If a hypothesis test is performed and the null hypothesis is rejected in favor of the alternative​ hypothesis, does the test prove that the alternative hypothesis is​ correct? ExplainChoose the correct answer below.A.The test does not prove the alternative hypothesis​ correct, because only one test was​ done, and it takes at least β hypothesis tests to prove a claim about a population parameter.B.The test does not prove the alternative hypothesis​ correct, because of the possibility of rejecting the null hypothesis when the null hypothesis is true.C.The test proves the alternative hypothesis​ correct, because once the null hypothesis is​ rejected, the only possibility that remains is for the alternative hypothesis to be true.D.The test proves the alternative hypothesis​ correct, because it shows that all the evidence suggests that the alternative hypothesis is true.

Answers

Answer 1

The test does not prove the alternative hypothesis correct, because of the possibility of rejecting the null hypothesis when the null hypothesis is true.

The test does not prove the alternative hypothesis correct, because when performing a hypothesis test, the null hypothesis is rejected in favor of the alternative hypothesis. However, rejecting the null does not necessarily mean that the alternative hypothesis is true. It is possible for the null hypothesis to be rejected even when it is true, due to the occurrence of random fluctuations. Therefore, the test does not prove that the alternative hypothesis is correct, as there is always a possibility that the null hypothesis is true despite being rejected. To prove that the alternative hypothesis is correct, a series of hypothesis tests must be conducted to show that the population parameter is consistent with the alternative hypothesis.

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Related Questions

A student placed a straw into the water and blew bubbles into the water for 30 seconds. The pH of the glass of
tested again.
ater was
Use the pH scale below to determine the pH value of the water in this test. Record the value. Also, determine whether the
pH stayed the same, became more acidic, or became more alkaline compared to the first test.

Answers

Answer:

the water would most likely become more acidic.

Step-by-step explanation:

this is due to carbon dioxide being slightly acidic, it dissolves into the water inturn decreasing the pH.

a club sells 40 tickets to a raffle. issac bought one ticket. the probability that he will win the raffle is

Answers

Isaac has a 1/40 chance of winning the raffle, or a 2.5% chance. This indicates that he has a 2.5% probability of having his ticket chosen out of the 40 tickets that were sold.

Isaac has a 1/40 chance of winning the raffle, or a 2.5% chance. This indicates that he has a 2.5% probability of having his ticket chosen out of the 40 tickets that were sold. This is because there is only one raffle winner and it is impossible to predict which ticket will be picked.

It's also crucial to remember that his odds of winning are entirely independent of those of any other ticket holder; nobody else's ticket will affect the outcome of the raffle. As a result, Isaac has the same chance of winning as any other ticket holder. It's also vital to remember that regardless of how many tickets are sold, the likelihood of winning stays the same. Therefore, regardless of how many raffle tickets are sold, there is a 2.5% chance of winning.

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Please help me find the exponential function of the following graph, needed NOW!!! First to answer gets 10 points!

Answers

The exponential function is given as follows:

y = 64(0.5)^(x/5).

How to define the exponential function?

The standard definition of an exponential function is given as follows:

y = a(b)^(x/n).

In which the parameters are given as follows:

a is the initial value.b is the rate of change.n is the time needed for the rate of change.

Considering the initial value of 64, along with the fact that the amount halves each five days, the parameter values are given as follows:

a = 64, b = 0.5, n = 5.

Hence the function is defined as follows:

y = 64(0.5)^(x/5).

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A number cube is tossed 60 times.


Outcome Frequency
1 12
2 13
3 11
4 6
5 10
6 8


Determine the experimental probability of landing on a number less than 4.
6 over 60
36 over 60
38 over 60
42 over 60

Answers

Step-by-step explanation:

Probability works in fractions. The first part says a cube was tossed 60 times. That confirms that 60 is the denominator. So let's start that fraction.

[tex] \frac{x}{60} [/tex]

Next, what numbers are less than 4? 1, 2, and 3. So let's add the results of 1, 2, and 3

1 was 12

2 was 13

3 was 11

12 + 13 + 11 = 36. 36 is our other number, making the answer

[tex] \frac{36}{60} = 36 \: over \: 60[/tex]

In a soccer game, 1/5 of the players on Team A and 1/11 of the players on Team B score a goal. A total of 5 players on Team A and 2 players on Team B score a goal. How many players are on each team?

Answers

Let's call the number of players on Team A as "A" and the number of players on Team B as "B".

We know that 1/5 of the players on Team A score a goal, so:

5 players / (1/5) = A players

5 * (1/5) = A

A = 25

We also know that 1/11 of the players on Team B score a goal, so:

2 players / (1/11) = B players

2 * (1/11) = B

B = 22

So there are 25 players on Team A and 22 players on Team B.

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3/4 Divided by 6 2/3 as a fraction in simplest form

Answers

let's convert the mixed fractions to improper fractions first.

[tex]\stackrel{mixed}{6\frac{2}{3}}\implies \cfrac{6\cdot 3+2}{3}\implies \stackrel{improper}{\cfrac{20}{3}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{3}{4}\div \cfrac{20}{3}\implies \cfrac{3}{4}\cdot \cfrac{3}{20}\implies \cfrac{9}{80}[/tex]

Answer:

9/80.

Step-by-step explanation:

1. Write the expression.

[tex]\frac{\frac{3}{4}}{(6+\frac{2}{3} )}[/tex]

2.Simplify the denominator.

[tex]6+\frac{2}{3}=\\ \\\frac{18}{3}+\frac{2}{3} =\\ \\\frac{18+2}{3} =\\ \\\frac{20}{3}[/tex]

3. Rewrite the original expression.

[tex]\frac{\frac{3}{4}}{(\frac{20}{3} )}[/tex]

4. Use the rules of fractions to rewrite the operation.

Check the attached image.

[tex]\frac{3}{4} *\frac{3}{20}=\frac{3*3}{4*20} =\frac{9}{80}[/tex]

5. Express the final result.

9/80.

Subtract and reduce to lowest terms: 3 1/4 - 1 1/8
A. 2 1/8
B. None
c. 2 0/4
d. 17/8

Answers

The correct answer is option A. 2 1/8 when reduced to the lowest terms.

To subtract 3 1/4 - 1 1/8, we need to convert the fractions to a common denominator. The common denominator for 3 1/4 and 1 1/8 is 8. To convert 3 1/4 to 8, we multiply both the numerator and denominator by 2, resulting in 6/8. To convert 1 1/8 to 8, we multiply both the numerator and denominator by 8, resulting in 8/8.

Now we have two fractions with a common denominator of 8. To subtract them, we subtract the numerators and keep the same denominator. We have 6/8 - 8/8, which is -2/8. To reduce this fraction to the lowest terms, we divide the numerator and denominator by the greatest common factor (GCF), which is 2. -2/8 divided by 2 is -1/4. Finally, we add -1/4 to 1 1/8 to get the answer 2 1/8.

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9n^2=4+7n solve using quadratic formula

Answers

By using quadratic formula we solve 9n² = 4 + 7n, we get [tex]n = \frac{7 \pm \sqrt{193} }{18}[/tex]

What is Quadratic Formula?

Quadratic formula is the simplest way to find the roots of a quadratic equation. There are certain quadratic equations that cannot be easily factorized, and here we can conveniently use this quadratic formula to find the roots in the quickest possible way. The roots of the quadratic equation further help to find the sum of the roots and the product of the roots of the quadratic equation. The two roots in the quadratic formula are presented as a single expression. The positive sign and the negative sign can be alternatively used to obtain the two distinct roots of the equation.

The roots of a quadratic equation ax² + bx + c = 0 are given by x = [tex]\frac{-b \pm \sqrt{b^2 - 4ac} }{2a}[/tex]

Given:

The equation:

9n² = 4 + 7n

First rearrange the terms

9n² = 4 + 7n

9n² 7n + 4

9n² = 7n + 4

9n² - 7n - 4 = 0

By using quadratic formula, we get

a = 9, b = - 7, c = - 4

n = [tex]\frac{-(-7) \pm \sqrt{(-7)^2 - 4 .9.(-4)} }{2.9}[/tex]

[tex]n = \frac{7 \pm \sqrt{(-7)^2 - 4.9.(-4)} }{2.9}[/tex]

[tex]n = \frac{7 \pm \sqrt{49 - 4.9(-4)} }{18}[/tex]

[tex]n = \frac{7 \pm \sqrt{49 + 144} }{18}[/tex]

[tex]n = \frac{7 \pm \sqrt{193} }{18}[/tex]

To solve for the unknown variable, separate into two equations: one with a plus and the other with a minus.

