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4 years ago

Is the point 3/5 and 4/5 corresponds to an angle in the unit circle what is the csc

Mathematics

1 answer:

Mariulka [41]4 years ago

8 0

Answer:

csc = 5/4

Step-by-step explanation:

Assuming that the two given points 3/5 and 4/5 are the two sides of a triangle and a right angle 0 with legs x and y and z as its hypotenuse.

Then using Pythagoras Theorem:

$z^2=x^2+y^2$

$z^2=(\frac{3}{5} )^2+(\frac{4}{5} )^2$

$z^2 = \frac{9}{25} + \frac{16}{25}$

$z^2=\frac{25}{25}$

$z^2=1$

Taking square root on both the sides:

$z=1$

Now, $sin\alpha=\frac{4}{5}$

and we know that $csc = \frac{1}{sin\alpha }$

Therefore, csc = 5/4.

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A random sample of 100 teletype operators indicates that their salaries fluctuate quite a bit. The sample Standard deviation of

ELEN [110]

Answer:

$\frac{(99)(10)^2}{123.225} \leq \sigma^2 \leq \frac{(99)(10)^2}{77.046}$

$80.341 \leq \sigma^2 \leq 128.495$

Now we just take square root on both sides of the interval and we got:

$8.963 \leq \sigma \leq 11.336$

Step-by-step explanation:

Data given and notation

s=10 represent the sample standard deviation

$\bar x$ represent the sample mean

n=100 the sample size

Confidence=90% or 0.90

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population mean or variance lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

The Chi Square distribution is the distribution of the sum of squared standard normal deviates .

Calculating the confidence interval

The confidence interval for the population variance is given by the following formula:

$\frac{(n-1)s^2}{\chi^2_{\alpha/2}} \leq \sigma^2 \leq \frac{(n-1)s^2}{\chi^2_{1-\alpha/2}}$

The next step would be calculate the critical values. First we need to calculate the degrees of freedom given by:

$df=n-1=100-1=99$

Since the Confidence is 0.90 or 90%, the value of $\alpha=0.1$ and $\alpha/2 =0.05$ , and we can use excel, a calculator or a table to find the critical values.