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4 years ago

What are the center and radius of the circle defined by the equation x2 + y2 -6 x + 10y + 25 = 0

Mathematics

2 answers:

Natasha_Volkova [10]4 years ago

5 0

Answer:

(3,-5), radius 3

Step-by-step explanation:

levacccp [35]4 years ago

4 0

To determine the center points and the radius of the circle, we can either graph the equation or write it in a form where the center and the radius can be easily be seen. For this, we use the second method. The form should be:

(x - h)^2 + (y-k)^2 = r^2

(h,k) represent the center and r the radius

We do as follows:
x2 + y2 -6x + 10y + 25 = 0
x2 -6x + y2 + 10y = - 25
x2 - 6x + 9 + y2 + 10y + 25 = -25 + 9 + 25 = 9
(x - 3)^2 + (y + 5)^2 = 3^2

Therefore, the center is at ( 3,-5) and the radius is 3 units.

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When a scientist conducted a genetics experiments with peas, one sample of offspring consisted of 943 peas, with 717 of them hav

pshichka [43]

Using the normal approximation to the binomial distribution, it is found that:

a) 0.242 = 24.2% probability of getting 717 or more peas with red flowers.

b) Since Z < 2, 717 peas with red flowers is not significantly high.

c) Since 717 peas with red flowers is not a significantly high result, we cannot conclude that the scientist's assumption is wrong.

For each pea, there are only two possible outcomes. Either they have a red flower, or they do not. The probability of a pea having a red flower is independent of any other pea, which means that the binomial distribution is used to solve this question.

Binomial distribution:

Probability of x successes on n trials, with p probability.

Normal distribution:

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

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

It 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, which is the percentile of X.

If Z > 2, the result is considered significantly high.

If $np \geq 10$ and $n(1-p) \geq 10$ , the binomial distribution can be approximated to the normal with:

$\mu = np$

$\sigma = \sqrt{np(1-p)}$

In this problem:

943 peas, thus, $n = 943$
3/4 probability of being red, thus $p = \frac{3}{4} = 0.75$ .

Applying the approximation:

$\mu = np = 943(0.75) = 707.25$

$\sigma = \sqrt{np(1-p)} = \sqrt{943(0.75)(0.25)} = 13.297$

Item a:

Using continuity correction, this probability is $P(X \geq 717 - 0.5) = P(X \geq 716.5)$ , which is 1 subtracted by the p-value of Z when X = 716.5.

Then:

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

$Z = \frac{716.5 - 707.25}{13.297}$

$Z = 0.7$

$Z = 0.7$ has a p-value of 0.758.

1 - 0.758 = 0.242

0.242 = 24.2% probability of getting 717 or more peas with red flowers.

Item b:

Since Z < 2, 717 peas with red flowers is not significantly high.

Item c:

Since 717 peas with red flowers is not a significantly high result, we cannot conclude that the scientist's assumption is wrong.

A similar problem is given at brainly.com/question/25212369

6 0

3 years ago

PLEASE HELP THIS A QUIZ DUE AT 9:00!

Svetllana [295]

Answer:

mmmm 7$ per week

Step-by-step explanation:

just divide 28/4=7

6 0

3 years ago

Read 2 more answers

Ronald is making hats and scarves for charity. He has enough yarn to make 5 hats and 8 scarves. It takes him 12 hours to knit a

Illusion [34]

X+y<=20 is false, because it tries to correlate the amount of hats and scarfs with the time, without considering the time to knit each object

x<=5 is correct, he can at most make 5 hats for more he is missing yarn

y<=8 is correct, same reasoning but with scarfs

5x+8y<=20 is false, it compares the yarn requirements with the total time

12x+6y<=20 is correct, a corrected version of the first constraint which uses the worktime of each object essentially meaning "the time worked on all objects has to be less than the 20 hour time total"

so
x<=5
y<=8
12x+6y<=20
are correct

6 0

3 years ago

Read 2 more answers

Assume that x has a normal distribution with the specified mean and standard deviation. Find the indicated probability. (Round y

Anarel [89]

Answer:

P(x ≥ 30) = 0.3859

Step-by-step explanation:

When the distribution is normal, we use 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.

In this question, we have that:

$\mu = 29, \sigma = 3.4$