Please help show your work and 20 points.

tan(41π/36) can be written in terms of the tangent of a positive acute angle as (tan((1/9)π) + tan((37/36)π)) / (1 - tan((1/9)π)tan((37/36)π))

To express tan(41π/36) in terms of the tangent of a positive acute angle, we need to find an angle within the range of 0 to π/2 that has the same tangent value.

First, let's simplify 41π/36 to its equivalent angle within one full revolution (2π):

41π/36 = 40π/36 + π/36 = (10/9)π + (1/36)π

Now, we can rewrite the angle as:

tan(41π/36) = tan((10/9)π + (1/36)π)

Next, we'll use the tangent addition formula, which states that:

tan(A + B) = (tan(A) + tan(B)) / (1 - tan(A)tan(B))

In this case, A = (10/9)π and B = (1/36)π.

tan(41π/36) = tan((10/9)π + (1/36)π) = (tan((10/9)π) + tan((1/36)π)) / (1 - tan((10/9)π)tan((1/36)π))

Now, we need to find the tangent values of (10/9)π and (1/36)π. Since tangent has a periodicity of π, we can subtract or add multiples of π to get equivalent angles within the range of 0 to π/2.

For (10/9)π, we can subtract π to get an equivalent angle within the range:

(10/9)π - π = (1/9)π

Similarly, for (1/36)π, we can add π to get an equivalent angle:

(1/36)π + π = (37/36)π

Now, we can rewrite the expression as:

tan(41π/36) = (tan((1/9)π) + tan((37/36)π)) / (1 - tan((1/9)π)tan((37/36)π))

Since we are looking for an angle within the range of 0 to π/2, we can further simplify the expression as:

tan(41π/36) = (tan((1/9)π) + tan((37/36)π)) / (1 - tan((1/9)π)tan((37/36)π))

Therefore, tan(41π/36) can be written in terms of the tangent of a positive acute angle as the expression given above.

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\(\textit{area of a sector of a circle}\\\\ A=\cfrac{\theta \pi r^2}{360} ~~ \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ r=8\\ \theta =135 \end{cases}\implies A=\cfrac{(135)\pi (8)^2}{360}\implies A=24\pi \implies A\approx 75.4\)

The Michelson-Morley experiment was conducted in 1887 to detect the existence of the luminiferous ether, which was thought to be the medium through which light traveled.

Here is the procedure for the Michelson-Morley experiment:

1. Set up a light source, a half-silvered mirror, two mirrors, and two detectors in a square configuration.

2. Split the light beam using the half-silvered mirror so that one beam goes to one mirror and the other beam goes to the other mirror.

3. Reflect the beams back to the half-silvered mirror and combine them to produce an interference pattern.

4. Rotate the entire apparatus by 90 degrees and repeat the measurement.

5. Compare the interference patterns from the two orientations.

If there is a luminiferous ether, the speed of light should be faster in the direction of the ether flow and slower in the perpendicular direction. This should produce a difference in the interference patterns.

However, the Michelson-Morley experiment showed that there was no difference in the interference patterns, indicating that the luminiferous ether did not exist.

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The Mean Absolute Error (MAE) is [Insert value]. The Mean Squared Error (MSE) is [Insert value].

To calculate the Mean Absolute Error (MAE) and Mean Squared Error (MSE) using exponential smoothing, we need to find the optimum alpha value that minimizes the MSE. Excel Solver can be used to determine this value.

Organize the data: Arrange the given data in a column in Excel: 155, 145, 155, 162, 180, 165, 172, 149, 170, 172.

Set up the exponential smoothing model: Define the forecast for each period using the formula: Forecast = α * Actual + (1 - α) * Forecast(t-1)

Calculate the MAE and MSE: For each period, calculate the forecasted value using the exponential smoothing model. Then, calculate the absolute error by taking the absolute difference between the forecasted value and the actual value. Square each absolute error to obtain the squared error. Finally, calculate the average of the absolute errors to find the MAE and the average of the squared errors to find the MSE.

Use Excel Solver: To determine the optimum alpha value, you can set up Excel Solver to minimize the MSE by changing the alpha value. The objective is to find the alpha value that gives the lowest MSE.

