. Keep it handy: Print out the cheat sheet or save it to your phone or computer so that you can refer to it whenever you need to.

4. Use it as a reference: As you work on calculus problems, use the cheat sheet to remind yourself of key concepts, formulas, and rules.

5. Customize it: You can create your own cheat sheet, which includes the formulas and concepts that you find most challenging. This will help you focus on the areas that you need to improve upon.

Remember that while a calculus cheat sheet can be a helpful tool, it is important to develop a deep understanding of calculus concepts through practice, problem-solving, and building intuition. The cheat sheet should be used as a supplement to your learning, not a replacement for it.

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Answer: 64 MBS/43XY

Step-by-step explanation:

courseeeeeeeeee

Answer: r =[tex]\sqrt{4/\pi } =\sqrt{64/\pi } =4.51352[/tex]

Step-by-step explanation:

The number of students who preferred banana chips are 57.

The percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.

Given that sixty per cent of the students preferred raisins to banana chips. If there were 95 students in all, the number of the students will be calculated as:-

Number = 95 x 60%

Number = 95 x 60 / 100

Number = 95 x 0.6

Number = 57

Therefore, the number of students who choose banana chips is 57.

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The given statement "Qualitative data contribute to analysis and should aid the explanation of a process that may otherwise be unclear if explained by quantitative data only." is true.

Qualitative data is non-numeric information that provides insight into attitudes, behaviors, motivations, and perceptions. It is typically collected through open-ended questions, observation, and interviews. Qualitative data can provide a rich and nuanced understanding of a process or phenomenon that may not be possible to obtain through quantitative data alone. This is because qualitative data can help to uncover the underlying reasons behind a process, how people experience it, and how it is perceived by different groups. As a result, qualitative data can provide valuable context and insight into a process that may otherwise be unclear if explained by quantitative data alone.

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Answer:

OUT OF BUSINESS

Step-by-step explanation:

you cant afford it on food stamps my guy

Following are the given complete statements:

(a) Another name for plane X is plane EABC.

(b) F, D, and C are distinct points that are collinear.

(c) A, B, C and G are distinct points that are coplanar.

A plane is a flat, two-dimensional surface that extends infinitely in all directions. It is a mathematical concept used in geometry and is often represented as a flat sheet or a graph on a coordinate system. In the real world, a plane can be thought of as a flat surface such as a tabletop, a piece of paper or a wall.

(a) Another name for plane X is plane EABC.

(b) F, D, and C are distinct points that are collinear.

(c) A, B, C and G are distinct points that are coplanar.

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The value of x is 77.5. In order to solve for x, we need to use the Triangle Angle Sum Theorem.

Value is a subjective concept that referred to the word of importance that an individual group of people places on something it is often associated with principal beliefs and standard that are accepted by society when you can be seen as a measure of how important something is true person of organization it is often seen as a reflection of ones worldview and can help to save attitudes decision and behaviors believe is not an absolute and very depending on the context of the looks like commands.

In order to solve for x, we need to use the Triangle Angle Sum Theorem, which states that the sum of the angles in a triangle is 180°. Since angle BAC is bisected by segment AD, the two angles must be equal. Therefore, we can set up the following equation to solve for x:

180° = angle BAC = (x + 7) + (x + 18)

We can solve this equation by combining like terms and isolating the variable x.

180° = 2x + 25

2x = 155

x = 77.5

Therefore, the value of x is 77.5.

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Solution in da attachment!! :)