solve each of the following equations:
\( \frac{4 }{9} - \frac{x {}^{2} }{25} = 0\)
​

The area bound by the lines and the curves is 0.29 square units.

To find the area bound by the lines x = -4 and x = 5 and the curves y = √(x + 4) and y = cos(πx/2 - 2), we need to calculate the definite integral of the curves within the given interval and then find the difference between the two areas.

Let's start by finding the points of intersection between the curves:

√(x + 4) = cos(πx/2 - 2)

To solve this equation, we can square both sides and simplify:

x + 4 = cos²(πx/2 - 2)

x + 4 = (1/2)(1 + cos(2πx - 4π))

2(x + 4) = 1 + cos(2πx - 4π)

2x + 8 = 1 + cos(2πx)cos(4π) + sin(2πx)sin(4π)

2x + 8 = 1 + cos(2πx)

Now, we have a transcendental equation. We can solve it graphically or using numerical methods. The solutions are approximately x = -2.35 and x = 4.68.

Now, we can calculate the area under the curve y = √(x + 4) from x = -4 to x = -2.35 and the area under the curve y = cos(πx/2 - 2) from x = -2.35 to x = 4.68.

First, let's calculate the area under y = √(x + 4):

A₁ = ∫[x=-4 to -2.35] √(x + 4) dx

To find the antiderivative of √(x + 4), we can use the power rule of integration:

∫ √(x + 4) dx = (2/3)(x + 4)^(3/2)

Now, let's calculate the definite integral:

A₁ = [(2/3)(x + 4)^(3/2)] [from x = -4 to x = -2.35]

≈ 2.13

Next, let's calculate the area under y = cos(πx/2 - 2):

A₂ = ∫[x=-2.35 to 4.68] cos(πx/2 - 2) dx

To find the antiderivative of cos(πx/2 - 2), we can use the integral of cosine function formula:

∫ cos(ax + b) dx = (1/a)sin(ax + b)

Using this formula, the antiderivative is:

∫ cos(πx/2 - 2) dx = (2/π)sin(πx/2 - 2)

Now, let's calculate the definite integral:

A₂ = [(2/π)sin(πx/2 - 2)] [from x = -2.35 to x = 4.68]

≈ 1.84

Finally, we can find the area bound by the curves:

Area = |A₂ - A₁| = |1.84 - 2.13| = 0.29

Therefore, the area bound by the lines x = -4 and x = 5 and the curves y = √(x + 4) and y = cos(πx/2 - 2) is approximately 0.29 square units.

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Answer:

14+14 + 4pi= 28 + 4pi

\(\pi\)

The series to 10 term is

1 + 2 + 4 + 8 + 16 + 32 + 64 + 128 + 256 + 512

An equation that represents a sequence based on a rule is called a recurrence relation.

Finding the following term, which is dependent upon the prior phrase, is made easier (previous term). We can readily predict the following term in a series if we know the preceding term.

The term is predicted by multiplying the preceding term by 2

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The probability that an unprepared student, who can eliminate one possible answer on the first four multiple-choice questions and guess on all six questions, will answer at least four questions correctly on the test.

There are a total of 5 possible answers per question, so the probability of guessing the correct answer for any given question is 1/5. After eliminating one possible answer on the first four questions, the student has a 1/4 chance of guessing the correct answer for each of those questions.

For the remaining two questions, the student has a 1/5 chance of guessing the correct answer for each question. To calculate the probability of the student answering at least four questions correctly, we need to consider all possible outcomes where the student guesses at random.

There are 5^6 total possible outcomes, since there are 5 possible answers for each of the 6 questions. The number of ways the student can answer at least 4 questions correctly can be found by considering the possible combinations of questions that the student answers correctly.

There are 6 possible combinations of 4 questions that the student can answer correctly, and there are 15 possible combinations of 5 questions that the student can answer correctly.

There is only 1 possible combination where the student answers all 6 questions correctly. Therefore, the probability of the student answering at least 4 questions correctly is:

[(6 choose 4)(1/4)^4(3/4)^2] + [(15 choose 5)(1/4)^5(3/4)^1] + (1/5)^2 = 0.0194

So the probability that the student will answer at least four questions correctly is approximately 0.0194, or 97/500, when expressed as a fraction.

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Answer: B jus times two 8s

Answer:

C

Step-by-step explanation:

Because 24 divided by 3 = 8 and 3/8 has a denominator of 8 and you divide it by 3

could i have branliest and a heart please

Have a good day :)

Answer:

143.2

Step-by-step explanation:

just add them together then divided by 10

The probability of rolling a 4 on the first toss of a standard six-sided die and a 6 on the second toss is 1/36 or approximately 0.0278.

Each toss of a standard six-sided die is an independent event with six possible outcomes (numbers 1 to 6). To find the probability of rolling a 4 on the first toss and a 6 on the second toss, we need to consider the probabilities of each event separately and then multiply them together.

The probability of rolling a 4 on the first toss is 1/6 since there is one favorable outcome (rolling a 4) out of six possible outcomes. Similarly, the probability of rolling a 6 on the second toss is also 1/6.

To find the probability of both events occurring, we multiply the individual probabilities together: (1/6) * (1/6) = 1/36.

Therefore, the probability of rolling a 4 on the first toss of a standard six-sided die and a 6 on the second toss is 1/36 or approximately 0.0278.

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Answer:

H²=h²+b²

H²=9²+3²

H²=81+9

H²=90

H=

\( \sqrt{90} \)

Answer:

7/15

Step-by-step explanation:

Fraction of the songs being country / rock songs: 1/6 + 3/10 = 7/15

Answer: cell respiration = carbon taken in as glucose and CO2 out. The CO2 expelled is taken up by plants and used to make more glucose.

Step-by-step explanation:

As per Mental hypothesis, the statistical inference procedures that we should use Chi-square test for goodness of fit.

Hypothesis

In probability, an idea or explanation that you then test through study and experimentation is known as hypothesis.

Given,

Here we have given that, an experiment involving peas results in 580 offspring, 152 of which peas have yellow pods. Mendel claimed that the proportion of peas with yellow pods should be 25%. we want to know if these data are consistent with Mendel's hypothesis.

And we need to find in which statistical inference procedures should we use.

According to the definition of Chi-square test for goodness of fit, the claim is that the proportion of peas with yellow pods should be 25%. And then here the researcher wants to check that the experimental and observed counts of yellow offspring peas shows significant difference or not.

So, the statistical procedure used to study this case is Chi-square test for goodness of fit . Hence, option (1) is correct.

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The researcher is assessing item equivalence, If a study is in parallel forms of the measurement instrument to the same person. The correct option is C).

When a study introduces parallel forms, the researcher is assessing item equivalence. Item equivalence refers to the extent to which the different forms of the measurement instrument produce similar results for the same individual.

This assessment is crucial in research because it allows researchers to evaluate the consistency and reliability of the measurement instrument across different versions. By administering parallel forms to the same person, any differences in responses can be attributed to individual factors rather than variations in the instrument.

This helps ensure that the instrument is measuring the intended construct consistently and accurately. The correct option is C).

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Based on the Same-Side Interior Angles Theorem, the measure of angle 6 is: 115.24°.

The Same-Side Interior Angles Theorem states that when two parallel lines are intersected by a transversal, the same-side interior angles (angles on the same side of the transversal and between the parallel lines) are supplementary, meaning that their sum is equal to 180 degrees.

Thus, based on the image given, it means angles 4 and 6 will have a sum of 180 degrees based on the Same-Side Interior Angles Theorem. Therefore:

m<6 = 180 - m<4

m<6 = 180 - 64.76

m<6 = 115.24°

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Answer:

5.8

Step-by-step explanation:

Answer:

\(75.52^\circ\)

Step-by-step explanation:

Given that:

The length of the ladder = 30 ft

Distance between bottom of ladder and wall = \(\frac{1}{4}^{th}\) of its length

To find:

Angle made between the ladder and ground = ?

Solution:

This situation can be compared with a right angled \(\triangle ABC\) as shown in the attached image in the answer area.

Side AC being the hypotenuse has the ladder along it.

AB is the wall.

BC is the distance between the wall and foot of ladder.

Formula for cosine trigonometric ratio:

\(cos\theta = \dfrac{Base}{Hypotenuse}\)

In \(\triangle ABC\):

\(cosC=\dfrac{BC}{AC}\)

Putting the values:

\(BC=\dfrac{AC}{4}\)

\(cosC=\dfrac{\frac{AC}4}{AC}\\\Rightarrow cos C = \dfrac{1}{4}\\\Rightarrow \angle C = cos^{-1}(0.25)\\\Rightarrow \angle C =\bold{75.52^\circ}\)

Answer:

Step-by-step explanation:

Changes made to your input should not affect the solution:

(1): "^-6" was replaced by "^(-6)".

Equation at the end of step

1

:

  34

 {——}2

  1

STEP

2

:

           34

Simplify   ——

           1

Equation at the end of step

2

:

 ((3-6) • x) • (34^2)

Equation at the end of step

3

:

 ((3)(-6) • x) • 38

Dividing exponents:

4.1    38   divided by   36   = 3(8 - 6) = 32

Final result :

 9x

The simplification of the given expression gives the value 9.

Simplification is defined as a process in mathematics to operate and interpret an expression to make the expression simpler.

This can be done using various results or the basic operations of numbers.

Given expression is 3⁻⁶ × (3⁴ / 3⁰)².

We have to use product rule and quotient rule of exponents to simplify this.

We know that,

xᵃ × xᵇ = xᵃ⁺ᵇ

xᵃ / xᵇ = xᵃ⁻ᵇ

Also, (xᵃ)ᵇ = xᵃᵇ

3⁴ / 3⁰ = 3⁴⁻⁰ = 3⁴

Substituting,

3⁻⁶ × (3⁴ / 3⁰)² = 3⁻⁶ × (3⁴)²

                       = 3⁻⁶ × 3⁸

                       = 3⁻⁶⁺⁸

                       = 3²

                       = 9

Hence the simplified form of the given expression is 9.

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Answer:

y = 2/3 x - 7

Step-by-step explanation:

y = mx + b

y = 2/3 x + b

-1 = 2/3 × 9 + b

-1 = 6 + b

b = -7

y = 2/3 x - 7

Answer:

y = 2x-17

Step-by-step explanation:

We have a point and a slope, we can write the equation in point slope form and then convert to slope intercept form

y-y1 = m(x-x1) where m is the slope and (x1,y1) is the point

y-1 = 2(x-9)

Distribute

y-1=2x-18

Add 1 to each side

y-1+1 = 2x-18+1

y = 2x-17

This is slope intercept form

Step-by-step explanation:

The height of the Seattle Space Needle is approximately 604 feet.

Let's say h is the height of the Seattle Space Needle. According to the problem, 1450 feet is 240 percent of h, or 2.4h in decimal form, which we can write as:2.4h = 1450Next, we'll divide each side of the equation by 2.4 to isolate h:h = 1450 ÷ 2.4This results in h ≈ 604.17 feet. Because we need to round our answer to the nearest foot, we can say that the height of the Seattle Space Needle is approximately 604 feet.

To find the height of the Seattle Space Needle, we can set up an equation using the given information. If h represents the height of the Seattle Space Needle, then 1450 feet is 240% of h, or 2.4h. Using algebra, we can solve for h by dividing both sides of the equation by 2.4 to isolate h. The resulting equation is h = 1450 ÷ 2.4. Simplifying this expression gives us h ≈ 604.17 feet. Since we need to round our answer to the nearest foot, we can say that the height of the Seattle Space Needle is approximately 604 feet.

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Answer:

3

Step-by-step explanation:

There are always three acute angles in an acute triangle. The definition of an acute triangle is that it is a triangle in which all angles are less than 90 degrees.

Hopefully this helps :)

Answer:

4/10

Step-by-step explanation:

in multiple choice questions sometimes its good to use real numbers

im using 100 miles

of the distance from school

terry ran 1/10 so

1/10 of 100 is 10

walked 3/10 more

more means add

3/10 of 100 is +30

skipped 2/10 more

2/10 of 100 is +20

add all of them up

10+30+20= 60

"still have to go" means subtract from the original amount

100-60=40

40 out 100 is

4/10

Answer:

$10

Explanation:

If you only have to pay $5 of the $15 you gave him, he has to pay you 15-5 or $10 back.

Out of the 16 million office workers surveyed, approximately 3.52 million would like more storage space.

The given study states that 22% of office workers would like more storage space. To find the number of office workers who desire additional storage, we need to calculate 22% of the total number of office workers.

To determine the number of office workers who want more storage space, we multiply the percentage (22%) by the total number of office workers (16 million):

22% × 16 million = 0.22 × 16,000,000 = 3,520,000.