[tex]n = \frac{7 + \sqrt{193} }{18}[/tex] or [tex]n = \frac{7 - \sqrt{193} }{18}[/tex]

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area can you pls help me

Answers

Answer:

6/5

Step-by-step explanation:

Answer:

6/5

Step-by-step explanation:

1/2×3/5×4

=12/10

divide by 2.

=6/5.

Translate the equation 3(g+h)=12 into a sentence.

Answers

Answer:

The equation "3(g + h) = 12" can be translated into a sentence as: "Three times the sum of g and h equals 12."

Hope this helps.

Answer: 3 times g plus h equals 12

Step-by-step explanation:

3 times g + h = 3(g+h)

equals 12 = =12

Hope this helps!

Write it in the form (x+a)+b

Answers

Answer:

in form of what?and what's the question

What is the answer to 5 x6/8?

Answers

Answer:

3.75

Step-by-step explanation:

Answer:

3.75

Step-by-step explanation:

How much is 600 divide by 50 + 30 x 100 - 600 divide by 0 don’t use the calculator

Answers

Answer:

The result is 9000.

Step-by-step explanation:

The calculation is done as follows:

600 ÷ 50 = 12

12 + 30 x 100 = 3200

3200 - 600 ÷ 0 = 9000

However, dividing by 0 is undefined and results in an error.

A company manufactures a special type of sensor, and packs them in boxes of 4 for shipment. Then a new design increases the weight of each sensor by 9 grams. The new package of 4 sensors weighs 76 grams. How much did each sensor weigh originally?

Answers

As the firm develops a specific sort of sensor and ships them in boxes of four, each sensor weighed 10 grams at first.

What is equation?

In its most basic form, an equation is a mathematical statement that indicates that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign. A mathematical phrase with two equal sides separated by an equal sign is called an equation. An example of an equation is 4 + 6 = 10.

Here,

Let's call the original weight of each sensor "w". The total weight of 4 sensors would be 4w.

With the new design, each sensor weighs 9 grams more, so each sensor weighs w + 9 grams. The total weight of 4 sensors is 76 grams, so we can write an equation:

4(w + 9) = 76

Expanding the left-hand side and solving for w, we have:

4w + 36 = 76

4w = 40

w = 10

So each sensor originally weighed 10 grams as company manufactures a special type of sensor, and packs them in boxes of 4 for shipment.

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Encuentre la solución general de la ecuación diferencial.
(Use C para la constante de integración.)

Answers

La solución de la ecuación diferencial dy / dx = [(12 - 9 · x²) / √(x³ - 4 · x + 4)] es la ecuación y = - 3 · ㏑ |x³ - 4 · x + 4| + C.

¿Cómo resolver una ecuación diferencial con variables separables?

En este problema tenemos el caso de una ecuación diferencial ordinaria con variables separables, esto es, que las variables x, y pueden ser apartadas a cada lado de la identidad. A continuación, se presenta el procedimiento de la solución de la ecuación diferencial.

Primero, se escribe la ecuación diferencial y se separan las variables:

dy = [(12 - 9 · x²) / √(x³ - 4 · x + 4)] dx

Segundo, se simplifica la expresión y se aplica la integral a ambos lados:

∫ dy = - 3 ∫ [(3 · x² - 4) / √(x³ - 4 · x + 4)] dx

Tercero, emplear la fórmula de sustitución algebraica u = x³ - 4 · x + 4:

du = 3 · x² - 4 dx

∫ dy = - 3 ∫ [du / u]

Cuarto, integral la expresión resultante:

y = - 3 · ㏑ |u| + C, donde C es la constante de integración.

Quinto, reversar la fórmula de sustitución algebraica:

y = - 3 · ㏑ |x³ - 4 · x + 4| + C

Observación

No existen problemas verificados en español, de modo que se añade una pregunta en inglés.

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Determine the value of x.
X
12 cm
4 cm
Give your answer correct to 1 decimal place.

