A flagpole is 10 feet tall. Its shadow is 12 feet long. How far is it from the top of the flagpole to the end of its shadow

Preston started the summer owing $15 to his brother and $20 to his sister. He earned $75 mowing lawns, and paid his brother and

joja [24]

Answer:

$75 - $15 - $20 = $40

Step-by-step explanation:

Given that:

Money owed by Preston to his brother = $15

Money owed by Preston to his sister = $20

Total money earned by Preston = $75

Now, the money is paid back that he owed to his sister and brother.

To find:

The expression to represent the amount of money left with Preston after clearing all his dues?

Solution:

Once Preston pays back the money that he owed to his brother and sister, he will not have all $75 left with him.

He will have lesser amount of money.

Money left with Preston = Total money earned by Preston - Money owed to brother - Money owed to sister

Putting the values given as per the question statement, we get:

Money left with Preston = $75 - $15 - $20 = $40

Therefore, the expression to represent the amount of money left with Preston =<em> $75 - $15 - $20 = $40</em>

8 0

3 years ago

The distribution of the number of people in line at a grocery store has a mean of 3 and a variance of 9. A sample of the numbers

Airida [17]

Answer:

a) $P(\bar X >4)=P(Z>\frac{4-3}{\frac{3}{\sqrt{50}}}=2.357)$

$P(Z>2.357)=1-P(Z$

b) $P(\bar X \frac{2.5-3}{\frac{3}{\sqrt{50}}}=-1.179)$

$P(Z$

c)

$P(2.5 < \bar X< 3.5) = P(\frac{2.5-3}{\frac{3}{\sqrt{50}}}$

$P(-1.179$ Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

Part a

Let X the random variable that represent the number of people of a population, and for this case we know that:

Where $\mu=3$ and $\sigma=\sqrt{9}=3$

The central limit theorem states that "if we have a population with mean μ and standard deviation σ and take sufficiently large random samples from the population with replacement, then the distribution of the sample means will be approximately normally distributed. This will hold true regardless of whether the source population is normal or skewed, provided the sample size is sufficiently large".

From the central limit theorem we know that the distribution for the sample mean $\bar X$ is given by: