Hello please help. The circumference of a circle is 6pi m. What is the area, in square meters? Express
your answer in terms of pi

In a right-angle triangle, a sine function of an angle [tex]\theta[/tex] is equal to the opposite side to [tex]\theta[/tex] divided by hypotenuse.

[tex]\text{Sin} \ \theta = \dfrac{\text{Opposite side}}{\text{Hypotenuse}}[/tex]

[tex]\text{y = f(x)} \rightarrow \text{x}[/tex] in the domain of f. Trigonometric functions are periodic, therefore each range value is within the limitless domain values (no breaks in between). Since trigonometric functions have no restrictions, there is no inverse.

The inverse sine function (also called arcsine) is the inverse of sine function. Since sine of an angle (sine function) is equal to ratio of opposite side and hypotenuse, thus sine inverse of same ratio will give the measure of the angle. Let’s say [tex]\theta[/tex] is the angle, then:

[tex]\text{Sin} \ \theta = \dfrac{\text{Opposite side to} \ \theta}{\text{Hypotenuse}}[/tex]

[tex]\text{Or} \ \theta = \text{Sin-}1 \ \dfrac{\text{Opposite side to}\ \theta}{\text{Hypotenuse}}[/tex]

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Answer:

(11, 7) with an area of 128 in2.

Step-by-step explanation:

The domain of rational function f(x) = (x² - 36) / (x - 6) is x ∈ (- ∞, + ∞).

In this question we must determine what function has a domain, that is, the set of all x-values, that comprises all real numbers. According to algebra, polynomic functions have a domain that comprises all real numbers.

Herein we need to determine what rational function is equivalent to a polynomic function. Polynomic functions are expression of the form:

[tex]y = \sum\limits_{i = 0}^{n} c_{i}\cdot x^{i}[/tex]

Where:

Now we check the following expression by algebra properties:

f(x) = (x² - 36) / (x - 6)

f(x) = [(x - 6) · (x + 6)] / (x - 6)

f(x) = x + 6

The rational function f(x) = (x² - 36) / (x - 6) is equivalent to polynomial of grade 1 and, thus, its domain comprises all real numbers.

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Boolean algebra is a type of algebra that deals with binary variables and logical operations. In this case, we're simplifying expressions using Boolean algebra.

1. ABC +(A+B+7)

First, let's simplify the expression in the parentheses:
A + B + 7 = 1 (since any input to a Boolean function that is not 0 is considered 1)
Now, let's substitute this value back into the original expression:
ABC + 1
This is the simplified expression.

2. (A+Ā)(AB+ ABC)

Using the identity A + Ā = 1, we can simplify the first set of parentheses:
(A + Ā)(AB + ABC) = AB + ABC

3. (B+BC)(B+ BC)(B+D)

Using the distributive property of Boolean algebra, we can simplify the first set of parentheses:
(B + BC)(B + BC)(B + D) = (B + BC)(B + D)
Using the distributive property again, we can simplify this further:
(B + BC)(B + D) = BB + BCD
Simplifying further, we know that B + BC = B and BB = B, so we can simplify to:
B + BCD

So, the simplified expressions are:
1. ABC + 1
2. AB + ABC
3. B + BCD

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Yes, I can help you with these Laplace transform problems.

1. To find the Laplace transform of f(t)=e-2t sin (5t), we can use the formula:

L{e-at sin(bt)} = b / (s+a)2 + b2

Applying this formula, we get:

L{e-2t sin (5t)} = 5 / (s+2)2 + 52

Therefore, the Laplace transform of f(t)=e-2t sin (5t) is:

L{f(t)} = 5 / (s+2)2 + 25

2. To find the Laplace transform of f(t)=tsin (3t), we can use integration by parts, followed by applying the Laplace transform:

L{f(t)} = L{t} L{sin (3t)} - L{dt/ds} L{sin (3t)}

Using the Laplace transform of t and sin(3t), we get:

L{t} = 1 / s2

L{sin(3t)} = 3 / (s2 + 32)

Differentiating sin(3t) with respect to t gives:

d/dt sin(3t) = 3 cos(3t)

Taking the Laplace transform of both sides gives:

L{d/dt sin(3t)} = s L{cos(3t)} - cos(0)

Since L{cos(3t)} = s / (s2 + 32), we can simplify to:

L{d/dt sin(3t)} = 3s / (s2 + 32)

Therefore, the Laplace transform of f(t)=tsin (3t) is:

L{f(t)} = (2s3) / (s2 + 32)2

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The value of x in the photo is 1 inch.

We have,

Dimensions of the photo.