Answers

The value of the angle x is 18. 4°

How to determine the value of the variable

it is important to note the six types of trigonometric identities, they are;

sinecosinetangentcotangentcosecantsecant

sin θ = opposite/hypotenuse

cos θ = adjacent/hypotenuse

tan θ = opposite/adjacent

From the diagram shown, we have the opposite and adjacent sides, then;

tan x = 4/12

Divide the values

tan x = 0. 3333

take the tangent inverse of the value

x = 18. 4°

Hence, the value is 18. 4°

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finding a parametric description of the solution set of a linear system is the same as solving the system. True/False ?

Answers

The answer is True. Finding a parametric description of the solution set of a linear system is the same as solving the system.

Finding a parametric description of the solution set of a linear system is equivalent to solving the system. A parametric description of the solution set of a linear system is a way of representing all solutions to the system in terms of a set of parameters. Solving a linear system involves finding the specific values of the variables that satisfy the constraints specified by the system. By finding a parametric description of the solution set, we are effectively solving the system and finding all possible solutions. In this sense, finding a parametric description of the solution set and solving the system are equivalent.

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What percent of the figure is shaded?

A circle divided into ten equal parts. Seven of the parts are shaded.

Answers

By the figure of a circle, 70% of the figure is shaded.

What is mean by Percentage?

A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.

Given that;

A circle divided into ten equal parts. Seven of the parts are shaded.

Now, Number of total parts = 10

And, Shaded parts of a circle = 7

Hence, The percent of shaded part is,

⇒ Shaded part / Total parts × 100

⇒ 7/10 × 100

⇒ 70%

Thus, There are 70% of the figure is shaded.

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did Kelly earn this week delivering packages?
Kelly makes $5.15 per package delivery. This week she delivered 3 packages on Monday, 5 on Wednesday and 9 on Saturday. How much

Answers

Using unit value, Kelly earned a total of $87.55 this week.

The meaning of a unit value

In most cases, the unit value is obtained by dividing the cost or value of a group of objects by the total number of items.

The appraisal of a single item or component within a group is known as unit value. The concept of unit value is applicable in a variety of contexts, including building, inventory control, sales, and stock trading. The unit value is typically the result of dividing the price or worth of a set of things by the total number of items.

Kelly delivered three packages on Monday, five on Wednesday, and nine on Saturday in light of this.

There have been 17 shipments delivered in all.

Additionally, she earns $5.15 for every shipment she delivers.

Kelly made a total of $5.15 × 17.

= $87.55

Kelly consequently made $87.55 in total for the week.

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a professor is deciding which classes to teach in the fall. she chooses math 341 with probability 3/7 and math 340 with probability 1/4 and neither class with probability 1/2. a. what's the probability that she chooses to teach both classes?

Answers

The probability that the student chooses both math and Spanish is 0.5.  

What is the probability?

Probability refers to a possibility that deals with the occurrence of random events.

The probability of all the events occurring need to be 1.

P(E) = Number of favorable outcomes / total number of outcomes

Given that professor is deciding which classes to teach in the fall.

The chooses math 341 with probability 3/7 and math 340 with probability 1/4 and neither class with probability 1/2.

P(M) = 3/7

P(S) = 1/4

P (M' ∩ S') = 1/2

According to De-Morgans law

P (M ∩ S) = P(M) + P(S) - P (M' ∩ S')

P (M ∩ S) =1/2

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you just built a large pool and you have to figure out how much it will cost to fill it with water. the pool is 10 ft wide. if the water company charges $0.02 per gallon, how much will it cost to fill the pool?

Answers

As per unitary method, the amount it will cost to fill the pool is $2.68

The Unitary Method is a mathematical concept which encourages students to use one single rule or principle to solve a problem. It can be used to solve a variety of mathematical problems in algebra, geometry, and other areas.

In this case, the pool is 10 ft wide. To calculate the capacity of a pool with a rectangular shape, you need to multiply its width by its length and then multiply that result by its depth.

If we assume that the length and depth of the pool are both equal to 10 ft, then the capacity of the pool can be calculated as follows:

=> 10 ft x 10 ft x 10 ft = 1,000 cubic feet.

To convert the capacity to gallons, you need to divide

=> 1,000  / 7.48 = 133.89

gallons of water required to fill the pool.

Finally, to calculate the cost of filling the pool, you just need to multiply the number of gallons by the cost per gallon of water ($0.02).

=> 133.89 x 0.02 = 2.68

This gives us a total cost of $2.68 to fill the pool with water.

