Solve the following rational expression. Once solved, plug your solution back into the original problem to verify that it is correct. 2/9 + 3/8 = 6/ x

Statistical power is a measure of the ability to reject the null hypothesis when it is false. It represents the probability of correctly identifying a true effect or relationship in a statistical hypothesis test.

A high statistical power indicates a greater likelihood of detecting a significant result if the null hypothesis is indeed incorrect. The power of a statistical test depends on several factors, including the sample size, the effect size (the magnitude of the true effect or difference), the chosen significance level (often denoted as α), and the variability or noise in the data. Increasing the sample size or effect size generally increases the statistical power, while a lower significance level or higher variability decreases it.

Power analysis is commonly used to determine an appropriate sample size for a study, ensuring that it is adequately powered to detect the desired effect. A higher power is desirable as it reduces the chances of a Type II error (failing to reject the null hypothesis when it is false) and increases the chances of correctly detecting real effects or relationships.

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The correct answers from the given lists are given as follows: Relation (a) a is (strictly) older than bA. irreflexiveB. asymmetricC. antisymmetricD. reflexiveE. transitive Relation (b) a and b have a common grandparentA.

irreflexiveB. antisymmetricC. symmetricD. reflexiveE. transitiveRelation (c) a has the same first name as bA. transitiveB. irreflexiveC. antisymmetricD. symmetricE. reflexiveRelation (d) a and b were born on the same dayA. transitiveB. reflexiveC. irreflexiveD. antisymmetricE. symmetric.

The given lists include different types of relations. Let's discuss the given relations one by one.(a) a is (strictly) older than b:This relation is irreflexive because a person can't be older than oneself. This relation is asymmetric because if a is older than b then it can't be possible that b is older than a.

This relation is antisymmetric because if a is older than b and b is older than a, then it means that a and b are the same person which is not possible. This relation is not reflexive because there is no one who is older than oneself. This relation is transitive because if a is older than b and b is older than c then a is also older than c.(b) a and b have a common grandparent:This relation is irreflexive because a person can't have a common grandparent with oneself. This relation is antisymmetric because if a has a common grandparent with b then it can't be possible that b has a common grandparent with a. This relation is symmetric because if a has a common grandparent with b then b also has a common grandparent with a. This relation is not reflexive because there is no one who has a common grandparent with oneself. This relation is transitive because if a has a common grandparent with b and b has a common grandparent with c then a also has a common grandparent with c.(c) a has the same first name as b:

This relation is transitive because if a has the same first name as b and b has the same first name as c then a has the same first name as c. This relation is irreflexive because a person can't have the same name as oneself. This relation is antisymmetric because if a has the same name as b then it can't be possible that b has the same name as a. This relation is symmetric because if a has the same name as b then b also has the same name as a. This relation is not reflexive because there is no one who has the same name as oneself.

(d) a and b were born on the same day: This relation is transitive because if a was born on the same day as b and b was born on the same day as c then a was born on the same day as c. This relation is reflexive because every person is born on the same day as oneself. This relation is irreflexive because no person is born on a different day than oneself. This relation is antisymmetric because if a was born on the same day as b then it can't be possible that b was born on the same day as a. This relation is symmetric because if a was born on the same day as b then b was also born on the same day as a.

The correct answers for each given relation are listed above.

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Answer:

5/18 is a rational number because a rational number is any integer,fraction terminating decimal,or repeating decimal.

5/18 is rational number.

The word "ratio" is where the word "rational" first appeared. Rational numbers are therefore closely tied to the idea of fractions, which stand for ratios. In other terms, a number is a rational number if it can be written as a fraction in which the numerator and denominator are both integers.

Any number of the form p/q, where p and q are integers and q is not equal to 0, is a rational number. The letter Q stands for the set of rational numbers. Look at the following illustration to see what a rational number looks like.

Given:

5/18

For rational we need to first divide the fraction and then check whether the fraction is a decimal or not.

Or if it is a decimal then it is terminating or non terminating

5/18 = 0.2777777777777778

Hence, it is terminating  because rational number is any integer, fraction terminating decimal or repeating decimal.

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Answer: x = 8.7

Step-by-step explanation:

You are given the reference angle: 60°, the hypotenuse and the leg of which to find.

X is opposite in reference to 60° and you are given the hypotenuse.

Sine works with the hypotenuse and the opposite: sin∅ = opp/hyp

sin(60°) = x/10

To figure out x, you must transpose, to make x the subject. X is being divided by 10, so to undo that you must multiply, and what you do to one side, you must do to the next to balance the equation.

