i need help on this question

Answer:

what this basicaly means is that we have to multiply 3 by every thing inside the parethese

3*2x=6x

3*1=3

6x+3

Hope This Helps!!!

Answer:

6x + 3

Step-by-step explanation:

Like regular distributive property, a(bx+c), we will multiply them together. Using the previous example, we know that it will turn into abx + ac. Now, lets substitute a to 3, b to 2, c to 1. Now, we can get 6x +1. I really like brainliest.

Answer:

\(t_{1} = 0.422\pi \pm \pi\cdot i\), \(\forall \,i \in \mathbb{N}_{O}\)

\(t_{2} = 1.422\pi \pm \pi\cdot i\), \(\forall \,i \in \mathbb{N}_{O}\)

Step-by-step explanation:

In the case of parametric equations, the slope of the curve is equal to:

\(\frac{dy}{dx} = \frac{\frac{dy}{dt} }{\frac{dx}{dt} }\)

Where \(\frac{dx}{dt}\) and \(\frac{dy}{dt}\) are the first derivatives of \(x\) and \(y\) regarding \(t\). Let be \(x(t) =2\cdot \cos t\) and \(y(t) = 8\cdot \sin t\), their first derivatives are found:

\(\frac{dx}{dt} = -2\cdot \sin t\) and \(\frac{dy}{dt} = 8\cdot \cos t\)

Thus, equation for the slope is:

\(\frac{dy}{dx} = -\frac{8\cdot \cos t}{2\cdot \sin t}\)

\(\frac{dy}{dx} = -\frac{4}{\tan t}\)

If \(\frac{dy}{dx} = -1\), then:

\(-1 = -\frac{4}{\tan t}\)

\(\tan t = 4\)

Tangent is positive at 1st quadrant and is a function with a periodicity of \(\pi\), the set of solutions are:

\(t_{1} = 0.422\pi \pm \pi\cdot i\), \(\forall \,i \in \mathbb{N}_{O}\)

\(t_{2} = 1.422\pi \pm \pi\cdot i\), \(\forall \,i \in \mathbb{N}_{O}\)

Answer:

5 x - 4

Step-by-step explanation:

Since g(f(x))=x g ( f ( x ) ) = x , f−1(x)=x5+45 f - 1 ( x ) = x 5 + 4 5 is the inverse of f(x)=5x−4 f ( x ) = 5 x - 4 .

Answer:

the correct answer is 290 / 605

The equation for the graph above is y = 5sin(2x/3).

In Mathematics and Geometry, a sine wave is sometimes referred to as a sinusoidal wave, or sinusoid and it can be defined as a fundamental waveform that is typically used for the representation of periodic oscillations, in which the amplitude of displacement at each interval is directly proportional to the sine of the displacement's phase angle.

Mathematically, a sine wave can be represented or modelled by this mathematical equation:

y = asin(bx)

Where:

Based on the graph of this sine wave, we have:

Amplitude, a = 5.

Periodicity, b = 2π/period = 2π/(3π) = 2/3

Therefore, the required sine wave function is given by;

y = asin(bx)

y = 5sin(2x/3)

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Answer:

1/2

Step-by-step explanation:

Slope formula:

\( \boxed{ \purple{ \sf \: m = \frac{ y_{2} - y_{1}}{x_{2} -x_{1} } }}\)

P.S. Slope is denoted by letter m

We have;

\( \red \implies \green{ \tt \: m = \frac{2 - ( - 4)}{5 - 2} }\)

\( \red \implies \green{ \tt \: m = \frac{ \cancel6}{ \cancel3} }\)

\( \red \implies \green{ \tt \: m = \frac{ 2}{ 1} = 2} \)

Answer:

Below

Step-by-step explanation:

If d is a positive number then the greatest common factor is 108d.

To get it isolate d and d^2 from the numbers.

108 divides 216. (216 = 2×108)

Then the greatest common factor of 216 and 108 is 108.