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Makayla leans a 26-foot ladder against a wall so that it forms an angle of 69∘
with the ground. What’s the horizontal distance between the base of the ladder and the wall? Round your answer to the nearest tenth of a foot if necessary.

Answers

Answer:

Step-by-step explanation:

bc=12.605

The horizontal distance between the base of the ladder and the wall is  8.9 feet.

What is Trigonometry?

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

If we draw a right triangle with the ladder being the hypotenuse, the angle between the ladder and the ground is given as 69 degrees.

We can use trigonometric functions to solve for the horizontal distance between the base of the ladder and the wall.

Let x be the horizontal distance between the base of the ladder and the wall.

cos(69°) = x/26

Solving for x, we get:

x = 26 cos(69°)

Using a calculator, we find that cos(69°) ≈ 0.342, so:

x ≈ 26 × 0.342 ≈ 8.892

Therefore, the horizontal distance between the base of the ladder and the wall is approximately 8.9 feet.

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7 increased by 200% I just don't get it please help I need it FAST

Answers

Answer:

21

Step-by-step explanation:

how do i set up this problem

Answers

Therefore , the solution of the given problem of quadrilateral comes out to be x value is  8.13 .

A quadrilateral is what?

A rectangle is a four-sided, four-cornered object in mathematics. Either the Latin quartet or creative portfolio are the terms' sources (meaning "side"). Four states, corners, and provincial assemblies make up the three divisions of a rectangle. Convex and curved surfaces can be broadly divided into two categories. Convex quadrilaterals also include parallelograms, triangles, rhombuses, rectangles, and trapezoids as subcategories.

Here,

Given :

=> 11x + 4 , 18x - 2 and 114 degree ,

Let m∠B is x:

So ,

According to angle sum property :

=> 11x + 4 + 18x - 2 + 114 + x = 360

=> 116 + 30x = 360

=> 30x = 360 - 116

=> 30x = 244

=> x = 244/30

=> x = 8.13

Therefore , the solution of the given problem of quadrilateral comes out to be x value is  8.13 .

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ow many data points are plotted incorrectly on the scatter plot graph, if any?
Responses
A 00
B 11
C 22
D 3

Answers

The solution is Option A.

The number of data points that are incorrectly marked on the scatter plot is none

What is a Scatter Plot?

Dots are used in a scatter plot to show the values of two different numerical variables. Each dot's location on the horizontal and vertical axes represents a data point's values. To view relationships between variables, utilize scatter plots.

The closer the data points come to forming a straight line when plotted, the higher the correlation between the two variables, or the stronger the relationship. If the data points make a straight line going from near the origin out to high y-values, the variables are said to have a positive correlation.

Using end behavior, turning points, intercepts, and the Intermediate Value Theorem, plot the graph of a polynomial function.

Given data ,

Let the equation of graph be represented as A

Now , the value of A is

Let the values of x be = { 1 , 2 , 3 , 4 , 6 , 8 , 10 , 12 }

Let the values of y be = { 2.5 , 7.6 , 12.5 , 17.1 , 24.3 , 37.9 , 49.2 , 54.9 }

So , the points on the graph will be

A ( 1 , 2.5 ) , B ( 2 , 7.6 ) , C ( 3 , 12.5 ) , D ( 4 , 17.1 ) , E ( 6 , 24.3 ) , F ( 8 , 37.9 ) , G ( 10 , 49.2 ) , H ( 12 , 54.9 )

There are no points marked incorrectly on the scatter plot

Hence , the graph is plotted and there are no incorrect data points on the scatter plot

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2) During a portage, the leader of a scout troop decided to save time by hiking around a
wooded area between the base camp and a lake. The troop reached the lake by walking for
30 minutes on a bearing of N60°E, then for 45 minutes on a bearing of N80°W. The leader
figured that they walked at an average speed of 3km/h. If they could have walked straight
through the forested area at 1km/h, did the troop save any time by going around? If so, how
much?

Answers

Answer:

could have walked straight

through the forested area at 1km/h, did the troop save any time by going around

if a function is not continuous at a point, then it is not defined at that point. True/False ?

Answers

False. Despite not being continuous at that point, a function can nevertheless be defined there. For instance, even when a function is defined at a certain place, it may nevertheless have a finite jump there.