10 x sin(60) = x/10 x 10

= X = sin(60) x 10

sin(60) = 0.866

X = 0.866 x 10

X = 8.66

You can round off to one decimal place or leave the answer as is.

X = 8.7 (1 d.p)

Answer:

\(-\frac{5}{3}\)

Step-by-step explanation:

Given expression:

                 (w)(3w + 5) = 0

  Expand the parentheses;

                   3w² + 5w  = 0

                    3w²  = -5w

Divide both sides by w;

                    3w  = - 5

                       w = \(-\frac{5}{3}\)

Answer:

Step-by-step explanation:

Its B

Answer:

b.

$109.58

Step-by-step explanation:

s is based on only nine independent pieces of information when 10 observations are taken randomly from a population to compute the estimate of σ.

When 10 observations are chosen randomly from a population to compute s, the estimate of σ, even though there are 10 observations, s is really based on only nine independent pieces of information.

This is because the sum of the deviations from the mean must equal zero (Σ(x - µ) = 0) in order to avoid double counting.

When a sample is taken from a population, the sum of the deviations from the sample mean is usually zero.

As a result, only n - 1 degrees of freedom are left for estimation, since the nth deviation can be obtained by subtracting the sum of the other n - 1 deviations from zero.

As a result, when estimating σ, one must subtract one from the sample size to obtain n - 1 degree of freedom. The estimate of the population standard deviation is given by the sample standard deviation, which is computed using n - 1 degrees of freedom (s = sqrt [Σ (Xi - Xbar)² / (n - 1)]).

Therefore, s is based on only nine independent pieces of information when 10 observations are taken randomly from a population to compute the estimate of σ.

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The local maximums of f(x,y) = sin(x)sin(y) occur at (nπ, mπ) and the local minimums occur at (nπ + π/2, mπ + π/2), where n and m are integers.

The given function f(x,y) = sin(x)sin(y) is a product of two periodic functions, each with a period of 2π. Hence, the function f(x,y) also has a periodicity of 2π in both x and y directions. To find the local maximums and minimums of the function, we need to look for points where the partial derivatives with respect to x and y are equal to zero.

Taking the partial derivative of f(x,y) with respect to x, we get cos(x)sin(y), which is equal to zero at points (nπ, mπ), where n and m are integers. Similarly, taking the partial derivative of f(x,y) with respect to y, we get cos(y)sin(x), which is also equal to zero at points (nπ, mπ). Therefore, the local maximums of f(x,y) occur at these points.

On the other hand, taking the partial derivative of f(x,y) with respect to x, we get cos(x)sin(y), which is equal to π/2 at points (nπ + π/2, mπ), where n and m are integers. Similarly, taking the partial derivative of f(x,y) with respect to y, we get cos(y)sin(x), which is equal to π/2 at points (nπ, mπ + π/2). Therefore, the local minimums of f(x,y) occur at these points.

In summary, the local maximums of f(x,y) = sin(x)sin(y) occur at (nπ, mπ) and the local minimums occur at (nπ + π/2, mπ + π/2), where n and m are integers.

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Answer:

see below

Step-by-step explanation:

1 B    Answer :

\(7\times7\times7\times7\times7/7\times7\times7\times7=7\)    or    \(7^{2+3}/7^{4} =7^{5-4} =7^{1} =7\)

2 B    Answer :

\(k^{4\times2} \times k^{5} =k^{8+5} =k^{13}\)

3B    Answer :

\(5a-15-a/1=5a-a-15=4a-15\)

Hope that help

Let X be the height of women in college. We are told that this variable is distributed as a normal distribution with mean 65 and a standard deviation of 2.5. To solve this problem, we will use a standard normal distribution table. So, the first step is to transform X to a variable Z where Z is a standar normal distribution. We do this by subtracting the mean and dividing by the standard deviation.

Recall that the problem is asking the following probability P(61<=X <= 68).

So, now, lets subtract 65 to the inequality, we get

P(-4<=X-65<=3). Now, we divide everything by the standard deviation, so we get

Now, call Z = (X-65)/2.5. With this transformation Z is distributed now with a standard normal distribution. So the question to answer is

P(-1.6<=Z<=1.2)

This translates to calculating the area under the curve as follows

We can picture two areas

So the area we want to calculate is the sames as the red area minus the blue area. Then, we have the following

Using a standard deviation table, we have that P(Z<=1.2) = 0.8849 and P(Z<=-1.6) = 0.1446

Then

which means that 74.03% of women in college have a height between 61 and 68 inches

Answer:

10.8

Step-by-step explanation:

30% of 36

= 30/100 * 36

= 3/10 * 36

= 108/10

= 54/5

= 10.8

Hope this helps and feel free to mark this as brainliest :)

Answer:

  24 min

Step-by-step explanation:

Time is proportional to distance at constant speed, so it will take 18/45 = 2/5 of an hour. That's 2/5 of 60 minutes, or 24 minutes.

