Kind people!help me please...And a detailed solution/THANKS sin^2x-0,5sin2x=0

1 answer:

Volgvan3 years ago

8 0

This will be easier to write, and a lot easier to read, if we temporarily
use another symbol ... say, 'Q' ... to represent ' sin(2x) ' .
Here we go:

Original equation:    Q² - 0.5 Q = 0

Factor the left side:    Q (Q - 0.5) = 0

This equation is true if either factor is zero:

-- If Q=0, then sin(2x) = 0

   2x = 0°, 180°, 360°

   x = 0°, 90°, 180°

-- If (Q-0.5) = 0, then    Q = 0.5

      sin(2x) = 0.5

   2x = 30°, 150°

   x = 15°, 75°

The whole collection of solutions
between 0° and 360° :

      x = 0°, 15°, 75°, 90°, 180° .

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Answer:

99.5% of all samples of 21 of today's women in their 20's have mean heights of at least 65.86 inches.

Step-by-step explanation:

We are given that a half-century ago, the mean height of women in a particular country in their 20's was 64.7 inches. Assume that the heights of today's women in their 20's are approximately normally distributed with a standard deviation of 2.07 inches.

Also, a samples of 21 of today's women in their 20's have been taken.

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The z-score probability distribution for sample mean is given by;

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where, $\mu$ = population mean height of women = 64.7 inches

$\sigma$ = standard deviation = 2.07 inches

The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X.

Now, Probability that the sample of 21 of today's women in their 20's have mean heights of at least 65.86 inches is given by = P( $\bar X$ $\geq$ 65.86 inches)

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