The lengths of the legs of a right triangle are 6 cm and 3 cm.

Valentin [98]

The you are asking for is is 239

8 0

3 years ago

Life Expectancies In a study of the life expectancy of people in a certain geographic region, the mean age at death was years an

Sphinxa [80]

Answer:

The probability that the mean life expectancy of the sample is less than X years is the p-value of $Z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}$ , in which $\mu$ is the mean life expectancy, $\sigma$ is the standard deviation and n is the size of the sample.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the z-score of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value 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. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

We have:

Mean $\mu$ , standard deviation $\sigma$ .

Sample of size n:

This means that the z-score is now, by the Central Limit Theorem:

$Z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}$

Find the probability that the mean life expectancy will be less than years.

The probability that the mean life expectancy of the sample is less than X years is the p-value of $Z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}$ , in which $\mu$ is the mean life expectancy, $\sigma$ is the standard deviation and n is the size of the sample.

8 0

2 years ago

Gasoline costs 1.05 euro per liter in France. What is the price in dollars per gallon?

Alecsey [184]

The price in dollars per gallon is 4.02 dollars per gallons.

<h3>How to find the price of gasoline in dollars per gallon?</h3>

Gasoline costs 1.05 euro per litre in France.

The first thing to do is to determine the equivalent amount of the same litre in dollar while in France.

Then, equate it the quantity of litres to gallons.

Hence,

1 euro = 1.01 dollars

1.05 euro = ?

cross multiply

price = 1.05 × 1.01

price = 1.0605 dollars

1 litres = 0.264172 gallons

Therefore,

cost = 1.0605 / 0.264172

cost = 4.01552442257 dollars per gallons

cost = 4.02 dollars per gallons

Therefore, the price in dollars per gallon is 4.02 dollars per gallons.

learn more on price here: brainly.com/question/14501882

#SPJ1

6 0

1 year ago

State if the two triangles are similar and the rule that applies.

kobusy [5.1K]

Answer:

The SAS rule states that two triangles are similar if the ratio of their corresponding two sides is equal and also, the angle formed by the two sides is equal. Side-Side-Side (SSS) rule: Two triangles are similar if all the corresponding three sides of the given triangles are in the same proportion.

Step-by-step explanation:

3 0

1 year ago

Multiply.

Nady [450]

$\boxed{3\sqrt{22}\sqrt{58}\sqrt{18}=18\sqrt{638}}$