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nadezda [96]
3 years ago
13

Which trigonometric functions always have values less than 1? Explain your answer.

Mathematics
1 answer:
raketka [301]3 years ago
3 0

Answer:

Notice that the values of sine and cosine are between 0 and 1. You found them by dividing the length of a leg by the hypotenuse. The hypotenuse is the longest side, so the numerator is less than the denominator. That means the output of the sine or cosine function is always less than 1.

Step-by-step explanation:

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You'll need to convert both speeds into yards per minute.

12 mph = 12 mph     1760 yd    60 min
                ---------- * ------------ * ----------
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Note that "miles" cancels.  So does "hours."  Finish this work.

Then convert   4.4 ft/sec into yards per minute.

Then, finally, compare your two rates via subtraction of the smaller from the larger.
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Suppose a simple random sample of size nequals36 is obtained from a population with mu equals 74 and sigma equals 6. ​(a) Descri
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Part a)

The simple random sample of size n=36 is obtained from a population with

\mu = 74

and

\sigma = 6

The sampling distribution of the sample means has a mean that is equal to mean of the population the sample has been drawn from.

Therefore the sampling distribution has a mean of

\mu = 74

The standard error of the means becomes the standard deviation of the sampling distribution.

\sigma_ { \bar X }  =  \frac{ \sigma}{ \sqrt{n} }  \\ \sigma_ { \bar X }  =  \frac{ 6}{ \sqrt{36} }  = 1

Part b) We want to find

P(\bar X \:>\:75.9)

We need to convert to z-score.

P(\bar X \:>\:75.9)  = P(z \:>\: \frac{75.9 - 74}{1} )  \\  = P(z \:>\: \frac{75.9 - 74}{1} ) \\  = P(z \:>\: 1.9) \\  = 0.0287

Part c)

We want to find

P(\bar X \: < \:71.95)

We convert to z-score and use the normal distribution table to find the corresponding area.

P(\bar X \: < \:71.95)  = P(z \: < \: \frac{71.9 5- 74}{1} )  \\  = P(z \: < \: \frac{71.9 5- 74}{1} ) \\  = P(z \: < \:  - 2.05) \\  = 0.0202

Part d)

We want to find :

P(73\:

We convert to z-scores and again use the standard normal distribution table.

P( \frac{73 - 74}{1} \:< \: z

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