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4 years ago

Which equation represents a circle with a center at (-4,9) and a diameter of 10 units?

Mathematics

1 answer:

Dennis_Churaev [7]4 years ago

7 0

Answer:

$(x+4)^2 + (y-9)^2 = 25$

Step-by-step explanation:

To write the equation of a circle, use the formula $(x-h)^2+(y-k)^2 = r^2$ where the center of the circle is (h, k).

This means the equation is $(x--4)^2 + (y-9)^2 = r^2\\\(x+4)^2 + (y-9)^2 = r^2$ .

Find the radius r by dividing the diameter of 10 in 2. The radius is 5.

So the equation of the circle is $(x+4)^2 + (y-9)^2 = 25$

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3 years ago

wo balls are chosen randomly from an um containing 8 white, 4 black,and 2 orange balls. Suppose that we win $2 for each black ba

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Answer:

The probability distribution is shown below.

Step-by-step explanation:

The urn consists of 8 white (W), 4 black (B) and 2 orange (O) balls.

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Win $2 for each black ball selected.
Lose $1 for each white ball selected.

There are 8 + 4 + 2 = 14 balls in the urn.

The number of ways to select two balls is, ${14\choose 2}=91$ ways.

The distribution of amount won or lost is as follows:

Outcomes: WW WO WB BB BO OO

X: -2 -1 1 4 2 0

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The number of ways to select 2 white balls is, ${8\choose 2}=28$ ways.

The probability of WW is,

$P(WW)=\frac{n(WW)}{N}=\frac{28}{91}=0.3077$

Compute the probability of selecting 1 white ball and 1 orange ball as follows:

The number of ways to select 1 white ball and 1 orange ball is, ${8\choose 1}\times {2\choose 1}=16$ ways.

The probability of WO is,

$P(WO)=\frac{n(WO)}{N}=\frac{16}{91}=0.1758$

Compute the probability of selecting 1 white ball and 1 black ball as follows:

The number of ways to select 1 white ball and 1 black ball is, ${8\choose 1}\times {4\choose 1}=32$ ways.

The probability of WB is,

$P(WB)=\frac{n(WB)}{N}=\frac{32}{91}=0.3516$

Compute the probability of selecting 2 black balls as follows:

The number of ways to select 2 black balls is, ${4\choose 2}=6$ ways.

The probability of BB is,

$P(BB)=\frac{n(BB)}{N}=\frac{6}{91}=0.0659$

Compute the probability of selecting 1 black ball and 1 orange ball as follows:

The number of ways to select 1 black ball and 1 orange ball is, ${4\choose 1}\times {2\choose 1}=8$ ways.

The probability of BO is,

$P(BO)=\frac{n(BO)}{N}=\frac{8}{91}=0.0879$

Compute the probability of selecting 2 orange balls as follows:

The number of ways to select 2 orange balls is, ${2\choose 2}=1$ ways.

The probability of OO is,

$P(OO)=\frac{n(OO)}{N}=\frac{1}{91}=0.0110$

The probability distribution of X is:

Outcomes: WW WO WB BB BO OO

X: -2 -1 1 4 2 0

P (X): 0.3077 0.1758 0.3516 0.0659 0.0879 0.0110

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