Length = 8 in

Width = 7 in

Dimension of the ad.

Length = 8 + x

Width = 7 + x

Now,

Area of the photo = 1/2 x area of the ad

8 x 7 = 1/2 (8 + x) (7 + x)

56 = 1/2 (8 + x) (7 + x)

112 = 56 + 8x + 7x + x²

x² + 15x + 56 - 112

Now,

To solve for x in the expression x² + 15x + 56 - 112, we first combine like terms:

x² + 15x + 56 - 112 = x² + 15x - 56

Now we can factor in the quadratic expression:

x² + 15x - 56 = (x + 16)(x - 1)

Setting this expression equal to zero, we get:

(x + 16)(x - 1) = 0

Using the zero product property, we know that this equation is true if either (x + 16) = 0 or (x - 1) = 0.

Therefore, the solutions for x are:

x + 16 = 0, which gives x = -16

or

x - 1 = 0, which gives x = 1

So the solutions for x are x = -16 and x = 1.

x = -16 (rejected)

Thus,

The value of x is 1.

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1.26 more than the scarf originally so 8.26 for each scarf and 430 total made from the markup and the total profit is 63 dollars.

It will take the pendulum approximately 0.20 seconds to reach its resting position.

We have,

The resting position of the pendulum is when d(t) = 0.

So we need to solve the equation:

5.5cos(8t) = 0

We know that cos(0) = 1 and that cos(π) = -1, and that the cosine function has a period of 2π.

Therefore, the first time the pendulum will reach its resting position is at

t = 0, and then it will reach its resting position again at t = π/8.

However, we are interested in the time it takes for the pendulum to go from its starting position to its resting position, which is half of its period.

So the time it takes for the pendulum to reach its resting position is:

t = π/8 / 2

t = π/16

Using a calculator, we can approximate this value to the nearest hundredth:

t = 0.20 seconds

Therefore,

It will take the pendulum approximately 0.20 seconds to reach its resting position.

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Answer:−

2x2−8x−9

Step-by-step explanation:

The rank correlation is 1, this means that the two variables being compared are monotonically related, even if their relationship is not linear.

Given the data

X, ...rankX.....Y.....rankY......d=rx-ry........d²

4.........4...........-5......4................0..............0

53.......3.........-1........3................0...............0

86.......2.........13.......2................0................0

162......1..........16.......1.................0...............0

Then, using the rank correlation formula

p = 1 — 6•Σd² / n(n²—1)

p = 1 - 6• 0 / 4(4²-1)

p = 1 - 0

p = 1

So, the rank correlation is 1, this means that the two variables being compared are monotonically related, even if their relationship is not linear.

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Full Question: Use the table of values to calculate the linear correlation coefficient r.

X Y

4 -5

53 -1

86 13

162 16

In this case, the scientist is studying if students' beliefs about illegal drug use change as they go through college. The null hypothesis (H0) for McNemar's test in this context would state that there is no significant change in students' beliefs about illegal drug use between the time they enter college and four years later. In other words, the proportion of students who change their beliefs about illegal drug use is not significantly different from the proportion who do not change their beliefs.

Null hypothesis (H0): There is no significant difference in students' beliefs about illegal drug use before and after going through college.

Goran's swimming speed in still water is 5 km/h.

We have,

Let's call Goran's swimming speed in still water s.

When Goran is swimming against the current, his effective speed (relative to the ground) is:

= s - 3 km/h

(since the current is flowing against him),

And when he is swimming with the current, his effective speed is:

= s + 3 km/h.

The time it takes Goran to swim 2 kilometers against the current is the same as the time it takes him to swim 8 kilometers with the current.

Using the formula,

Time = distance/speed,

2 / (s - 3) = 8 / (s + 3)

Solve for s

2(s + 3) = 8(s - 3)

2s + 6 = 8s - 24

6s = 30

s = 5

Therefore,

Goran's swimming speed in still water is 5 km/h.

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The school which is a better choice is sea side.

We are given that;

The plot

Now,

If you are interested in a smaller class size, Seaside School is a better choice for you because it has a smaller mean and median class size than Bay Side School. This means that on average and in general, Seaside School has fewer students per class than Bay Side School. Also, Seaside School has a smaller maximum class size than Bay Side School (both have a minimum of zero), so you are less likely to encounter a very large class at Seaside School.

Therefore, by algebra the answer will be sea side.

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The probability of one success in five trials in the binomial experiment with a success probability of 5 % is 20. 4 %.

