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storchak [24]
3 years ago
14

3 A buoy is 30 feet from the shore. You swim 3/5 the way to the buoy. How much farther do you have to swim to reach the buoy?​

Mathematics
1 answer:
disa [49]3 years ago
8 0

Answer:

12 feet

Step-by-step explanation:

30 divided by 5= 6

6 times 3= how far youve already swam(18 feet)

6 times 2= how far you have left(12 feet)

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

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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.  

The excel commands would be: "=CHISQ.INV(0.05,99)" "=CHISQ.INV(0.95,99)". so for this case the critical values are:

\chi^2_{\alpha/2}=123.225

\chi^2_{1- \alpha/2}=77.046

And replacing into the formula for the interval we got:

\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:

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