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3 years ago

Write the equation of the circle R that passes through (1, 1) and has a center C(2, 2).

1 answer:

6 0

$(x-x_0)^2+(y-y_0)^=r^2

(x-2)^2+(y-2)^=2$ Firstly, we need to find out the radius of the circle

and this is accomplished by the distance formula $r=\sqrt{(y_2-y_1)^2+(x_2-x_1)^2} \\
r=\sqrt{(2-1)^2+(2-1)^2} \\
r=\sqrt{1+1} \\
r=\sqrt{2}

hence:\\
\\
r^2=2$

then the equation of the circle is:

$(x-x_0)^2+(y-y_0)^2=r^2\\
\\(x-2)^2+(y-2)^2=2$

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For a certain river, suppose the drought length Y is the number of consecutive time intervals in which the water supply remains

AnnZ [28]

Answer:

a) There is a 9% probability that a drought lasts exactly 3 intervals.

There is an 85.5% probability that a drought lasts at most 3 intervals.

b)There is a 14.5% probability that the length of a drought exceeds its mean value by at least one standard deviation

Step-by-step explanation:

The geometric distribution is the number of failures expected before you get a success in a series of Bernoulli trials.

It has the following probability density formula:

$f(x) = (1-p)^{x}p$

In which p is the probability of a success.

The mean of the geometric distribution is given by the following formula:

$\mu = \frac{1-p}{p}$

The standard deviation of the geometric distribution is given by the following formula:

$\sigma = \sqrt{\frac{1-p}{p^{2}}$

In this problem, we have that:

$p = 0.383$

$\mu = \frac{1-p}{p} = \frac{1-0.383}{0.383} = 1.61$

$\sigma = \sqrt{\frac{1-p}{p^{2}}} = \sqrt{\frac{1-0.383}{(0.383)^{2}}} = 2.05$

(a) What is the probability that a drought lasts exactly 3 intervals?

This is $f(3)$

$f(x) = (1-p)^{x}p$

$f(3) = (1-0.383)^{3}*(0.383)$

$f(3) = 0.09$

There is a 9% probability that a drought lasts exactly 3 intervals.

At most 3 intervals?

This is $P = f(0) + f(1) + f(2) + f(3)$

$f(x) = (1-p)^{x}p$

$f(0) = (1-0.383)^{0}*(0.383) = 0.383$

$f(1) = (1-0.383)^{1}*(0.383) = 0.236$

$f(2) = (1-0.383)^{2}*(0.383) = 0.146$

Previously in this exercise, we found that $f(3) = 0.09$

$P = f(0) + f(1) + f(2) + f(3) = 0.383 + 0.236 + 0.146 + 0.09 = 0.855$

There is an 85.5% probability that a drought lasts at most 3 intervals.

(b) What is the probability that the length of a drought exceeds its mean value by at least one standard deviation?

This is $P(X \geq \mu+\sigma) = P(X \geq 1.61 + 2.05) = P(X \geq 3.66) = P(X \geq 4)$ .

We are working with discrete data, so 3.66 is rounded up to 4.

Either a drought lasts at least four months, or it lasts at most thee. In a), we found that the probability that it lasts at most 3 months is 0.855. The sum of these probabilities is decimal 1. So:

$P(X \leq 3) + P(X \geq 4) = 1$

$0.855 + P(X \geq 4) = 1$

$P(X \geq 4) = 0.145$

There is a 14.5% probability that the length of a drought exceeds its mean value by at least one standard deviation

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3 years ago

What is the answer in the remainder

ira [324]

Answer:

12 with a remainder of 5

Step-by-step explanation:

have a good day! :)

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2 years ago

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How does substitution help you to solve systems of equations?

kipiarov [429]

In solving equations, each must have vales of x and y. X is any number and Y is the output of any number. If you substitute x for a number, you can solve the equation for y.

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3 years ago

Please answer this correctly Is the answer 5:15pm 6:03am 2:15pm 7:03am

mrs_skeptik [129]

Answer:

2:15 PM

Step-by-step explanation:

When the plane arrives in Seattle, the time in eastern time period would be 5:15 PM. From eastern to pacific, the time goes back 3 hours. 5:15 - 3 hours is 2:15. Since the time is still in the afternoon, it is still PM.

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4 years ago

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How do you solve 4377 divided by 8

alisha [4.7K]

Answer:

4,337 goes on top & 8 on the bottom

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8 & the answer is 542.12

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