After performing the calculations and using Excel Solver to find the optimum alpha value, you can obtain the Mean Absolute Error (MAE) and Mean Squared Error (MSE) for the given data. These values will provide a measure of the accuracy of the exponential smoothing forecast.

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A = 120/2

B=120/4

Car A traveled 60 miles per hour

car B traveled 30 miles per hour

Answer:

car A traveled 60 miles per hour

car B traveled 30 miles per hour

Step-by-step explanation:

I did 2/120 for car A and got 60

then I sid 4/120 for car B and got 30

The postfix expression of "7+5-3*2(6*7)/4" is "7 5 + 3 2 * 6 7 * 2 * - 4 /". Evaluating the postfix expression gives the result of the expression. The prefix expression for the given infix expression is "/ - + 7 5 * 3 * 2 ( * 6 7 ) 4".

To convert the infix expression "7+5-3*2(6*7)/4" into postfix expression, we follow the rules of operator precedence and associativity. The postfix expression is obtained by placing operators after their operands.

The postfix expression for the given infix expression is:

"7 5 + 3 2 * 6 7 * 2 * - 4 /"

To evaluate the postfix expression, we use a stack data structure. We scan the postfix expression from left to right and perform the corresponding operations.

Starting with an empty stack, we encounter the operands "7" and "5". We push them onto the stack. Then we encounter the operator "+", so we pop the last two operands from the stack (5 and 7), perform the addition operation (7 + 5 = 12), and push the result back onto the stack.

We continue this process for the remaining operators and operands in the postfix expression. Finally, after evaluating the entire expression, the result left on the stack is the final answer.

To convert the infix expression into prefix expression, we follow similar rules but scan the expression from right to left. The prefix expression is obtained by placing operators before their operands.

The prefix expression for the given infix expression is:

"/ - + 7 5 * 3 * 2 ( * 6 7 ) 4"

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Answer: 1/45

Step-by-step explanation:

The probability that it will rain this week and then rain next week will be the multiplication of the both the probability that it'll rain this week and probability that it'll rain next week.

Therefore, the answer will be:

= P(rain this week) × P(rain next week)

= 1/9 × 1/5

= 1/45

Therefore, the answer is 1/45.

Answer:

the answer is negative 3/7

Accoding to the calculations , the correct answer is:

A) Depreciation charge 16,000; revaluation surplus £20,000

According to IAS 16 Property, Plant and Equipment, the depreciation charge for an asset should be based on its carrying amount, useful life, and residual value.

In this case, the buildings were purchased for £400,000 (£480,000 - £80,000) and had a useful life of 25 years. Since there is no residual value, the depreciable amount is equal to the initial cost of the buildings (£400,000).

To calculate the annual depreciation charge, we divide the depreciable amount by the useful life:

£400,000 / 25 = £16,000

Therefore, the depreciation charge for the year ended 30 September 2021 is £16,000.

Now, let's calculate the balance on the revaluation surplus as at that date.

The revaluation surplus is the difference between the fair value of the property and its carrying amount. On 1 October 2020, the property was revalued to £500,000, and the carrying amount was £480,000 (£400,000 for buildings + £80,000 for land).

Revaluation surplus = Fair value - Carrying amount

Revaluation surplus = £500,000 - £480,000

Revaluation surplus = £20,000

Therefore, the balance on the revaluation surplus as at 30 September 2021 is £20,000.

Based on the calculations above, the correct answer is:

A) Depreciation charge £16,000; revaluation surplus £20,000

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Answer:

The answer is:

u = 7

Step-by-step explanation:

7 x 1 = 7

7 x u = 7u

So..

u = 7

To determine which point lies on circle A, we need to calculate the distance between the center of the circle (A) and each of the given points. The point is on the circle if the distance is equal to the circle's radius. So, the points O(6, -1) and O(3, 5) lie on circle A.

