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2 years ago

What is the diameter of a circle with the equation x2 + y2 - 8x + 2y - 8 = 0?

Mathematics

2 answers:

Zinaida [17]2 years ago

7 0

Answer:

Step-by-step explanation:

x2 + y2 - 8x + 2y - 8 = 0

first we find the radius with the equation.

write the equation in standard form.

x2 + y2 - 8x + 2y - 8 = 0

(x-4)^2 + (y+1)^2 = 25

(x-h)² + (y-k)² = r²

this means 25 is the radius and the diameter is two times the radius so,

25 x 2 = 50

bazaltina [42]2 years ago

6 0

Answer:

Diameter is 10 units

Step-by-step explanation:

<u>Convert standard form to general form by completing the square:</u>

$x^2+y^2-8x+2y-8=0$

$x^2-8x+y^2+2y-8=0$

$x^2-8x+y^2+2y=8$

$x^2-8x+16+y^2+2y+1=8+16+1$

$(x-4)^2+(y+1)^2=25$

$(x-4)^2+(y+1)^2=5^2$

So, since the radius of the circle is 5 units, then the diameter is twice the radius, which is 10 units.

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3 years ago

The distribution of weekly salaries at a large company is right skewed with a mean of $1000 and a standard deviation of $350. Wh

Shtirlitz [24]

Answer:

68.76% probability that the sampling error made in estimating the mean weekly salary for all employees of the company by the mean of a random sample of weekly salaries of 50 employees will be at most $50

Step-by-step explanation:

To solve this question, we have to understand 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 random variable X, with mean $\mu$ and standard deviation $\sigma$ , a large sample size can be approximated to a normal distribution with mean $\mu$ and standard deviation, which is also called standard error $s = \frac{\sigma}{\sqrt{n}}$

In this problem, we have that:

$\mu = 1000, \sigma = 350, n = 50, s = \frac{350}{\sqrt{50}} = 49.5$

What is the probability that the sampling error made in estimating the mean weekly salary for all employees of the company by the mean of a random sample of weekly salaries of 50 employees will be at most $50

This is the pvalue of Z when X = 1000+50 = 1050 subtracted by the pvalue of Z when X = 1000-50 = 950. So

X = 1050

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

By the Central Limit Theorem

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