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3 years ago

Find an equation of the circle that has center (-1,2) and passes through (5,-4).

1 answer:

8 0

General equation for a circle
(x - a)² + (y - b)² = r²
with (a,b) represents the center, (x,y) represents one of the points lie on the circle, and r represents the radius

Determine r² by substituting the points into the general equation
(x - a)² + (y - b)² = r²
(5 - (-1))² + (-4 - 2)² = r²
(5 + 1)² + (-6)² = r²
6² + 36 = r²
36 + 36 = r²
72 = r²

Determine the equation of the circle
(x - a)² + (y - b)² = r²
(x - (-1))² + (y - 2)² = 72
(x + 1)² + (y - 2)² = 72 (This is the equation of the circle)

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The average zinc concentration recovered from a sample of measurements taken in 36 different locations in a river is found to be

vazorg [7]

Answer:

The 95% confidence interval for the mean zinc concentration in the river is between 1.75 and 3.45 grams per milliliter.

The 99% confidence interval for the mean zinc concentration in the river is between 1.48 and 3.72 grams per milliliter.

Step-by-step explanation:

95% confidence interval:

We have that to find our $\alpha$ level, that is the subtraction of 1 by the confidence interval divided by 2. So:

$\alpha = \frac{1 - 0.95}{2} = 0.025$

Now, we have to find z in the Ztable as such z has a pvalue of $1 - \alpha$ .

That is z with a pvalue of $1 - 0.025 = 0.975$ , so Z = 1.96.

Now, find the margin of error M as such

$M = z\frac{\sigma}{\sqrt{n}}$

In which $\sigma$ is the standard deviation of the population and n is the size of the sample.

$M = z\frac{\sigma}{\sqrt{n}}$

$M = 1.96\frac{2.6}{\sqrt{36}}$

$M = 0.85$

The lower end of the interval is the sample mean subtracted by M. So it is 2.6 - 0.85 = 1.75 grams per milliliter.

The upper end of the interval is the sample mean added to M. So it is 2.6 + 0.85 = 3.45 grams per milliliter.

The 95% confidence interval for the mean zinc concentration in the river is between 1.75 and 3.45 grams per milliliter.

99% confidence level:

By the same logic as for the 95% confidence interval, we have that $Z = 2.575$ . So

$M = z\frac{\sigma}{\sqrt{n}}$

$M = 2.575\frac{2.6}{\sqrt{36}}$

$M = 1.12$

The lower end of the interval is the sample mean subtracted by M. So it is 2.6 - 1.12 = 1.48 grams per milliliter.

The upper end of the interval is the sample mean added to M. So it is 2.6 + 1.12 = 3.72 grams per milliliter.

The 99% confidence interval for the mean zinc concentration in the river is between 1.48 and 3.72 grams per milliliter.

5 0

2 years ago

Can somebody help me out with this please?

Crank

Answer:

2 marbles

Step-by-step explanation:

Lana has 3 bags with x marbles in each bag totaling 12 marbles

3x=12

Divide by 3

3x/3 =12/3

x =4

Each bag has 4 marbles

Markus has 3 bags with y marbles totaling 18 marbles

3y =18

Divide each side by 3

3y/3 =18/3

y =6

Each bag has 6 marbles

6-4 =2

There are 2 more marbles in Markus' bags than in Lara's

4 0

3 years ago

Identify the number of decimal places in each factor.

const2013 [10]

Answer:

Step-by-step explanation:

4 0

3 years ago

Chapter : Circles 1 question

erica [24]

We can solve this question in 2 ways: either using degrees or converting the degrees into radians.

Since, the question says degrees itself and there is no specification of using radians only, so I have solved it using degrees itself.

Part (a):

Perimeter of sector ORS = 2*Radius + Arc RS = 2*21 + $60* \frac{ \pi }{180} *21 = \frac{ \pi }{3} *21 = 7 \pi$

Part (b):

Area of sector ORS = $\frac{60}{360} * \pi * 21^{2} = \frac{1}{6} * \pi *21*21= \frac{147}{2} \pi$

Area of sector POQ = $\frac{36}{360} * \pi * 14^{2} = \frac{1}{10} * \pi * 196 = \frac{196}{10} \pi$

Thus, area of shaded region
= Area of sector ORS - Area of sector POQ

= $\frac{147}{2} \pi - \frac{196}{10} \pi = \frac{735 - 196}{10} \pi = \frac{539}{10} \pi = 53.9 \pi$

5 0

3 years ago

Which number is IRRATIONAL? A) 47 B) 0.09 C) 15 D) 8 45

Elanso [62]

Your answer would be B. 0.09, the reason being is that any number that has a 0 and then a decimal point is irrational (or a regular fraction

6 0

3 years ago