__

The time required is ...

  time = distance / speed

  time = (18 mi)/((45 mi)/(60 min)) = (18×60/45) min =  24 min

It would take 24 minutes.

Slope intercept form is y=mx+b. So let's use the given equation and turn it into this form.

\(3x-5y=-30\)

Move the -3x to the right side

\(-5y=-3x-30\)

Divide both sides by -5

\(y=\dfrac{3}{5}x+6\)

This should be your answer, let me know if you need any clarifications, thanks!

Step-by-step explanation:

5= 0.3 x

=> both sides times 10

50 = 3x

x = 50/3

x = 16.67 (C)

Answer:

C

Step-by-step explanation:

5÷ 0.3= 16.666 ⇒ 16.67

Answer: 26-5

Step-by-step explanation:

literally you take 5 aways from 26

The calculated vertex of the graph represented in the figure is (-3, -3)

Given that we have the graph

The curve on the graph is a quadratic function

As a general rule, the vertex of a graph is the minimum or the maximum point on a graph

From the graph, we have the minimum point to be

Minimum = (-3, -3)

This means that

Vertex = (-3, -3)

Hence, the vertex is (-3, -3)

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Answer:

3 dollars 6 cents or 3.6

Step-by-step explanation:

you need to divide the 30 percent by the twelve dollars to get your answer

Answer:

The angles opposite each other when two lines cross. In the figure, the 1 and 3 are vertically opposite angles and they are always equals. Same goes for angles 2 and 4. The angles in matching corners when two lines are crossed by another line, called the transversal.

Step-by-step explanation:

1. Complementary Angles

Definition

Complementary angles are two positive angles whose sum is 90 degrees.

Examples

For example, complementary angles can be adjacent, as seen in with ∠ABD and ∠CBD in the image below. Or they can be two acute angles, like ∠MNP and ∠EFG, whose sum is equal to 90 degrees. Both of these graphics represent pairs of complementary angles.

complementary angles example

Complementary Angles Example

2. Supplementary Angles

Definition

Supplementary angles are two positive angles whose sum is 180 degrees.

Examples

For example, supplementary angles may be adjacent, as seen in with ∠ABD and ∠CBD in the image below. Or they can be two angles, like ∠MNP and ∠KLR, whose sum is equal to 180 degrees. Both of these graphics represent pairs of supplementary angles.

supplementary angles example

Supplementary Angles Example

What is important to note is that both complementary and supplementary angles don’t always have to be adjacent angles.

3. Adjacent Angles

Definition

Adjacent angles are two angles in a plane that have a common vertex and a common side but no common interior points.

Examples

Angles 1 and 2 are adjacent angles because they share a common side.

adjacent angles examples

Adjacent Angles Examples

And as Math is Fun so nicely points out, a straightforward way to remember Complementary and Supplementary measures is to think:

C is for Corner of a Right Angle (90 degrees)

S is for Straight Angle (180 degrees)

Now it’s time to talk about my two favorite angle-pair relationships: Linear Pair and Vertical Angles.

4. Linear Pair

Definition

A linear pair is precisely what its name indicates. It is a pair of angles sitting on a line! In fact, a linear pair forms supplementary angles.

Why?

Because, we know that the measure of a straight angle is 180 degrees, so a linear pair of angles must also add up to 180 degrees.

Examples

∠ABD and ∠CBD form a linear pair and are also supplementary angles, where ∠1 + ∠2 = 180 degrees.

linear pair example

Linear Pair Example

5. Vertical Angles

Definition

Vertical angles are two nonadjacent angles formed by two intersecting lines or opposite rays.

Huh?

Think of the letter X. These two intersecting lines form two sets of vertical angles (opposite angles). And more importantly, these vertical angles are congruent.

Examples

In the accompanying graphic, we see two intersecting lines, where ∠1 and ∠3 are vertical angles and are congruent. And ∠2 and ∠4 are vertical angles and are also congruent.

vertical angles examples

Vertical Angles Examples

Together we are going to use our knowledge of Angle Addition, Adjacent Angles, Complementary and Supplementary Angles, as well as Linear Pair and Vertical Angles to find the values of unknown measures.

