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2 years ago

What is the result of isolating y^2 in the equation below? (x+4)^2+y^2=22

Mathematics

2 answers:

Anon25 [30]2 years ago

7 0

Answer: y² = 22 - (x+4)² or

y² = -x²-8x+6 (simplified form)

Step-by-step explanation:

Hi, to answer this question we have to isolate the term y².

(x+4)² +y² =22

y² = 22 - (x+4)²

That is the result without simplifying. If we simplify the sum raised to a power, we have to apply the method (a+b)^2 = a^2 + 2ab + b^2.

y²= 22 - (x²+2.x.4+4²)

y² = 22 - (x² +8x +16)

y²= 22 -x² -8x-16

y² = -x²-8x+6 (simplified result)

Feel free to ask for more if it´s necessary or if you did not understand something.

Mekhanik [1.2K]2 years ago

6 0

Solve is in the pixture

Good luck :)

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Let X represent the amount of gasoline (gallons) purchased by a randomly selected customer at a gas station. Suppose that the me

Alexus [3.1K]

Answer:

a) 18.94% probability that the sample mean amount purchased is at least 12 gallons

b) 81.06% probability that the total amount of gasoline purchased is at most 600 gallons.

c) The approximate value of the 95th percentile for the total amount purchased by 50 randomly selected customers is 621.5 gallons.

Step-by-step explanation:

To solve this question, we use the normal probability distribution and the central limit theorem.

Normal probability distribution

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes 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.

For sums, we can apply the theorem, with mean $\mu$ and standard deviation $s = \sqrt{n}*\sigma$

In this problem, we have that:

$\mu = 11.5, \sigma = 4$

a. In a sample of 50 randomly selected customers, what is the approximate probability that the sample mean amount purchased is at least 12 gallons?

Here we have $n = 50, s = \frac{4}{\sqrt{50}} = 0.5657$

This probability is 1 subtracted by the pvalue of Z when X = 12.

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

By the Central Limit theorem

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

$Z = \frac{12 - 11.5}{0.5657}$

$Z = 0.88$

$Z = 0.88$ has a pvalue of 0.8106.

1 - 0.8106 = 0.1894

18.94% probability that the sample mean amount purchased is at least 12 gallons

b. In a sample of 50 randomly selected customers, what is the approximate probability that the total amount of gasoline purchased is at most 600 gallons.

For sums, so $mu = 50*11.5 = 575, s = \sqrt{50}*4 = 28.28$

This probability is the pvalue of Z when X = 600. So

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

$Z = \frac{600 - 575}{28.28}$

$Z = 0.88$

$Z = 0.88$ has a pvalue of 0.8106.

81.06% probability that the total amount of gasoline purchased is at most 600 gallons.

c. What is the approximate value of the 95th percentile for the total amount purchased by 50 randomly selected customers.

This is X when Z has a pvalue of 0.95. So it is X when Z = 1.645.

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

$1.645 = \frac{X- 575}{28.28}$

$X - 575 = 28.28*1.645$

$X = 621.5$

The approximate value of the 95th percentile for the total amount purchased by 50 randomly selected customers is 621.5 gallons.

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2 years ago

A video game randomly chooses your car color and type. The probability of getting a red car is 0.20, and the probability of gett

pishuonlain [190]

Answer: Option 'D' is correct.

Step-by-step explanation:

Since we have given that

Event A: You get a red car

and

$P(A)=0.20$

Similarly,

Event B: You get a convertible

and

$P(B)=0.40$

So, if A and B are independent , then they must satisfy,

$P(A).P(B)=P(A\cap B)$

So,

$P(A\cap B)=0.4\times 0.2=0.08$

Hence, Option 'D' is correct, which states that the probability of getting a red convertible is 0.08.

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Answer:

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Answer:

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Step-by-step explanation:

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Answer:

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Step-by-step explanation:

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