Given:

Center of circle A: A(3, -1)

The radius of circle A: 6

Let's calculate the distance between the center of the circle and each given point:

Distance between A(3, -1) and O(9, -7):

Distance = √( \((9-3)^{2}\) + \((-7-(-1))^{2}\) )

= √( \(6^{2}\) + \((-6)^{2}\) )

= √(36 + 36)

= √72

= 6√2

The distance is not equal to the radius, so O(9, -7) does not lie on circle A.

Distance between A(3, -1) and O(0, 2):

Distance = √( \((0-3)^{2}\) +\((2-(-1))^{2}\) )

= √( \((-3)^{2}+3^{2}\) )

= √(9 + 9)

= √18n= 3√2

The distance is not equal to the radius, so O(0, 2) does not lie on circle A.

Distance between A(3, -1) and O(6, -1):

Distance = √( \((6 - 3)^2 + (-1 - (-1))^2\) )

= √(\(3^2 + 0^2\))

= √9 = 3

The distance is equal to the radius, so O(6, -1) lies on circle A.

Distance between A(3, -1) and O(3, 5):

Distance = √( \((3 - 3)^2 + (5 - (-1))^2\) )

= √(\(0^2 + 6^2\))

= √36 = 6

The distance is equal to the radius, so O(3, 5) lies on circle A.

Therefore, the points O(6, -1) and O(3, 5) lie on circle A.

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Because the two angles are complementary, the value of x must be 11.5

In the image we can see that the two given angles are complementary, which means that their measures add up to 90°, then we can write:

(7x - 5)° + (x + 3)° = 90°

Now we can solve that linear equation to find the value of x, we iwll get:

7x + x - 5 + 3 = 90

8x - 2 = 90

8x = 92

x = 92/8

x = 11.5

That is the value of x.

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The estimated forward LIBOR interest rate for the period between 6.00 and 6.25 years in the future is approximately 7.495%.

To estimate the forward LIBOR interest rate for the period between 6.00 and 6.25 years in the future, given the 3-month Eurodollar futures price of 95.20 and a standard deviation of the change in the short-term interest rate in 1 year of 1.1%, follow these steps:

1. Convert the Eurodollar futures price to an implied interest rate:
 Implied Interest Rate = (100 - Eurodollar Futures Price) = (100 - 95.20) = 4.80%

2. Calculate the number of standard deviations for the 6-year period:
  Number of Standard Deviations = √(6 years) = √6 ≈ 2.45

3. Multiply the number of standard deviations by the annual standard deviation of the change in the short-term interest rate:
  Change in Interest Rate = Number of Standard Deviations × Annual Standard Deviation = 2.45 × 1.1% = 2.695%

4. Add the change in the interest rate to the current implied interest rate to get the forward LIBOR interest rate for the period between 6.00 and 6.25 years in the future:
  Forward LIBOR Interest Rate = Implied Interest Rate + Change in Interest Rate = 4.80% + 2.695% = 7.495%

So, the estimated forward LIBOR interest rate for the period between 6.00 and 6.25 years in the future is approximately 7.495%.

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Answer:

a. x = 4.8989794855663561963945681494118 or 4.9 rounded

b. x = 8.6023252670426267717294735350497 or 8.6 rounded

Step-by-step explanation:

7² - 5² = x²

49 - 25 = x

49 - 25 = 24

√24 = 4.8989794855663561963945681494118

7² + 5² = x²

49 + 25 = x

49 + 25 = 74

√74 = 8.6023252670426267717294735350497

Answer:

The answer is -46

Answer:

12 feet

Step-by-step explanation:

you would need to divide the total square feet by the width

108/9=12

therefore, the length is 12 feet

\(\sqrt[4]{81} -8( \sqrt[3]{216}) +15( \sqrt[5]{32}) +\sqrt{225}\) when simplified gives 0

Indices are small number that tells us how many times a term has been multiplied by itself. Indices are also the power or exponent which is raised to a number or a variable.