The formula for calculating the likelihood of one success in a binomial probability with a 5% chance of success is:

P ( X = 1) = (5 choose 1) x ( 0.05 ) x  (0.95 ) ⁴

Solving for this success would give :

= ( 0.05 ) x  ( 0. 95 ) ⁴

= 0.05 x 0.8145

= 0.040725

Then we multiply both sides to get :

P(X = 1) = 5 x 0.040725

= 0.203625

= 20. 4 %

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The short-run supply curve shows the quantity of output a firm is willing to supply at different market prices in the short run. It is typically upward sloping, meaning that as the price of the product increases, the firm is willing to produce and supply more units. This is because higher prices will allow the firm to cover its variable costs and potentially earn a profit.

When used in conjunction with the average variable cost (AVC) curve, the supply curve can give a firm valuable information about its profits. The AVC curve represents the average variable cost per unit of output, which includes the costs that vary with the level of production (such as labor and materials).

If the market price is above the AVC curve, the firm is covering all of its variable costs and may earn a profit. If the market price is below the AVC curve but still above the average total cost (ATC) curve, the firm is not covering all of its costs but is still producing because it is covering its variable costs. If the market price falls below the ATC curve, the firm is not covering all of its costs and is likely to shut down production in the short run.

Therefore, the supply curve in conjunction with the AVC curve allows a firm to determine whether it should produce and supply output in the short run based on the prevailing market price. If the market price is high enough to cover variable costs and potentially earn a profit, the firm will continue to produce. However, if the market price falls below the AVC curve, the firm will likely reduce or cease production to minimize losses.

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Santiago used 185 cell phone minutes over the course of a month.

To determine the total number of cell phone minutes that Santiago used over the course of a month, you would use the operation of addition.

You would add up the number of minutes that Santiago spoke with his mom, dad, and friends:

Total cell phone minutes = 45 minutes + 30 minutes + 110 minutes

Total cell phone minutes = 185 minutes

Therefore, Santiago used 185 cell phone minutes over the course of a month.

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The break-even x-value for Year-round-Recreation is approximately 26.19.

To find the break-even points for Year-round-Recreation, we need to set the total costs equal to total revenues and solve for x. In this case, the total costs are given by C(x) = 2750 + 30x + 2, and the total revenues are given by R(x) = 135x.

The break-even point is when C(x) = R(x), so:

2750 + 30x + 2 = 135x

Now, we need to solve for x:

1. Subtract 30x from both sides:
2750 + 2 = 105x

2. Subtract 2 from both sides:
2750 = 105x

3. Divide both sides by 105:
x = 2750 / 105
x ≈ 26.19

The break-even x-value for Year-round-Recreation is approximately 26.19.

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a. i) The standard form of equation of circle is (x + 3)² + (y + 9)² = 1

ii) The center and radius of the circle is: centre (-3, -9) and the radius is √1 = 1.

b. The domain of (fog)(x) is (-∞, 2) ∪ (2, ∞).

A circle is a closed curve that is drawn from the fixed point called the center, in which all the points on the curve are having the same distance from the center point of the center. The equation of a circle with (h, k) center and r radius is given by:

(x-h)² + (y-k)² = r²

a. i) To write the equation of the circle in standard form, we need to complete the square for both x and y terms:

x² + 6x + y² + 18y + 89 = 0

(x² + 6x + 9) + (y² + 18y + 81) = -89 + 9 + 81

(x + 3)² + (y + 9)² = 1

ii) Comparing the equation with the standard form of a circle:

(x - h)² + (y - k)² = r²

We can see that the center is (-3, -9) and the radius is √1 = 1.

b. (fog)(x) means we need to plug g(x) into f(x):

f(g(x)) = f(x - 2)

Without knowing what f(x) is, we can't simplify the expression further. However, we can determine the domain of (fog)(x) based on the domain of g(x), which is all real numbers except x = 2 (since we can't divide by zero). So the domain of (fog)(x) is (-∞, 2) ∪ (2, ∞).

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The equation when solved for x gives x = √3 - 5y

It is important to note that the subject of formula in an equation is the variable that is being worked out.

This variable is made to stand alone on one end of the equality sign.

From the information given, we have the equation;

y = 3√(x²+3)÷15

cross multiply the values

15y = 3√(x²+3)

Divide both sides by the coefficient of √(x²+3)

15y/3 = √(x²+3)

Divide the values

5y = √(x²+3)

Find the square of both sides

25y² = x² + 3

collect terms

x² = 3 - 25y²

Find the square root

x = √3 - 5y

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Answer:I can't see the question

Step-by-step explanation:

If x represents the smaller of the two numbers, then the larger number can be represented as x + 56 (since the difference between the two numbers is 56).

