Whats is six over 9 + 1 over 3 ​

Answer:

How far did the ship travel between the two observations of the lighthouse  = 9.29

Step-by-step explanation:

the first step to answer this question is drawing the illustration as the attachment.

P is the ship, R is the light house and Q is the bearing.

PR is the distance between the ship and the light house, PR = 10.5

∠P = 42.8°, ∠Q = 59.7°

Thus, ∠R = 180° - ∠P  - ∠Q

               = 180° - 42.8°- 59.7°

               = 77.5°

PQ is the the distance of the ship moving. We can use the sinus equation

=

=

PQ = ()(sin 59.7°)

     = 9.29

Final answer:

Using trigonometric principles, the ship is estimated to have traveled approximately 19.8 miles between the two observations.

Explanation:

Your question involves the application of trigonometry in real life, in this case, calculating the distance traveled by a ship. The first sighting puts the lighthouse at N 42.8 degrees E, and the second sighting puts it at S 59.7 degrees E. So, the angle turned by the ship, relative to the lighthouse is 42.8 degrees + 59.7 degrees = 102.5 degrees.

We know the distance to the lighthouse from the first sighting is 10.5 units (let's say miles), and we need to find the distance traveled by the ship in the meantime. So, if we draw this situation it will resemble a triangle with the lighthouse as one point, and the initial and final positions of the ship as other points. The triangle will have one angle (between the initial position of the ship, the lighthouse, and the final position of the ship) of 102.5 degrees and one side (distance from the lighthouse to the initial position of the ship) of 10.5 miles. Now, the side of a triangle opposite an angle in a triangle is given by the side adjacent to the angle times the tangent of the angle.

So, the distance traveled by the ship = 10.5 * tan(102.5) = 19.8 miles approximately.

Learn more about Trigonometry here:

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Answer:120

Step-by-step explanation: 1/5 x 1/4 = 120.

Answer:

The graphs are attached.

Answer:

She worked 18 hours of overtime.

Step-by-step explanation:

If she works 40 hours per week and gets $200, subtract $380 - $200 = $180.

If you multiply $180 by 0.1 (which is 10% converted to a decimal), you get 18 which is your final answer.

The probability that a randomly selected adult has a height over 7 feet is nearly 100%, which means it's very likely that a randomly selected adult will have a height over 7 feet in this normal distribution.

To find the probability that a randomly selected adult has a height over 7 feet in a normal distribution with a mean of 5.5 feet and a standard deviation of 0.5 feet, you can use the Z-score and the standard normal distribution table.

First, calculate the Z-score for a height of 7 feet using the formula:

Where:

- X is the value you're interested in (in this case, 7 feet).

- μ (mu) is the mean (5.5 feet).

- σ (sigma) is the standard deviation (0.5 feet).

Now, you have the Z-score, which represents how many standard deviations above the mean the height of 7 feet is.

Next, you can use a standard normal distribution table or calculator to find the probability associated with a Z-score of 3. In most standard normal distribution tables, a Z-score of 3 corresponds to a probability close to 1 (or 100%).

To know more about  normal distribution:

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