False. Despite not being continuous at that point, a function can nevertheless be defined there. Functions that have a limit that is equal to their value at a particular point are said to be continuous functions. A function is said to be continuous at a particular location if it is. A function can, however, be defined at a location yet not be continuous there. For instance, even when a function is defined at a certain place, it may nevertheless have a finite jump there. This suggests that the function is not continuous at that point since the left-hand limit and the right-hand limit of the function at that point are not equal. So, even though a function is defined at a certain location, it may not be continuous there.

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E (-7,-4) , F (2,-3), G (0,-7), H(-9,-8) prove the quadrilateral is a parallelogram

Answers

By applying the properties of a parallelogram, it can be concluded that the quadrilateral would be a parallelogram since the opposite sides EF and GH are congruent and parallel.

Parallelogram is a 2-D shape formed by two pairs of sides, each of which is the same length (congruent) and parallel to its pair, and has two pairs of angles, each of which is equal to the angle opposite it.

Distance between two points is the length of the line segment that connects the two points in a plane.

d = √((x₂ – x₁)² + (y₂ – y₁)²)

Slope of a line is its vertical change divided by its horizontal change.

m = (y₂ - y₁) / (x₂ - x₁)

We have these points E (-7,-4), F (2,-3), G (0,-7), and H(-9,-8), and we want to prove that they formed a parallelogram.

To do so, we have to prove that EF and GH are congruent by calculating the distance between EF and GH:

EF = √((x₂ – x₁)² + (y₂ – y₁)²)

    = √((2 + 7)² + (-3 + 4)²)

    = √(9² + 1²)

    = √82

GH = √((x₂ – x₁)² + (y₂ – y₁)²)

     = √((-9 – 0)² + (-8 + 7)²)

     = √((-9)² + (-1)²)

     = √82

Because EF = GH = √82, they are congruent.

In the second step, we have to prove that EF and GH are parallel by calculating their slope:

slope of EF = (y₂ - y₁) / (x₂ - x₁)

                   = (-3 + 4) / (2 + 7)

                   = 1/9

slope of GH = (y₂ - y₁) / (x₂ - x₁)

                    = (-8 + 7) / (-9 – 0)

                    = 1/9

Because EF and GH have the same slope, they are parallel.

Thus, since the opposite sides EF and GH are congruent and parallel, so the quadrilateral would be a parallelogram.

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Megan tiled a rectangle with an area of 24 square centimeters. Which of these could not be Megan ‘s rectangle

Answers

Megan tiled a rectangle with an area of 24 square centimeters, the Megan ‘s rectangle is 2 centimeters by 12 centimeters.

Megan tiled a rectangle with an area of 24 square centimeters,

A = 24 square centimeters

Area of the rectangle = length x breadth

A = l x b

24 = 12 x 2

Therefore, length= 12cm and breadth is 2 cm.

The area occupied by the rectangle within its perimeter may be calculated using the formula for the area of a rectangle. A rectangle's area is calculated by multiplying its length by its width (breadth). As a result, the area of a rectangle whose length and breadth are "l" and "w," respectively, may be calculated using the following formula. L * W = the rectangle's area. Therefore, the area of a rectangle is equal to (length width).

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Complete question:

Megan drew a rectangle that has an area of 24 square centimeters. Which of the following could be the dimensions of her rectangle?

2 centimeters by 12 centimeters3 centimeters by 9 centimeters4 centimeters by 20 centimeters6 centimeters by 6 centimeters12 centimeters by 12 centimeters

consider the nonlinear equation for population growth ax, where a > 0. a) does this equation exhibit over-, under- or exact compensation?b) does it have a non-trivial steady state?

Answers

For the given nonlinear equation for population growth ax where a>0,  a0 the equation exhibits exact compensation  whereas b) it has a non-trivial steady state.

The equation describes a population that grows at a rate that is proportional to its size. Specifically, the equation states that the population growth rate is equal to the product of a constant multiplier, a, and the size of the population, x. This means that when the population size increases, the rate of growth increases in proportion, causing the population to grow at a steady rate. the equation expresses a population growth rate that is proportional to the population size.

This means that when the population size is large enough, any further increases in the population size will be met with an equal increase in the population growth rate. This causes the population growth rate to remain constant, which is the definition of a non-trivial steady state

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