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3 years ago

The center of a circle is at (2, −5) and its radius is 12.

Mathematics

1 answer:

stiv31 [10]3 years ago

7 0

Answer:

The equation of the circle is (x - 2)² + (y + 5)² = 144 ⇒ A

Step-by-step explanation:

The form of the equation of the circle is (x - h)² + (y - k)² = r², where

r is the radius of the circle

h, k are the coordinates of the center of the circle

Let us solve the question

∵ The center of the circle is at (2, -5)

→ From the rule above

∴ h = 2 and k = -5

∵ The radius of the circle is 12

∴ r = 12

→ Substitute the values of r, h, and k in the form of the equation above

∵ (x - 2)² + (y - -5)² = (12)²

∴ (x - 2)² + (y + 5)² = 144

∴ The equation of the circle is (x - 2)² + (y + 5)² = 144

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g A psychic was tested for extrasensory perception (ESP). The psychic was presented with cards face down and asked to determine

diamong [38]

Answer:

Step-by-step explanation:

Hello!

The objective is to test ESP, for this, a psychic was presented with cards face down and asked to determine if each of the cards was one of four symbols: a star, cross, circle, square.

Be X: number of times the psychic identifies the symbols on the cards correctly is a size n sample.

p the probability that the psychic identified the symbol on the cards correctly

You have to calculate the sample size n to estimate the proportion with a confidence level of 95% and a margin of error of d=0.01

The CI for the population proportion is constructed "sample proportion" ± "margin of error" Symbolically:

p' ± $Z_{1-\alpha /2} * (\sqrt{\frac{p'(1-p')}{n} } )$

Where $d= Z_{1-\alpha /2} * (\sqrt{\frac{p'(1-p')}{n} } )$ is the margin of error. As you can see, the formula contains the sample proportion (it is normally symbolized p-hat, in this explanation I'll continue to symbolize it p'), you have to do the following consideration:

Every time the psychic has to identify a card he can make two choices:

"Success" he identifies the card correctly

"Failure" he does not identify the card correctly

If we assume that each symbol has the same probability of being chosen at random P(star)=P(cross)=P(circle)=P(square)= 1/4= 0.25

Let's say, for example, that the card has the star symbol.

The probability of identifying it correctly will be P(success)= P(star)= 1/4= 0.25

And the probability of not identifying it correctly will be P(failure)= P(cross) + P(circle) + P(square)= 1/4 + 1/4 + 1/4= 3/4= 0.75

So for this experiment, we'll assume the "worst case scenario" and use p'= 1/4 as the estimated probability of the psychic identifying the symbol on the card correctly.

The value of Z will be $Z_{1-\alpha /2}= Z_{0.975}= 1.96$

Now using the formula you have to clear the sample size:

$d= Z_{1-\alpha /2} * (\sqrt{\frac{p'(1-p')}{n} } )$

$\frac{d}{Z_{1-\alpha /2}} = \sqrt{\frac{p'(1-p')}{n} }$

$(\frac{d}{Z_{1-\alpha /2}})^2 =\frac{p'(1-p')}{n}$

$n*(\frac{d}{Z_{1-\alpha /2}})^2 = p'(1-p')$

$n = p'(1-p')*(\frac{Z_{1-\alpha /2}}{d})^2$

$n = (0.25*0.75)*(\frac{1.96}{0.01})^2= 7203$

To estimate p with a margin of error of 0.01 and a 95% confidence level you have to take a sample of 7203 cards.

I hope this helps!

5 0

3 years ago

Read 2 more answers

Bruce walks 34 mile in 15 hour. What is his speed in miles per hour?

erastova [34]

Answer:

S=D/T

34/15=2.26 mph

Step-by-step explanation:

3 0

3 years ago

1.A cube has side lengths of 15 inches, what is the surface area and volume of the cube? 2. A cube has side lengths of 8 inches,

omeli [17]

Answer:

Cube 1: 3375 cubed inches, 1350 inches squared.

Cube 2: 512 cubed inches, 384 inches squared.

Step-by-step explanation:

Formula for Volume of a Cube: $V=s^3\\$ (s - side length)

Formula for Surface Area of a Cube: $SA=6s^2$ (s- side length)

The side length's 15 inches.

Find the volume:

$V=15^3\\\rightarrow 15*15*15=3375\\\boxed {V=3375}$

The volume of cube one is 3375in³.

Find the surface area:

$SA=6(15)^2\\\rightarrow 15^2 = 225\\SA = 6 * 225\\\boxed {SA=1350}$

The surface area of cube 1 is 1350in².

The side length's 8 inches.

Find the volume:

$V=8^3\\\rightarrow 8*8*8= 512\\\boxed {V=512}$

The volume of cube two is 512in³.

Find the surface area:

$SA=6(8)^2\\\rightarrow 8^2=64\\SA=6*64\\\boxed {SA=384}$

The surface area of cube 2 is 384in².

<em>Brainilest Appreciated. </em>

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Find that slope of a line that passes through each pair of points

Pie

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3 years ago

Find an ordered pair, x y that is a solution to the equation. 5x + y = 6

yarga [219]

Answer:

(0, -5)

Step-by-step explanation:

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