Rewrite the equation of the circle (x-2)^2+y^2=3 in general form

12-(x+3)=10

Simplify the equation.

12-x-3=10

Combine like terms.

(12-3)-x=10

Simplify.

9-x=10

Subtract 9 from both sides to get x by itself.

-x=1

Divide both sides by -1 to get x by itself.

x=-1

~Hope I helped!~

4 0

3 years ago

After the accounts have been adjusted at December 31, the end of the fiscal year, the following balances were taken from the led

Leni [432]

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8 0

3 years ago

A study of college football games shows that the number of holding penalties assessed has a mean of penalties per game and a sta

Alisiya [41]

Answer:

The probability that the mean number of holding penalties per game is of X or less is the p-value of $Z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}$ , in which $\mu$ is the mean number of penalties per game, $\sigma$ is the standard deviation and n is the number of games that will be sampled.

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

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

We have that:

The mean number of penalties per game is $\mu$ and the standard deviation is $\sigma$ .

Sample of n games:

This means that $s = \frac{\sigma}{\sqrt{n}}$

What is the probability that, for a sample of college games to be played next week, the mean number of holding penalties will be X penalties per game or less?

The probability that the mean number of holding penalties per game is of X or less is the p-value of $Z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}$ , in which $\mu$ is the mean number of penalties per game, $\sigma$ is the standard deviation and n is the number of games that will be sampled.

4 0

3 years ago