For d^2 and d we will follow the same strategy

d divides d^2 (d^2 = d*d)

Then the greatest common factor of them is d.

So the greatest common factor will be 108d if and only if d is positive. If not then 108 is the answer

Answer:

\(\boxed{108d}\)

Step-by-step explanation:

Part 1: Find GCF of variables

The equation gives d ² and d as variables. The GCF rules for variables are:

The GCF for the variables is d.

Part 2: Find GCF of bases (Method #1)

The equation gives 108 and 216 as coefficients. To check for a GCF, use prime factorization trees to find common factors in between the values.

Key: If a number is in bold, it is marked this way because it cannot be divided further AND is a prime number!

Prime Factorization of 108

108 ⇒ 54 & 2

54 ⇒ 27 & 2

27 ⇒ 9 & 3

9 ⇒ 3 & 3

Therefore, the prime factorization of 108 is 2 * 2 * 3 * 3 * 3, or simplified as 2² * 3³.

Prime Factorization of 216

216 ⇒ 108 & 2

108 ⇒ 54 & 2

54 ⇒ 27 & 2

27 ⇒ 9 & 3

9 ⇒ 3 & 3

Therefore, the prime factorization of 216 is 2 * 2 * 2 * 3 * 3 * 3, or simplified as 2³ * 3³.

After completing the prime factorization trees, check for the common factors in between the two values.

The prime factorization of 216 is 2³ * 3³ and the prime factorization of 108 is 2² * 3³.  Follow the same rules for GCFs of variables listed above and declare that the common factor is the factor of 108.

Therefore, the greatest common factor (combining both the coefficient and the variable) is \(\boxed{108d}\).

Part 3: Find GCF of bases (Method #2)

This is the quicker method of the two. Simply divide the two coefficients and see if the result is 2. If so, the lesser number is immediately the coefficient.

\(\frac{216}{108}=2\)

Therefore, the coefficient of the GCF will be 108.

Then, follow the process described for variables to determine that the GCF of the variables is d.

Therefore, the GCF is \(\boxed{108d}\).

Answer:

32,000

Step-by-step explanation:

10% of 320,000 is 32,000

Answer:

growth rate: 4

y-value: 19

equation: y=4x+19

Step-by-step explanation:

Growth Rate:
The growth rate of a linear function is constant. This means that the function will increase or decrease by the same amount for every unit increase in x.
This can be found by dividing the change in y-values by the change in x-values.

For the question:
The change in y-values is 11-7=4,

and the change in x-values is +1.

Therefore, the growth rate is 4.

\(\hrulefill\)

Initial Value: The initial value of a linear function is the value of the function when x is 0.

In this case, the initial value is 19.

This can be found by looking at the y-value of the point where x is 0.

In this case, the y-value is 19.

\(\hrulefill\)Equation: The equation of a linear function is y = mx + b, where m is the slope and b is the y-intercept.

Using the table you provided, we can find the slope by using two points on the line.

Let’s use (-3, 7) and (1, 23).

The slope is (y2-y1)/(x2-x1)=(23-7)(1-(-3)=16/4=4

Now,

Taking 1 point (-3,7) and slope 4.

we can find the equation by using formula:

y-y1=m(x-x1)

y-7=4(x+3)

y=4x+12+7

y=4x+19

Therefore, the equation of the given table is y=4x+19\(\hrulefill\)

Answer:

Growth rate:  4

Initial value:  19

Equation:  y = 4x + 19

Step-by-step explanation:

The slope of a linear function represents its growth rate.

Therefore, the growth rate of a linear function can be found using the slope formula.

Substitute two (x, y) points from the table into the slope formula, and solve for m.  Substituting points (0, 19) and (1, 23):

\(\textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{23-19}{1-0}=\dfrac{4}{1}=4\)

Therefore, the growth rate of the linear function is 4.

The initial value of a linear function refers to the y-intercept, which is the value of the y when x = 0.

From inspection of the given table, y = 19 when x = 0.

Therefore, the initial value of the linear function is 19.

To write a linear equation given the growth rate (slope) and initial value (y-intercept), we can use the slope-intercept formula, which is y = mx + b. The slope is represented by the variable m, and the y-intercept is represented by the variable b.

As the growth rate of the given linear function is 4, and the initial value is 19, substitute m = 4 and b = 19 into the slope-intercept formula to create the equation of the linear function represented by the given table:

\(\boxed{y=4x+19}\)

Plants A and B will have the same height on day 8.

A topic which requires a given statement to be expressed mathematically so as to determine the value of the required unknown is termed word problem.

In the given question, we have;

for plant A,

1 + 0.5n = m  ..................... 1

for plant B,

3 + 0.25n = m  ...................... 2

where n represents the number of days for the plant to grow.

So that equating the two, we have;

1 + 0.5n = 3 + 0.25n

0.25n = 2

n = 2/ 0.25

   = 8

Thus the number of days that both plants will have equal height is 8 days.

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The Probability that a randomly selected senior is both in the band and on the honor roll is 8/25.

To find the probability that a randomly selected senior is both in the band and on the honor roll, we need to divide the number of seniors who are in both categories by the total number of seniors.

Given:

Total number of seniors = 200

Number of seniors in the band = 32

Number of seniors in the band or on the honor roll = 64

Let's calculate the probability using these values:

Probability = Number of seniors in both categories / Total number of seniors

Probability = 64 / 200

To simplify this fraction, we can divide both the numerator and denominator by their greatest common divisor, which is 8:

Probability = (64 ÷ 8) / (200 ÷ 8)

Probability = 8 / 25

Therefore, the probability that a randomly selected senior is both in the band and on the honor roll is 8/25.

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Based on the given responses, the student who factored 20x^6 = (2x)(10x^5) correctly is Andrei. Therefore, the correct answer is (Choice A) Andrei.

Among the given responses, the student who factored 20x^6 = 20, x to the power of 6 correctly is Andrei. Andrei's factorization is (2x)(10x^5), which correctly represents the original term 20x^6. Therefore, the correct answer is (Choice A) Andrei.

Amit's factorization is (4x^3)(5x^3), which is incorrect because it breaks down the term into two factors with the same exponent, while the original term has an exponent of 6.

Andrew's factorization is (20x^2)(x^3), which is also incorrect as it does not accurately represent the original term 20x^6.

Hence, the only student who correctly factored 20x^6 = 20, x to the power of 6 is Andrei.

The right answer is A. Andrei who factored 20x^6 = (2x)(10x^5) correctly.

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Answer:

x=1 and y=-5

Step-by-step explanation:

i think that is right

-2

Step-by-step explanation:

12x＝x+26

-13x＝26

x＝-2

3.- If two parallel lines are cut by a transversal, alternate interior angles are congruent. Therefore:

4.-Angle-Angle Postulate states that two triangles are similar if they have two congruent angles.

Answer:

C. 101 3/4; $1017.50

Step-by-step explanation:

Correct on E2020!

Answer:

Option D: 2 is the correct answer.

Step-by-step explanation:

Given equation is:

2(x + 1) = 2x + ______

For balancing the equation, the variables and constants must be same on both sides of the equation.

Simplifying 2(x+1) gives us 2x+2

As 2x is already there, we will add 2 with it in the equation.

Hence,

Option D: 2 is the correct answer.

Answer:

3

Step-by-step explanation:

2 (n + 9) = 24 this is the equation

to solve for n (number):

2(n+9)=24 // Distribute the 2 into parentheses

2n + 18 = 24 // Subtract 18 on both sides of equal sign

      - 18   -18

      2n = 6 // Divide by 2 on both sides of equal sign

        2     2

      n = 3

Hope this helps :)

Answer:

Step-by-step explanation:

We can solve this with the help of Pythagoras theorem.

Hence, the value of x is 5 units.

Answer:

Answer: x is 5 units

Step-by-step explanation:

» From trigonometric ratios,

\({ \tt{ \red{ \sin( \theta) = \frac{opposite}{hypotenuse} }}} \\ \)

\({ \tt{ \sin(45 \degree) = \frac{x}{ \sqrt{50} } }} \\ \\ { \tt{x = \sqrt{50} \times \frac{1}{ \sqrt{2} } }} \\ \\ { \tt{x = \sqrt{ \frac{50}{2} } }} \\ \\ { \tt{x = \sqrt{25} }} \\ { \boxed{ \tt{x = 5 \: units}}}\)

Or, from pythogras theorem

\({ \tt{ {a}^{2} + {b}^{2} = {c}^{2} }}\)

\({ \tt{ {x}^{2} + {x}^{2} = {( \sqrt{50}) }^{2} }} \\ { \tt{2 {x}^{2} = 50 }} \\ { \tt{ {x}^{2} = 25}} \\ { \tt{x = \sqrt{25} }} \\ { \boxed{ \tt{x = 5 \: units}}}\)

Answer:   y=1/8*x+2

Step-by-step explanation:

The equation of any tangent line is y=a*x+b  (1)

To the equation of the tangent line we have to find the coefficients a and b   and the to substitute them to equation (1).

As we know  a=y'(x0) ( where x0=16)

So y'(x)= (√ (x) )' = 1/(2*√x)

a=y'(x0)= 1/(2*√16)=1/(2*4)=1/8

So lets substitute a in equation (1):

y=1/8 *x+b

Now we have to find b

We know that the point (16, 4) belongs to the tangent line.

That means

4=1/8*16+b => 4=2+b => b=2

SO the equation of the tangent line is y=1/8*x+2

The calculated area of the quadrilateral is 35.82 square units.

Given that

BAse = 6.5

Height = 5.51

To find the area of a quadrilateral, we need to multiply the base by the height.

Area of quadrilateral = base x height

Substituting the given values, we get:

Area = 6.5 x 5.51

Area = 35.815

Rounding to the nearest hundredth, the area of the quadrilateral is 35.82 square units.

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To determine if the mean reduction in blood pressure is different between the two groups, you can use a statistical test such as a two-sample t-test. This test compares the means of two groups and determines whether the difference between the means is statistically significant.

To conduct the t-test, you will need the following information:

Once you have this information, you can use a statistical software or calculator to perform the t-test and determine the p-value. The p-value is a measure of the probability that the difference between the means is due to chance.

If the p-value is less than the level of significance (5% in this case), then the difference between the means is statistically significant and you can conclude that there is a significant difference in the mean reduction in blood pressure between the two groups.

If the p-value is greater than the level of significance, then the difference between the means is not statistically significant and you cannot conclude that there is a difference in the mean reduction in blood pressure between the two groups.

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Answer:

3.5

Step-by-step explanation:

17.50 divided by 5 is 3.5 so 1 pound is 3.5

The number of advance tickets sold is 25 and same day tickets sold is 30.

Data Given;

Let the number of advance ticket be represented by x

Let the number of same-day ticket be represented by y

\(x + y = 60\\ 30x + 25y = 1625\)

From the system of equations above, we can easily pick any to start our calculation.

Using equation (i),

x + y = 60

x = 60 - y ...equation(iii)

Put equation (iii) into equation (ii)

\(30x + 25y = 1625\\ x = 60 - y\\ 30(60 - y) + 25y = 1625\\ 1800 - 30y + 25y = 1625\\ 1800 -5y = 1625\\ 5y = 1800 - 1625\\ 5y = 175\\ 5y/5 = 175/5\\ y = 35\)

Put the value of y into equation (i)

\(x+y = 60\\ x + 35 = 60\\ x = 60 - 35\\ x = 25\)

From the calculation above, the number of advance tickets sold is 25 and same-day tickets is 30.

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1.Bricks and timber purchased for construction. (Debit: Bricks - Rs 60,000, Debit: Timber - Rs 35,000, Credit: Bank - Rs 95,000)

2.Transfer of Rs 13,000 to fixed deposit account. (Debit: Fixed Deposit - Rs 13,000, Credit: Current Account - Rs 13,000)

3.Appointment of Mr. S.N. Rao as Accountant. (Debit: Salary Expense - Rs 300, Debit: Security Deposit - Rs 1,000, Credit: Accountant - Rs 300)

4.Goods sold to Shruti with discounts. (Debit: Accounts Receivable - Shruti - Rs 80,000, Credit: Sales - Rs 80,000)

5.Goods purchased from Richa with discounts. (Debit: Purchases - Rs 60,000, Credit: Accounts Payable - Richa - Rs 60,000)

6.Goods sold to Shilpa with discounts and received payment. (Debit: Accounts Receivable - Shilpa - Rs 50,000, Credit: Sales - Rs 50,000)

7.Goods sold to Garima with discounts and received partial payment. (Debit: Accounts Receivable - Garima - Rs 1,00,000, Credit: Sales - Rs 1,00,000)

8.Purchase of land with additional charges. (Debit: Land - Rs 2,00,000, Debit: Brokerage Expense - Rs 2,000, Debit: Registration Charges - Rs 15,000, Credit: Bank - Rs 2,17,000)

9.Proprietor took goods and cash for personal use. (Debit: Proprietor's Drawings - Rs 65,000, Credit: Goods - Rs 25,000, Credit: Cash - Rs 40,000)

10.Goods sold to Charu with profit and discount. (Debit: Accounts Receivable - Charu - Rs 1,20,000, Credit: Sales - Rs 1,20,000)

11.Rent paid for the building. (Debit: Rent Expense - Rs 60,000, Credit: Bank - Rs 60,000)

12.Goods sold to Sunil with profit and discount. (Debit: Accounts Receivable - Sunil - Rs 24,000, Credit: Sales - Rs 24,000)

13.Purchased goods from Nanda and supplied to Helen. (Debit: Purchases - Rs 1,000, Debit: Accounts Payable - Nanda - Rs 1,000, Credit: Accounts Receivable - Helen - Rs 1,300, Credit: Sales - Rs 1,300)

14.Purchased goods from Rohit and Sons and supplied to Madan. (Debit: Purchases - Rs 2,700, Credit: Accounts Payable - Rohit and Sons - Rs 2,700, Debit: Accounts Receivable - Madan - Rs 3,000, Credit: Sales - Rs 3,000)

Here are the journal entries for the given transactions:

1. Bricks and timber purchased for construction:

Debit: Bricks (Asset) - Rs 60,000

Debit: Timber (Asset) - Rs 35,000

Credit: Bank (Liability) - Rs 95,000

2. Transfer to fixed deposit account:

Debit: Fixed Deposit (Asset) - Rs 13,000

Credit: Current Account (Asset) - Rs 13,000

3. Appointment of Mr. S.N. Rao as Accountant:

Debit: Salary Expense (Expense) - Rs 300

Debit: Security Deposit (Asset) - Rs 1,000

Credit: Accountant (Liability) - Rs 300

4. Goods sold to Shruti:

Debit: Accounts Receivable - Shruti (Asset) - Rs 80,000

Credit: Sales (Income) - Rs 80,000

5. Goods purchased from Richa:

Debit: Purchases (Expense) - Rs 60,000

Credit: Accounts Payable - Richa (Liability) - Rs 60,000

6. Goods sold to Shilpa:

Debit: Accounts Receivable - Shilpa (Asset) - Rs 50,000

Credit: Sales (Income) - Rs 50,000

7. Goods sold to Garima:

Debit: Accounts Receivable - Garima (Asset) - Rs 1,00,000

Credit: Sales (Income) - Rs 1,00,000

8.Purchase of land:

Debit: Land (Asset) - Rs 2,00,000

Debit: Brokerage Expense (Expense) - Rs 2,000

Debit: Registration Charges (Expense) - Rs 15,000

Credit: Bank (Liability) - Rs 2,17,000

9. Goods and cash taken away by proprietor:

Debit: Proprietor's Drawings (Equity) - Rs 65,000

Credit: Goods (Asset) - Rs 25,000

Credit: Cash (Asset) - Rs 40,000

10. Goods sold to Charu:

Debit: Accounts Receivable - Charu (Asset) - Rs 1,20,000

Credit: Sales (Income) - Rs 1,20,000

Credit: Cost of Goods Sold (Expense) - Rs 80,000

Credit: Profit on Sales (Income) - Rs 40,000

11. Rent paid for the building:

Debit: Rent Expense (Expense) - Rs 60,000

Credit: Bank (Liability) - Rs 60,000

12. Goods sold to Sunil:

Debit: Accounts Receivable - Sunil (Asset) - Rs 24,000

Credit: Sales (Income) - Rs 24,000

Credit: Cost of Goods Sold (Expense) - Rs 20,000

Credit: Profit on Sales (Income) - Rs 4,000

13. Goods purchased from Nanda and supplied to Helen:

Debit: Purchases (Expense) - Rs 1,000

Debit: Accounts Payable - Nanda (Liability) - Rs 1,000

Credit: Accounts Receivable - Helen (Asset) - Rs 1,300

Credit: Sales (Income) - Rs 1,300

14. Goods received from Rohit and Sons and supplied to Madan:

Debit: Purchases (Expense) - Rs 2,700 (after 10% trade discount)

Credit: Accounts Payable - Rohit and Sons (Liability) - Rs 2,700

Debit: Accounts Receivable - Madan (Asset) - Rs 3,000

Credit: Sales (Income) - Rs 3,000

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This represents the distance that Mr. Stein drove, given that Mr. Smith drove x miles. The value of x must be between 0 and 140, since Mr. Smith cannot drive more than 140 miles and less than 0 miles.

An algebraic expression is a combination of variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. It can be simplified, evaluated, or manipulated using algebraic rules and properties.

Let x be the number of miles Mr. Smith drove. Then, the number of miles Mr. Stein drove is \(140 - x\)  , since they drove a total of 140 miles and Mr. Smith already drove x miles.

the algebraic expression for how many miles Mr. Stein drove is:

\(140 - x\)

Therefore, This represents the distance that Mr. Stein drove, given that Mr. Smith drove x miles. The value of x must be between 0 and 140, since Mr. Smith cannot drive more than 140 miles and less than 0 miles.

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Answer:

Solution ( Second Attachment ) : - 2.017 + 0.656i

Solution ( First Attachment ) : 16.140 - 5.244i

Step-by-step explanation:

Second Attachment : The quotient of the two expressions would be the following,

\(6\left[\cos \left(\frac{2\pi }{5}\right)+i\sin \left(\frac{2\pi \:}{5}\right)\right]\) ÷ \(2\sqrt{2}\left[\cos \left(\frac{-\pi }{2}\right)+i\sin \left(\frac{-\pi \:}{2}\right)\right]\)

So if we want to determine this expression in standard complex form, we can first convert it into trigonometric form, then apply trivial identities. Either that, or we can straight away apply the following identities and substitute,

( 1 ) cos(x) = sin(π / 2 - x)

( 2 ) sin(x) = cos(π / 2 - x)

If cos(x) = sin(π / 2 - x), then cos(2π / 5) = sin(π / 2 - 2π / 5) = sin(π / 10). Respectively sin(2π / 5) = cos(π / 2 - 2π / 5) = cos(π / 10). Let's simplify sin(π / 10) and cos(π / 10) with two more identities,

( 1 ) \(\cos \left(\frac{x}{2}\right)=\sqrt{\frac{1+\cos \left(x\right)}{2}}\)

( 2 ) \(\sin \left(\frac{x}{2}\right)=\sqrt{\frac{1-\cos \left(x\right)}{2}}\)

These two identities makes sin(π / 10) = \(\frac{\sqrt{2}\sqrt{3-\sqrt{5}}}{4}\), and cos(π / 10) = \(\frac{\sqrt{2}\sqrt{5+\sqrt{5}}}{4}\).

Therefore cos(2π / 5) = \(\frac{\sqrt{2}\sqrt{3-\sqrt{5}}}{4}\), and sin(2π / 5) = \(\frac{\sqrt{2}\sqrt{5+\sqrt{5}}}{4}\). Substitute,

\(6\left[ \left\frac{\sqrt{2}\sqrt{3-\sqrt{5}}}{4}+i\left\frac{\sqrt{2}\sqrt{5+\sqrt{5}}}{4}\right]\) ÷ \(2\sqrt{2}\left[\cos \left(\frac{-\pi }{2}\right)+i\sin \left(\frac{-\pi \:}{2}\right)\right]\)

Remember that cos(- π / 2) = 0, and sin(- π / 2) = - 1. Substituting those values,

\(6\left[ \left\frac{\sqrt{2}\sqrt{3-\sqrt{5}}}{4}+i\left\frac{\sqrt{2}\sqrt{5+\sqrt{5}}}{4}\right]\) ÷ \(2\sqrt{2}\left[0-i\right]\)

And now simplify this expression to receive our answer,

\(6\left[ \left\frac{\sqrt{2}\sqrt{3-\sqrt{5}}}{4}+i\left\frac{\sqrt{2}\sqrt{5+\sqrt{5}}}{4}\right]\) ÷ \(2\sqrt{2}\left[0-i\right]\) = \(-\frac{3\sqrt{5+\sqrt{5}}}{4}+\frac{3\sqrt{3-\sqrt{5}}}{4}i\),

\(-\frac{3\sqrt{5+\sqrt{5}}}{4}\) = \(-2.01749\dots\) and \(\:\frac{3\sqrt{3-\sqrt{5}}}{4}\) = \(0.65552\dots\)

= \(-2.01749+0.65552i\)

As you can see our solution is option c. - 2.01749 was rounded to - 2.017, and 0.65552 was rounded to 0.656.

________________________________________

First Attachment : We know from the previous problem that cos(2π / 5) = \(\frac{\sqrt{2}\sqrt{3-\sqrt{5}}}{4}\), sin(2π / 5) = \(\frac{\sqrt{2}\sqrt{5+\sqrt{5}}}{4}\), cos(- π / 2) = 0, and sin(- π / 2) = - 1. Substituting we receive a simplified expression,

\(6\sqrt{5+\sqrt{5}}-6i\sqrt{3-\sqrt{5}}\)

We know that \(6\sqrt{5+\sqrt{5}} = 16.13996\dots\) and \(-\:6\sqrt{3-\sqrt{5}} = -5.24419\dots\) . Therefore,

Solution : \(16.13996 - 5.24419i\)

Which rounds to about option b.

a.) The independent variable is the different types of music

b.) The dependent variable is the impact of listening felt by the rats

c.)An extraneous variable is the length of the maze.

d.) The control group is the rat in the quite room while the experimental groups are the ones in the maze listening to classical music, and listening to heavy metal music.

An independent variable is defined as the type of variable that cannot be manipulated by a researcher and isn't affected by what is being measured.

A dependent variable is the variable that can be manipulated by a researcher and is affected by what is being measured.

For question a.)

The independent variable is the different types of music

For question b.)

The dependent variable is the impact of listening felt by the rats

For question c.)

An extraneous variable is the length of the maze.

For question d.)

The control group is the rat in the quite room while the experimental groups are the ones in the maze listening to classical music, and listening to heavy metal music.

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https://brainly.com/question/30386143

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