How to determine this

\(\sqrt[4]{81} -8( \sqrt[3]{216}) +15( \sqrt[5]{32}) +\sqrt{225}\)

When all of then are perfect square

\(\sqrt[4]{81}\)= 3 * 3 *3 *3

\(\sqrt[3]{216}\) = 6 * 6 * 6

\(\sqrt[2]{32}\) = 2 * 2 * 2 * 2 * 2

\(\sqrt{225}\) = 15 * 15

Therefore,

3 - 8(6) + 15(2) + 15

3 - 48 + 30 + 15

By collecting like terms

3 + 30 + 15 - 48

48 - 48

= 0

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The answer of the question based on population growth is , the estimated population after one year is approximately 34 deer.

To estimate the population after one year, we can use the formula for exponential growth:

P = P0 * (1 + r)^t.

P0 represents the initial population (20 deer in this case), r represents the growth rate (70% or 0.7 as a decimal), and t represents the time period in years (1 year in this case).

Using these values, we can calculate the population after one year as follows:

P = 20 * (1 + 0.7)¹
P = 20 * 1.7
P ≈ 34

Therefore, the estimated population after one year is approximately 34 deer.

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Answer:

10/10 - 7/10 = 3/10

Step-by-step explanation:

Given:

Number of muffin made = 12

Number of muffin burned = 2

Number of muffin serve = 7 / 10

Find:

Equation for number of muffin remain

Computation:

Number of muffin remain = 12 / 2

Number of muffin remain = 10

Equation for number of muffin remain = Number of muffin remain  - Number of muffin serve

10/10 - 7/10 = 3/10

Answer:

Below.

Step-by-step explanation:

(a) Over the first 5 seconds rate of change of speed

= (9-1)/5

= 8/5

= 1.6m/s^2

(b) (21-9)/16-t) = 2

12/16-t = 2

32 - 2t = 12

32 - 12 = 2t

20 = 2t

t = 10 seconds

Step-by-step explanation:

Total Time Taken = 16secs

10a). We're asked to calculate the rate of speed change for the first 5secs.

This is another way of saying "Calculate Acceleration" in the first 5sec of Motion.

Why?

Acceleration is the rate of change of speed or the rate at which speed changes.

acceleration = v - u/t

where v = Final Speed

u = initial Speed.

Looking at the graph

You see that

Initial speed(u) = 1m/s

Final Speed(v) = 9m/s

t = 5secs

Acceleration = 9 - 1/ 5

a = 8/5

a = 1.6m/s².✅

10b)

We're asked to calc "t" from the graph.

Given that the acceleration at "t" untill 16sec(end of motion) is 2m/s².

This simply means that Constant Acceleration was held from "t" to the end of the Motion.

Do not confuse Constant Acceleration for Constant Velocity.

At Constant Velocity... Acceleration is zero(0)

At Constant Acceleration...Velocity Changes Uniformly or at the same rate each second and this is what we're dealing with in this question.

Taking the same step as we used in calculating acceleration above

Given a= 2m/s²

a = v - u/∆t

Where ∆t means time change or difference.

From "t" to 16

The change in time is 16 - "t"

2 = 21 - 9/( 16 - t)

2 = 12/16-t

16-t = 12/2

16 - t = 6

t = 16 - 6

t = 10secs.✅

Have a great Day!.

is it 10+8=18 is this it hopefully this helps

Answer:

Option C

Step-by-step explanation:

10 + n is the total number of computers Mr. James will sell this week, since he has already sold 10 computers and will sell n more. Because he wants to sell at least 18 computers, the correct symbol is ≥.

The area of the unshaded region is equal to 337.3yd² to the nearest tenth.

The figure is observed to have an unshaded arrow within, so we subtract the area of the arrow from the area of the entire figure to get the area of the shaded region.

For the entire figure it is a triangle and a semicircle so;

area of the triangle = 1/2 × 26yd × 30yd

area of the triangle = 360yd²

area of the semicircle = (22/7 × 12yd × 12yd) ÷ 2

area of the semicircle = 226.2857yd²

area of entire figure = 360yd² + 226.2857yd²

area of entire figure = 586.2857yd²

For the arrow figure inside, it comprises of a rectangle and a smaller triangle so;

area of the rectangle = 21yd × 5yd

area of the rectangle = 105yd²

area of the smaller triangle = 1/2 × 26yd × 12yd

area of the smaller triangle = 144yd²

area of the arrow figure = 105yd² + 144yd²

area of the arrow figure = 249yd²

area of the unshaded region = 586.2857yd² - 249yd²

area of the unshaded region = 337.3yd²

Therefore, the area of the unshaded region is equal to 337.3yd² to the nearest tenth.

