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masha68 [24]
3 years ago
15

Determine the coordinates of the point on the unit circle corresponding to the given central angle. If necessary round your resu

lts to the nearest hundredth 180

Mathematics
1 answer:
Olenka [21]3 years ago
3 0

Answer:

Option A. (-1, 0)

Step-by-step explanation:

In the figure attached,

Circle O is a unit circle (having radius r = 1 unit)

If a point A with central angles = θ, is lying on the circle then the coordinates of the point A will be,

x = r.cosθ

x = 1.cosθ = cosθ

and y = r.sinθ

y = 1.sinθ = sinθ

Therefore, coordinates representing the point A will be (cosθ, sinθ).

As per question the given point A is lying at P (a point having central angle θ = 180°)

Coordinates of point P will be

(x', y') → (cos180°, sin180°)

        → (-1, 0)

Therefore, Option A will be the answer.

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P(5.5

And we can find this probability using the normal standard distribution or excel and we got:

P(-2.769

Step-by-step explanation:

For this case we assume the following complete question: "The pucks used by the National Hockey League for ice hockey must weigh between 5.5 and 6 ounces. Suppose the weights of pucks produced at a factory are normally distributed with a mean of 5.86 ounces and a standard deviation of 0.13ounces. What percentage of the pucks produced at this factory cannot be used by the National Hockey League? Round your answer to two decimal places. "

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

Solution to the problem

Let X the random variable that represent the weights of a population, and for this case we know the distribution for X is given by:

X \sim N(5.86,0.13)  

Where \mu=5.86 and \sigma=0.13

We are interested on this probability

P(5.5

And the best way to solve this problem is using the normal standard distribution and the z score given by:

z=\frac{x-\mu}{\sigma}

If we apply this formula to our probability we got this:

P(5.5

And we can find this probability using the normal standard distribution or excel and we got:

P(-2.769

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