Large numbers are numbers that are larger than those used in everyday life, such as simple calculations or currency operations, and often appear in fields such as mathematics, cosmology, cryptography, and similar mathematical machine. These are usually good numbers or more likely really good numbers, but there may be other numbers in other situations.

Given that the difference between the two numbers is 56, and x represents the smaller number, the larger number can be represented as x + 56.

This is because the larger number is 56 units greater than the smaller one (x). So, the larger number is given by the expression: x + 56.

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To determine which offer will provide a greater total income after 5 years, we need to calculate the total amount of income earned from each offer over the 5-year period.

For Offer A:
Annual interest rate = 5%
Principal amount = $10,000
Time period = 5 years

Total amount earned = Principal x (1 + Annual interest rate)^Time period
= $10,000 x (1 + 0.05)^5
= $12,762.82

Total income earned = Total amount earned - Principal
= $12,762.82 - $10,000
= $2,762.82

For Offer B:
Annual interest rate = 4%
Principal amount = $12,000
Time period = 5 years

Total amount earned = Principal x (1 + Annual interest rate)^Time period
= $12,000 x (1 + 0.04)^5
= $14,612.52

Total income earned = Total amount earned - Principal
= $14,612.52 - $12,000
= $2,612.52

Therefore, Offer B will provide a greater total income after 5 years, with a total income earned of $2,612.52, compared to Offer A's total income earned of $2,762.82.

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The Cronbach's alpha coefficient α for these teacher-IQ ranks is 0.701.

To calculate the alpha coefficient for these data, we need to use a statistical software package or spreadsheet program that has this function built-in. Here is an example of how to calculate alpha using Microsoft Excel:

Enter the ranks and IQ scores into two columns.

Select the two columns of data.

Click on the "Data" tab in the Excel ribbon.

Click on "Data Analysis" in the "Analysis" section of the ribbon.

Select "Cronbach's Alpha" from the list of analysis tools.

Click "OK."

In the "Input Range" field, select the two columns of data.

In the "Item Labels" field, select the column with the ranks.

Click "OK."

The resulting Cronbach's alpha coefficient is 0.701, which indicates good internal consistency among the teacher's rankings.

This suggests that the teacher's rankings were not solely based on the children's IQ scores, as the alpha coefficient would be higher if that were the case.

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The same constant rate of change as Michael's is depicted in following ratio - 180 page in 2 hours, 225 pages in 150 minutes and 210 pages in 2 hour 20 minutes.

The rate of reading Michael is -

Rate = 135/90

Rate = 3:2

Now, we will check the options to see if they have same ratio.

Option 1 180 page in 2 hours

As known about time conversion that 1 hour has 60 minutes, 2 hours = 120 minutes

So, Rate = 180/120

Rate = 3:2

Option 2 60 pages in 30 minutes

Rate = 60/30

Rate = 2:1

Option 3 108 pages in 2 and half hours

Time = 2.5 hours

Time = 150 minutes

Rate = 108/150

Rate = 18:25

Option 4 150 page in 1 hour

Rate = 150/60

Rate = 5:2

Option 5 225 pages in 150 minutes

Rate = 225/150

Rate = 3:2

Option 6 210 pages in 2 hour 20 minutes

Time = 140 minutes

Rate = 210/140

Rate = 3:2

Hence, the same rate options are 180 page in 2 hours, 225 pages in 150 minutes and 210 pages in 2 hour 20 minutes.

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The complete question is -

Michael read 135 pages in 90 minutes. Select all of the rates that have the same constant rate of change as Michael's rate. 180 pages in 2 hours, 60 pages in 30 minutes, 108 pages in 2 and half hours, 150 pages in 1 hour, 225 pages in 150 minutes, 210 pages in 2 hour 20 minutes

Using the Law of Sines, we can solve the given triangle with B = 52, C = 15, and b = 43. The three angles of the triangle are approximately A = 112.94°, B = 52°, and C = 15°, and the lengths of the sides opposite these angles are approximately a = 28.29, b = 43, and c = 8.11.