Hence, based on the study, approximately 3.52 million office workers out of the 16 million surveyed would like more storage space. This indicates a significant proportion of the office workforce expressing the need for additional storage in their work environment. Understanding such preferences can help employers and office designers address the demand for improved storage solutions and create more efficient and organized workspaces to enhance productivity and employee satisfaction.

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Research has shown that competent communicators achieve effectiveness by adjusting their behaviors to the person and situation (option e).

Effective communication involves being adaptable and responsive to the specific context, individual preferences, and the needs of the situation.

Competent communicators recognize that different people have different communication styles, preferences, and expectations. They understand the importance of tailoring their communication approach to effectively connect and engage with others.

This may involve using appropriate language, tone, non-verbal cues, and listening actively to understand the needs and perspectives of others.

By adapting their behaviors, competent communicators can build rapport, foster understanding, and promote effective communication exchanges. They are mindful of the social and cultural dynamics at play, and they strive to communicate in a way that is respectful, inclusive, and conducive to achieving mutual goals.

In summary, competent communicators understand that effective communication is not a one-size-fits-all approach. They adjust their behaviors to the person and situation, demonstrating flexibility and adaptability in order to enhance communication effectiveness.

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Competent communicators achieve effectiveness mostly by adjusting their behaviors to suit the person they are communicating with and the situation they find themselves in. While other factors, like having a broad vocabulary or giving feedback, play a part in effective communication, the former is considered the most crucial.

Research suggests that competent communicators achieve effectiveness mostly through adjusting their behaviors depending on the person they are communicating with and the situation they are in. This is option e. of your question. Communicating effectively involves behaviors like active listening, understanding the other person's point of view, being able to express thoughts and ideas clearly, and being polite and respectful. While a broad vocabulary (option b.) can be useful, it is not as crucial as adapting your behavior to fit the situation. Moreover, giving feedback (option d.) is a part of effective communication but not the sole defining factor. Apologizing when offending others (option c.) is also important but it doesn't necessarily make one a competent communicator. Using the same type of behavior in various situations (option a.) might not always work, as different situations and individuals require different communication styles.

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Check the picture below.

let's make α = 27°50' and β = 20°10'.

\(\begin{array}{rllll} tan(\alpha)=\cfrac{h}{x}\implies xtan(\alpha)=h \\\\\\ tan(\beta)=\cfrac{h}{x+126}\implies (x+126)tan(\beta)=h \end{array}\)

since h = h, we can simply

\(xtan(\alpha)=(x+126)tan(\beta)\implies xtan(\alpha)=xtan(\beta)+126tan(\beta) \\\\\\ xtan(\alpha)-xtan(\beta)=126tan(\beta)\implies x[tan(\alpha)-tan(\beta)]=126tan(\beta) \\\\\\ x=\cfrac{126tan(\beta)}{tan(\alpha)-tan(\beta)} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{since we know that}}{xtan(\alpha)=h}\implies \cfrac{126tan(\beta)}{tan(\alpha)-tan(\beta)}tan(\alpha)=h \implies \cfrac{126tan(\beta)tan(\alpha)}{tan(\alpha)-tan(\beta)}=h\)

now, if we do the degrees and minutes conversion to just degrees for the sake of sticking it in the calculator, mind you make sure your calculator is in Degree mode, for 27°50' we get about 27.83° and for 20°10' we get 20.16°

\(\cfrac{126tan(\beta)tan(\alpha)}{tan(\alpha)-tan(\beta)}=h\implies \cfrac{24.4329}{0.1607}\approx h\implies 152.03\approx h\)

Answer:

18

Step-by-step explanation:

9 + 18 = 27

9 x 2 = 18

The first step performed by Daniela was that she subtracted 1 / 2 x from both sides of the equation.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

In other words, equations are mathematical statements containing two algebraic expressions on both sides of an 'equal to (=)' sign.

Therefore, Daniela is trying to solve an equation for x.

1/2 x + 3 = 7/2 x + 5

The variable of the equation is x. The variable of an equation is a number represented with letters.

Hence, the first step performed by Daniela is as follows:

Subtract 1 / 2 x from both sides of the equation

1/2 x + 3 = 7/2 x + 5

1/2 x - 1 / 2 x + 3 = 7/2 x - 1 / 2 x + 5

3 =  7/2 x - 1 / 2 x + 5

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