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3 years ago

Find the center and the radius of the circle defined by the equation x^2-8x+y+12y+36=0

Mathematics

1 answer:

choli [55]3 years ago

3 0

Hello,
center is (4,-6)
radius=4
since
$x^2-8x+y^2+12y+36=0\\

x^2-2*4x+16-16+y^2+2*6y+36=0\\

(x-4)^2+(y+6)^2=4^2

$

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Step-by-step explanation:

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3 years ago

Will mark brainiest!! Only answer questions a and b

k0ka [10]

Answer:

f1 ( x ) valid pdf . f2 ( x ) is invalid pdf

k = 1 / 18 , i ) 0.6133 , ii ) 0.84792

Step-by-step explanation:

Solution:-

A) The two pdfs ( f1 ( x ) and f2 ( x ) ) are given as follows:

- To check the legitimacy of a continuous probability density function the area under the curve over the domain must be equal to 1. In other words the following:

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- A random variable ( X ) denotes the resistance of a randomly chosen resistor, and the pdf is given as follows:

if 8 ≤ x ≤ 10

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... Answer

- To determine the CDF of the given probability distribution we will integrate the pdf from the initial point ( 8 ) to a respective value ( x ) as follows:

To determine the probability p ( 8.6 ≤ x ≤ 9.8 ) we will utilize the cdf as follows:

p ( 8.6 ≤ x ≤ 9.8 ) = F ( 9.8 ) - F ( 8.6 )

p ( 8.6 ≤ x ≤ 9.8 ) =

ii) To determine the conditional probability we will utilize the basic formula as follows:

p ( x ≤ 9.8 | x ≥ 8.6 ) = p ( 8.6 ≤ x ≤ 9.8 ) / p ( x ≥ 8.6 )

p ( x ≤ 9.8 | x ≥ 8.6 ) = 0.61333 / [ 1 - p ( x ≤ 8.6 ) ]

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p ( x ≤ 9.8 | x ≥ 8.6 ) = 0.61333 / [ 0.72333 ]

p ( x ≤ 9.8 | x ≥ 8.6 ) = 0.84792 ... answer

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2 years ago

small cubes with edge lengths of 1/4 inch will be packed into the right rectangular prism shown.( the base is 4 1/2, the width i

ss7ja [257]

General Idea:

We need to find the volume of the small cube given the side length of the small cube as 1/4 inch.

Also we need to find the volume of the right rectangular prism with the given dimension (the height is 4 1/2, the width is 5, and the length is 3 3/4).

To find the number of small cubes that are needed to completely fill the right rectangular prism, we need to divide volume of right rectangular prism by volume of each small cube.

Formula Used:

$Volume \; of \; Cube = a^3 \; \\\{where \; a \; is \; side \; length \; of \; cube\}\\\\Volume \; of \; Right \; Rectangular \; Prism=L \times W \times H\\\{Where \; L \; is \; Length, \; W \; is \; Width, \;and \; H \; is \; Height\}$

Applying the concept:

Volume of Small Cube:

$V_{cube}= (\frac{1}{4} )^3= \frac{1}{64} \; in^3\\\\V_{Prism}= 3 \frac{3}{4} \times 5 \times 4 \frac{1}{2} = \frac{15}{4} \times \frac{5}{1} \times \frac{9}{2} = \frac{675}{8} \\\\Number \; of \; small \; cubes= \frac{V_{Prism}}{V_{Cube}} = \frac{675}{8} \div \frac{1}{64} \\\\Flip \; the \; second \; fraction\; and \; multiply \; with \; the \; first \; fraction\\\\Number \; of \; small \; cubes \;= \frac{675}{8} \times \frac{64}{1} = 5400$

Conclusion:

The number of small cubes with side length as 1/4 inches that are needed to completely fill the right rectangular prism whose height is 4 1/2 inches, width is 5 inches, and length is 3 3/4 inches is 5400 

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3 years ago

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san4es73 [151]

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