What is the exact value of sin pi/3?

The measure of angle 1 is given as 130 degrees.the measure of angle 1 is 130 degrees provides specific information about the amount of rotation between the two rays or lines

An angle is a geometric figure formed by two rays or lines that share a common endpoint called the vertex. The measure of an angle is determined by the amount of rotation between the two rays or lines.

In this case, angle 1 has a measure of 130 degrees. This means that if we were to rotate one of the rays or lines forming the angle by 130 degrees, it would coincide with the other ray or line.

The degree is a unit of measurement for angles, and it is based on dividing a full circle into 360 equal parts. Each part, or degree, corresponds to a specific amount of rotation. In this case, angle 1 is measured to be 130 degrees, which is less than half of a full circle.

When interpreting the measure of angle 1, it's important to consider the context in which it is being used. Angles can be found in various settings, such as geometry, trigonometry, or real-world applications. Depending on the context, the measure of an angle can have different interpretations and implications.

In geometry, angles are used to describe the relationships between lines, shapes, and spatial configurations. They are often classified based on their measures, such as acute (less than 90 degrees), right (exactly 90 degrees), obtuse (greater than 90 degrees but less than 180 degrees), or straight (exactly 180 degrees).

In trigonometry, angles are used to define the ratios of sides in right triangles and to study periodic functions such as sine and cosine.

In real-world applications, angles can be used to measure directions, inclinations, or orientations of objects or phenomena.

Therefore, knowing that the measure of angle 1 is 130 degrees provides specific information about the amount of rotation between the two rays or lines

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We can use the logarithmic identity log_a(b) + log_a(c) = log_a(bc) to simplify the left side of the equation:

log_2(x) + log_4(x+1) = log_2(x) + log_2((x+1)^(1/2))

Using the rule log_a(b^c) = c*log_a(b), we can simplify further:

log_2(x) + log_2((x+1)^(1/2)) = log_2(x(x+1)^(1/2))

Now we can rewrite the equation as:

log_2(x(x+1)^(1/2)) = 3

Using the rule log_a(b^c) = c*log_a(b), we can rewrite this as:

x(x+1)^(1/2) = 2^3

Squaring both sides, we get:

x^2 + x - 8 = 0

This is a quadratic equation that can be solved using the quadratic formula:

x = (-b ± sqrt(b^2 - 4ac)) / 2a

where a = 1, b = 1, and c = -8. Plugging in these values, we get:

x = (-1 ± sqrt(1^2 - 4(1)(-8))) / 2(1)

x = (-1 ± sqrt(33)) / 2

x ≈ -2.54 or x ≈ 3.54

However, we must check our solutions to make sure they are valid. Plugging in x = -2.54 to the original equation results in an invalid logarithm, so this solution is extraneous. Plugging in x = 3.54 yields:

log_2(3.54) + log_4(4.54) = 3

0.847 + 0.847 = 3

So x = 3.54 is the valid solution to the equation.

Answer:

0.2369

Step-by-step explanation:

To find the probability of exactly 3 out of 12 randomly selected college students working full time, we can use the binomial probability formula.

The formula for the probability of exactly k successes in n trials, where the probability of success is p, is:

P(X = k) = (n choose k) * p^k * (1 - p)^(n - k)

In this case, n = 12 (number of trials), k = 3 (number of successes), and p = 0.20 (probability of success, i.e., percentage of college students working full time).

Plugging in the values:

P(X = 3) = (12 choose 3) * 0.20^3 * (1 - 0.20)^(12 - 3)

Calculating the expression:

P(X = 3) = (12! / (3! * (12 - 3)!)) * 0.20^3 * (0.80^9)

= (12! / (3! * 9!)) * 0.008 * 0.134217728

≈ 0.2369 (rounded to 4 decimal places)

Therefore, the probability that exactly 3 out of the 12 randomly selected college students work full time is approximately 0.2369.

Hope this helps!

The value of x is calculated as 30.

The value of y is calculated as 28.

The measure of x and y is calculated by applying the following circle theorem as follows;

If line XZ is the diameter of the circle, then angle XYZ will be equal to 90 degrees.

The value of x is calculated as;

3x = 90

x = 90 / 3

x = 30

The value of y is calculated as follows;

2y + 34 = 90 (complementary angles sum up to 90 degrees)

2y = 56

y = 56/2

y = 28

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Step-by-step explanation:

To eliminate x in the system of equations:

1. Multiply Equation 1 by 9 and multiply Equation 2 by -4, this gives:

Equation 1: 36x -54y = 90

Equation 2: -36x - 8y = -28

2. Add the two equations together to eliminate x:

(36x - 54y) + (-36x - 8y) = 90 - 28

Simplifying, we get:

-62y = 62

3. Solve for y:

y = -1

4. Substitute y = -1 into one of the original equations, say Equation 1:

4x - 6(-1) = 10

Simplifying, we get:

4x + 6 = 10

5. Solve for x:

4x = 4

x = 1

Therefore, the solution to the system of equations is x = 1 and y = -1. We can check that these values are correct by substituting them back into the original equations and verifying that they satisfy both equations.

1. The area of the Earth's surface covered in water is approximately 0.71 * 201,061,929 = 142,550,781 square miles.

2. Approximately 1.76% of the Earth's surface lies in the United States.

3. The volume of the entire Earth is approximately 268,082,573,106 cubic miles.

To answer Alonzo's questions, let's calculate the required values using the given information:

1. The area of the Earth's surface that is covered in water:

The Earth's surface area can be calculated using the formula for the surface area of a sphere: 4πr^2. Given that the radius of the Earth is approximately 4,000 miles, we have:

Surface area of the Earth = 4π(4,000)^2 = 4π(16,000,000) ≈ 201,061,929 square miles.

Alonzo can research and find that about 71% of the Earth's surface is covered in water. Thus, the area of the Earth's surface covered in water is approximately 0.71 * 201,061,929 = 142,550,781 square miles.

2. The percent of the Earth's surface that lies in the United States:

The land area of the United States is approximately 3,537,438 square miles. To calculate the percentage, we divide the land area of the United States by the total surface area of the Earth and multiply by 100:

Percentage = (3,537,438 / 201,061,929) * 100 ≈ 1.76%.

Therefore, approximately 1.76% of the Earth's surface lies in the United States.

3. The volume of the entire Earth:

The volume of a sphere can be calculated using the formula: (4/3)πr^3. Substituting the radius of the Earth, we have:

Volume of the Earth = (4/3)π(4,000)^3 = (4/3)π(64,000,000,000) ≈ 268,082,573,106 cubic miles.

Thus, the volume of the entire Earth is approximately 268,082,573,106 cubic miles.

These calculations provide Alonzo with the approximate values he needs regarding the Earth's surface area covered in water, the percentage of the Earth's surface within the United States, and the volume of the entire Earth.

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The pulley ratio is approximately 0.6667, calculated by dividing the Diameter of pulley A (5.74 cm) by the diameter of pulley B (8.61 cm).

The pulley ratio, we need to compare the diameters of the two pulleys. The pulley ratio is the ratio of the diameters of pulley A to pulley B.

Given that the diameter of pulley A is 5.74 cm and the diameter of pulley B is 8.61 cm, we can calculate the pulley ratio using the following steps:

Step 1: Write down the diameters of pulley A and pulley B.

  Diameter of pulley A = 5.74 cm

  Diameter of pulley B = 8.61 cm

Step 2: Calculate the pulley ratio.

  Pulley ratio = Diameter of pulley A / Diameter of pulley B

Substituting the given values, we have:

  Pulley ratio = 5.74 cm / 8.61 cm

Step 3: Simplify the ratio if possible.

  In this case, the ratio cannot be simplified further since the diameters do not have any common factors other than 1.

Step 4: Calculate the final result.

  Pulley ratio = 5.74 cm / 8.61 cm ≈ 0.6667 (rounded to four decimal places)

Therefore, the pulley ratio is approximately 0.6667.

When discussing technical concepts and calculations, it is important to maintain academic integrity and avoid plagiarism. Plagiarism involves using someone else's work or ideas without proper attribution. To ensure originality, it is essential to express the information in your own words and provide accurate calculations based on the given data.

In conclusion, the pulley ratio is approximately 0.6667, calculated by dividing the diameter of pulley A (5.74 cm) by the diameter of pulley B (8.61 cm).

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The probability of drawing a purple marble from the bag is 44%.

The probability of drawing a purple marble can be determined by subtracting the sum of the probabilities of drawing an orange and a white marble from 1, since these three events are mutually exclusive and exhaustive.

Given that there is a 36% chance of drawing an orange marble and a 20% chance of drawing a white marble, the sum of these probabilities is 36% + 20% = 56%.

To find the probability of drawing a purple marble, we subtract this sum from 100% (or 1):

1 - 56% = 44%.

Therefore, the probability of drawing a purple marble from the bag is 44%.

In summary, when randomly choosing a marble from the bag, there is a 36% chance of selecting an orange marble, a 20% chance of selecting a white marble, and a 44% chance of selecting a purple marble. These probabilities add up to 100%, ensuring that one of the three outcomes will occur.

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Jordan bikes at a Faster speed than Hayden because he covers a greater distance in the same amount of time.

To determine who bikes at a faster speed, we can compare the rates at which Hayden and Jordan cover distance over a given time period.

Hayden bikes 1.8 miles in 6 minutes, which can be expressed as a rate of 1.8 miles / 6 minutes = 0.3 miles per minute.

Jordan bikes 3.2 miles in 8 minutes, which can be expressed as a rate of 3.2 miles / 8 minutes = 0.4 miles per minute.

Comparing the two rates, we can see that Jordan bikes at a faster speed. Jordan covers a greater distance (3.2 miles) in the same amount of time (8 minutes) compared to Hayden, who only covers 1.8 miles in 6 minutes. Therefore, Jordan's rate of 0.4 miles per minute is greater than Hayden's rate of 0.3 miles per minute, indicating that Jordan bikes at a faster speed.

In summary, Jordan bikes at a faster speed than Hayden because he covers a greater distance in the same amount of time.

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The calculation of this can be done by first determining the future value of the monthly payments of $327.50

The future value of an annuity can be determined using a financial calculator, mathematical formula, or spreadsheet software. The future value of an annuity is calculated by multiplying the periodic payment amount by the future value factor,

which is based on the number of payments and the interest rate.For example, suppose we want to know the future value of a $500 end-of-month deposit into an annuity that pays 6% interest compounded monthly for five years.

The future value factor for 60 periods at 0.5 percent per month is 80.9747, which can be multiplied by the monthly deposit amount to find the future value of the annuity.500 × 80.9747 = 40,487.35

This means that a $500 end-of-month deposit into an annuity paying 6% interest compounded monthly for five years will have a future value of $40,487.35.

Therefore, to accumulate a $20,000 down payment for a home in five years, you would need to deposit $327.50 per month into the annuity.

 for 60 months using the formula and then solving for the monthly payment amount where FV = $20,000 and n = 60, r = 0.5%.FV = PMT [(1 + r)n – 1] / r$20,000 = PMT [(1 + 0.005)60 – 1] / 0.005PMT = $327.50 (rounded to the nearest cent).

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