Angle Relationships – Lesson & Examples (Video)

32 min

Introduction to Angle Pair Relationships

00:00:15 – Overview of Complementary, Supplementary, Adjacent, and Vertical Angles and Linear Pair

Exclusive Content for Member’s Only

00:06:29 – Use the diagram to solve for the unknown angle measures (Examples #1-8)

00:19:05 – Find the measure of each variable involving Linear Pair and Vertical Angles (Examples #9-12)

Practice Problems with Step-by-Step Solutions

Chapter Tests with Video Solutions

The required relationship between the angles 1, 2, and 3 is ∠1 +∠2 = ∠3.

Given that,
To determine the relationship between angles 1, 2, and 3.

The triangle is a geometric shape that includes 3 sides and the sum of the interior angle should not be greater than 180°

Here,
Angles 1 and 2 are remote interior angles while angle 3 is a remote exterior angle. So there is a property of a triangle in that the sum of the remote interior angles is equal to the remote exterior angle.
∠1 +∠2 = ∠3.

Thus, the required relationship between the angles 1, 2, and 3 is ∠1 +∠2 = ∠3.

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Answer:

Each person is gonna drink 12 ounces

Step-by-step explanation:

84 divided by 7 is 12

As it is 7 people sharing one drink that is 84 ounces I divided since they would be sharing equally and as it was the right thing to do.

Not a teacher

Answer:

c/sin(60°) = 14/sin(25°)

c = 14sin(60°)/sin(25°) = 28.7

Answer:

can u type it so i can answer, i cant see it

Step-by-step explanation:

Answer:

Step-by-step explanation:

Remove the brackets. Watch out for that minus sign. It affects all three terms in the right bracket.

(-3f - 4g + 9) - (2 - 6f + 5g)

-3f - 4g + 9 - 2 + 6f - 5g

+3f - 9g + 7 is your answer.

Answer:

3f−9g+7

Step-by-step explanation:

(−3f−4g+9)−(2−6f+5g)

To find the opposite of 2−6f+5g, find the opposite of each term.

−3f−4g+9−2−(−6f)−5g

The opposite of −6f is 6f.

−3f−4g+9−2+6f−5g

Subtract 2 from 9 to get 7.

−3f−4g+7+6f−5g

Combine −3f and 6f to get 3f.

3f−4g+7−5g

Combine −4g and −5g to get −9g.

3f−9g+7

Answer:

-123.76

Step-by-step explanation:

You just multiply -22.1 by -5.6 and you get -123.76.

The differences disappear on later tests due to the improved mathematics education and curriculum in the United States.

The initial lag in performance of U.S. middle school students compared to their Japanese counterparts in international algebra tests can be attributed to various factors, including differences in teaching methods, curriculum, and cultural emphasis on mathematics. However, over time, the differences tend to disappear as U.S. students progress through their education and benefit from improved mathematics education and curriculum.

In recent years, the United States has made efforts to enhance its mathematics education system, implementing reforms and adopting new teaching strategies to improve student outcomes. These changes aim to provide students with a deeper understanding of mathematical concepts and problem-solving skills. As a result, U.S. students have shown improvements in their performance on later tests, narrowing the gap with their Japanese peers.

While U.S. middle school students may initially lag behind their Japanese counterparts in international algebra tests, the differences tend to disappear on later tests due to the ongoing efforts to enhance mathematics education in the United States. Continuous improvements in curriculum, teaching methods, and student support contribute to closing the gap and ensuring that U.S. students can compete globally in mathematics proficiency.

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Based on the given information, it is not possible to determine the p-value, decision to reject (rh0) or failure to reject (frh0) without additional data or context.

To assess whether the relaxation exercise slowed brain waves, a statistical analysis should be conducted on a sample from the population.

The analysis would involve measuring brain waves before and after the exercise and comparing the results using appropriate statistical tests such as a t-test or ANOVA. The p-value would indicate the probability of observing the data if there was no effect, and the decision to reject or fail to reject the null hypothesis would depend on the predetermined significance level.

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Answer:

259.5

Step-by-step explanation:

8.1*12=97.2
Area of trapiezium = 1/2(b+a)h
(2.8+8.1)=10.9
10.9*3/2=16.35
16.35*2=32.7
2.8*12=33.6
33.6+32.7+97.2=163.5
4*12*2=96
163.5+96=259.5