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The graph of both modelling equations using a common coordinate system has been attached to this answer.

From the given table, we see that;

In Seattle = $38000

In Port Townsend = $84000

In Seattle = $8400

In Port Townsend = $168400

The red line on the attached graph represents the line for Port Townsend while the blue line represents Seattle.

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Given:

A fruit salad recipe calls for \(\dfrac{3}{4}\) pound of apples and \(\dfrac{2}{5}\) pound of dates.

To find:

The least common denominator of the fractions.

Solution:

The given fractions are:

\(\dfrac{3}{4}\) and \(\dfrac{2}{5}\)

The denominators of these fractions are 4 and 5 respectively.

Factor form of 4 is 2×2.

5 is a prime number, so factor form of 5 is 5×1.

Now, the least common denominator of the fractions is:

\(LCD=2\times 2\times 5\)

\(LCD=20\)

Therefore, the least common denominator of the fractions is 20.

Consider the system of inequalities,

Simplify the first inequality as follows,

So, the solution to this inequality will be the set of points including and lying on the left of point 4 on the number line.

Simplify the second inequality as follows,

So, the solution to this inequality will be the set of points including and lying on the right of point -6 on the number line.

The solution to the compound inequality will be the common solution of both the inequalities, that is, the set of real numbers ranging from -6 to 4.

The solution can be seen on the number line as follows,

Answer

Option A is correct.

B' (15, 6) is the answer.

Explanation

To dilate a given coordinate (x, y) about the origin by a scale factor of n, we will obtain (nx, ny).

So, for the given coordinate (5, 2), dilating by the scale factor of 3, we will obtain

B (5, 2) = B' (5×3, 2×3) = B' (15, 6)

Hope this Helps!!!

Answer:9x6y4

Step-by-step explanation: hope it helps, I tried my best

Answer: = 9x^6 - y^4

Step-by-step explanation:

(3x^3 -y^2)^2

3^2 - 3x3= 9x^3 - 3x2 = 9x^6

-y^2 x 2 = -y^4

= 9x^6 - y^4

Answer:

Step-by-step explanation:

To evaluate (f+g)(-2), we need to substitute -2 into the functions f(x) and g(x), and then add the results.

Given:

f(x) = 3x + 4

g(x) = x - x^2

First, we substitute -2 into f(x):

f(-2) = 3(-2) + 4

= -6 + 4

= -2

Next, we substitute -2 into g(x):

g(-2) = (-2) - (-2)^2

= -2 - 4

= -6

Now, we add the results of f(-2) and g(-2):

(f+g)(-2) = f(-2) + g(-2)

= -2 + (-6)

= -8

Therefore, (f+g)(-2) evaluates to -8.

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Ryan's paid $787 per month for 21 months.

The division in mathematics is one kind of operation. In this process, we split the expressions or numbers into the same number of parts.

Given:

Ryan's total payment for his loan was $16,534.

and, he paid for 21 months.

So, The monthly payment = Total payment / number of months

                                            = 16534 / 21

                                            = 787.333

                                            = $ 787

So, the monthly payment = $ 787.

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Given that IJKL is a square, Option A is correct. x = 2 and y = 8.

To solve for x and y, we can use the Pythagorean theorem which states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides. In this case, the length of the sides of the square IJKL is equal to the hypotenuse, so the theorem simplifies to x^2 + y^2 = IJKL^2.

Given that IJKL is a square, we know that IJKL = x = y, so we can substitute x for IJKL in the equation above and solve for x.

x^2 + x^2 = IJKL^2 becomes 2x^2 = IJKL^2

and x^2 = IJKL^2/2.

Since IJKL = x, x^2 = x^2/2, and 2x^2 = x^2, so x = √2.

And since IJKL = y, y = √2 as well. So, x = 2 and y = 8.

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