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3 years ago

What is the length of a radius of the circle represented by the equation below?

Mathematics

1 answer:

MakcuM [25]3 years ago

7 0

Answer:

Step-by-step explanation:

Given the circle: $x^2 + y^2 - 4x - 4y + 4 = 0$

To determine the length of the radius, we complete the square.

Step 1: Subtract 4 from both sides

$x^2 + y^2 - 4x - 4y + 4 -4= 0-4\\x^2 + y^2 - 4x - 4y = -4$

Step 2: Divide the coefficient of x and y by 2, square it and add it to both sides

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

Step 3: Factorize the Left Hand side and simplify the Right Hand side.

$(x-2)^2+ (y-2)^2 = 2^2$

Comparing with the standard form of the equation of a circle

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

r=2

Therefore, the radius of the circle is 2.

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Determine the number of degrees of freedom for the two-sample t test or CI in each of the following situations. (Round your answ

gulaghasi [49]

Answer:

Part a ) The degrees of freedom for the given two sample non-pooled t test is 24

Part b ) The degrees of freedom for the given two sample non-pooled t test is 30

Part c ) The degrees of freedom for the given two sample non-pooled t test is 30

Part d ) The degrees of freedom for the given two sample non-pooled t test is 25

Step-by-step explanation:

Degrees of freedom for a non-pooled two sample t-test is given by;

Δf = {[ s₁²/m + s₂²/n ]²} / {[( s₁²/m)²/m-1] + [(s₂²/n)²/n-1]}

Now given the information;

a) :- m = 12, n = 15, s₁ = 4.0, s₂ = 6.0

we substitute

Δf = {[ 4²/12 + 6²/15 ]²} / {[( 4²/12)²/12-1] + [(6²/15)²/15-1]}

Δf = 30184 / 1241

Δf = 24.3223 ≈ 24 (down to the nearest whole number)

b) :- m = 12, n = 21, s₁ = 4.0, s₂ = 6.0

we substitute using same formula

Δf = {[ s₁²/m + s₂²/n ]²} / {[( s₁²/m)²/m-1] + [(s₂²/n)²/n-1]}

Δf = {[ 4²/12 + 6²/21 ]²} / {[( 4²/12)²/12-1] + [(6²/21)²/21-1]}

Δf = 56320 / 1871

Δf = 30.1015 ≈ 30 (down to the nearest whole number)

c) :- m = 12, n = 21, s₁ = 3.0, s₂ = 6.0

we substitute using same formula

Δf = {[ s₁²/m + s₂²/n ]²} / {[( s₁²/m)²/m-1] + [(s₂²/n)²/n-1]}

Δf = {[ 3²/12 + 6²/21 ]²} / {[( 3²/12)²/12-1] + [(6²/21)²/21-1]}

Δf = 29095 / 949

Δf = 30.6585 ≈ 30 (down to the nearest whole number)

d) :- m = 10, n = 24, s₁ = 4.0, s₂ = 6.0

we substitute using same formula

Δf = {[ s₁²/m + s₂²/n ]²} / {[( s₁²/m)²/m-1] + [(s₂²/n)²/n-1]}

Δf = {[ 4²/10 + 6²/24 ]²} / {[( 4²/10)²/10-1] + [(6²/24)²/24-1]}

Δf = 1044 / 41

Δf = 25.4634 ≈ 25 (down to the nearest whole number).

6 0

3 years ago

if an ice cream factory makes 350 quart of ice cream in 2 hours?how many quarts could be made in 12 hours? what was the rate in

UkoKoshka [18]

2,100 quarts could be made in 12 hours. The rate for that day was 175 quarts every hour. We get this by dividing 350 by 2.

8 0

3 years ago

Ada, Betty, Chris and David have $45 in total Ada gota 52 fromBetty, Chris tripleshis money and Davids money is cut by hall four

andrezito [222]

Using a system of equations, it is found that initially Ada has $0.385.

For the system, we have that the variables are:

x is Ada's amount.
y is Betty's amount.
z is Chris's amount.
w is David's amount.

$45 total, hence:

$x + y + z + w = 45$

Ada gets 2 from Betty, hence:

$x + 2 = y - 2$

$x = y - 4$

$y = x + 4$

Chris triples his money and David's money is cut by half four of them have the same amount, hence:

$x + 4 = y = 3z = \frac{w}{2}$

Then:

$3z = x + 4$

$z = \frac{x + 4}{3}$

$x + 4 = \frac{w}{2}$

$w = 2x + 8$

Solving for w, we find Ada's initial amount.

$x + y + z + w = 45$

$x + x + 4 + \frac{x + 4}{3} + 2x + 8 = 45$

$4x + 12 + \frac{x + 4}{3} = 45$

$12x + 36 + x + 4 = 45$

$13x = 5$

$x = \frac{5}{13}$

$x = 0.385$

Initially, Ada has $0.385.

A similar problem is given at brainly.com/question/6120515

5 0

3 years ago

Please answer quickly and with the write answer.

r-ruslan [8.4K]

(2/5)(1/4) = 2/20 = 1/10

Choice A.

3 0

3 years ago

Which lists all the lines that are parallel to line s?

ValentinkaMS [17]

Is there a picture? You just threw it all in a sentence. It works better with a pic

4 0

2 years ago

Read 2 more answers