In the figure below, triangle RPQ is similar to triangle RTS.

Mathematics

2 answers:

kumpel [21]3 years ago

8 0

Answer:

The distance between P and Q is 54

Step-by-step explanation:

We are given that triangle RPQ is similar to triangle RTS.

Property of similar triangle: The ratio of any pair of corresponding sides is the same.

So, by property : $\frac{RP}{RT}=\frac{PQ}{ST}$

PR=42

PQ=x

ST=36

RT=28

So, $\frac{42}{28}=\frac{x}{36}$

$\frac{42 \times 36}{28}=x$

54=x

Hence the distance between P and Q is 54

Colt1911 [192]3 years ago

3 0

Answer:

Step-by-step explanation:

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The sugar content of the syrup in canned peaches is normally distributed. A random sample of n = 10 cans yields a sample standar

Serggg [28]

Answer:

The 95% confidence interval is given by:

3.30<σ<8.76

Step-by-step explanation:

1) Data given and notation

s=4.798 represent the sample standard deviation

$\bar x$ represent the sample mean

n=10 the sample size

Confidence=95% or 0.95

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 .

2) 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:

$df=n-1=10-1=9$

Since the Confidence is 0.95 or 95%, the value of $\alpha=0.05$ and $\alpha/2 =0.025$ , and we can use excel, a calculator or a tabel to find the critical values.