The Law of Sines states that in any triangle, the ratio of the length of a side to the sine of its opposite angle is the same for all sides and their opposite angles. Therefore, we can use the Law of Sines to solve the given triangle as follows

sin(A)/a = sin(B)/b = sin(C)/c

We are given B = 52, C = 15, and b = 43, so we can use the Law of Sines to find a

sin(A)/a = sin(B)/b

sin(A)/a = sin(52)/43

sin(A) = a sin(52)/43

a = 43 sin(A)/sin(52)

Similarly, we can use the Law of Sines to find c

sin(A)/a = sin(C)/c

sin(A)/a = sin(15)/c

sin(15)c = a sin(A)

c = a sin(A)/sin(15)

Now, we can substitute the expressions for a and c into the equation sin(A)/a = sin(B)/b and solve for sin(A)

sin(A)/(43 sin(A)/sin(52)) = sin(52)/43

sin(A) = (43 sin(52) sin(15))/c

Substituting the expression for c, we get

sin(A) = (43 sin(52) sin(15))/(a sin(A)/sin(15))

Simplifying, we get

sin²(A) = (43²sin²(52) sin²(15))/(a²sin²(A))

Multiplying both sides by a^2 sin^2(A), we get

a²sin⁴(A) = 43^2 sin²(52) sin²(15)

Taking the square root of both sides and solving for a, we get

a = √((43² sin₂(52) sin²(15))/(sin⁴A)))

Substituting the given values and solving for A, we get

a = 28.29 (approx)

A = 112.94° (approx)

c = 8.11 (approx)

Therefore, the three angles of the triangle are approximately A = 112.94°, B = 52°, and C = 15°, and the lengths of the sides opposite these angles are approximately a = 28.29, b = 43, and c = 8.11.

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Answer: 17/25 miles per hour

Step-by-step explanation:

In order to find your answer, you will need to divide 3 and 2/5 by 5 hours

or (3.4/5) which equals 0.68.

As a fraction, 0.68 is 17/25 which is your answer :)

And if you want to check your work, simply multiply 0.68 x 5 and you get 3.4 (which is 3 and 2/5's)!

Good Luck!

Sample = 102 nests
Failed nests = 64

Proportion of failed nests = p = 64/102 = 0.6275

95% interval is given as:

p ± z x √ ( p( 1-p /n))

Note that

z = z-score related to 95% = 1.96

so

0.6275 ± 1.96 x (√(0.6275 (1-0.6275) /102) )

0.6275  ±  0.09382660216

95% Confidence interval  = (0.721, 0.031)


b) H⁰ : P = 0.29
Ha : p > 0.29

z = (0.6275 - 0.29) / √(0.29(1-0.29)/102)

= 7.51182894275

= 7.51

Since the test is greater than the critical value, we must reject the null hypothesis.

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Full Question:

One difficulty in measuring the nesting success of birds is that the researchers must count the number of eggs in the nest, which is disturbing to the parents. Even though the researcher does not harm the birds, the flight of the bird might alert predators to the presence of a nest. To see if researcher activity might degrade nesting success, the nest survival of 102 nests that had their eggs counted, was recorded. Sixty-four of the nests failed (i.e. the parent abandoned the nest.)

a) Construct and interpret a 95% confidence interval for the proportion of nest failures in the population I

b) The usual nest failure rate of these birds is 29%. Based on the confidence interval from part (a), is this consistent with the theory that the researcher's activity affects nesting success? Justify your answer with an appropriate statistical

The GCF of 20xyz and 30x^2z is: 2*5*x*z = 10xz

To find the greatest common factor (GCF) of 20xyz and 30x^2z, we can factor out the common factors that they share.

Identifying the common factors in the two monomials:

20xyz = 2 * 2 * 5 * x * y * z

30x^2z = 2 * 3 * 5 * x * x * z

The GCF is the product of the common factors raised to the lowest power that they appear in both monomials.

Therefore, the GCF of 20xyz and 30x^2z is:

2 * 5 * x * z = 10xz

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The measurement which is closest to the length of each side of the tablecloth is 6.9 feet.

It follows from the task content that the measurement which is closest to the length of each side of the tablecloth in feet.

Total area of the square tablecloth = 48 square feet

Area of a square = Side length²

48 = Side length²

Find the square root of both sides

Side length = √48

= 6.928203230275

Approximately,

Side length = 6.9 feet

Therefore, the side length of the table cloth is 9.6 feet.

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The amount of money Lily spent on peanuts and water is 2.75 dollars.

Noah spent $2.50 on 2 bags of peanuts and 1 bottle of water at a baseball game.

Emily spent $4.25 on 3 bags of peanuts and 2 bottles of water.

Using equation,

where

Therefore,

2x + y = 2.50

3x + 2y = 4.25

multiply equation(i) by 2

4x + 2y = 5

3x + 2y = 4.25

x = 0.75 dollars

y = 2.50 - 2(0.75)

y = 2.50 - 1.5

y  = 1 dollars

Therefore,

cost of Lily expenses = 2(1) + 0.75(1)

cost of Lily expenses = 2 + 0.75

cost of Lily expenses = 2.75 dollars

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