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2 years ago

Write the standard equation for the circle center (–6, 7), r = 9.

Mathematics

2 answers:

HACTEHA [7]2 years ago

7 0

Answer:

Step-by-step explanation:

Given: The center of the circle is $(6,7)$ and the radius is $9$ .

To find: The standard equation for the circle.

Solution: The standard equation for the circle with center $(a,b)$ and radius $r$ is given as:

$(x-a)^2+(y-b)^2=r^2$

Now, the center is $(6,7)$ and the radius is $9$ , thus the equation of circle is:

$(x-(-6))^2+(y-7)^2=(9)^2$

$(x+6)^2+(y-7)^2=(9)^2$

which is the required equation of circle with center as $(6,7)$ and the radius is $9$ .

Advocard [28]2 years ago

4 0

The standard equation for the circle centre can be written by using this formula: (x-h)² + (y -k)² = r²

So, the equation in this case is: (x+6)² + (y-7)² = 81

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olga2289 [7]

Answer:

a) $E(Y) = \sum_{i=1}^n Y_i P(Y_i)$

And replacing we got:

$E(Y) =0*0.60 +1*0.25 +2*0.1 +3*0.05 = 0.60$

b) $E(Y^2) =0^2*0.60 +1^2*0.25 +2^2*0.1 +3^2*0.05 = 1.1$

And then the expected value would be:

$E(100Y^2) = 100*1.1= 110$

Step-by-step explanation:

We assume the following distribution given:

Y 0 1 2 3

P(Y) 0.60 0.25 0.10 0.05

Part a

We can find the expected value with this formula:

$E(Y) = \sum_{i=1}^n Y_i P(Y_i)$

And replacing we got:

$E(Y) =0*0.60 +1*0.25 +2*0.1 +3*0.05 = 0.60$

Part b

If we want to find the expected value of $100 Y^2$ we need to find the expected value of Y^2 and we have:

$E(Y^2) = \sum_{i=1}^n Y^2_i P(Y_i)$

And replacing we got:

$E(Y^2) =0^2*0.60 +1^2*0.25 +2^2*0.1 +3^2*0.05 = 1.1$

And then the expected value would be:

$E(100Y^2) = 100*1.1= 110$

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2 years ago

Can someone help me with number 8 please? Thank you.

Naddik [55]

Answer: $-4 \le x \le 5$
Note: to write the domain in interval notation, you'd write [-4,5]
if you need the domain in set-builder notation, then you'd write $\left\{x|x\in\mathbb{R}, \ -4\le x\le 5\right\}$

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Explanation:

The domain is the set of possible x input values. Look at the left most point (-4,-1). The x coordinate here is x = -4. This is the smallest x value allowed. The largest x value allowed is x = 5 for similar reasons, but on the other side of the graph.

So that's how I got $-4 \le x \le 5$ (x is between -4 and 5; inclusive of both endpoints)

Writing [-4,5] for interval notation tells us that we have an interval from -4 to 5 and we include both endpoints. The square brackets mean "include endpoint"

Writing $\left\{x|x\in\mathbb{R}, \ -4\le x\le 5\right\}$ is the set-builder notation way of expressing the domain. The $x\in\mathbb{R}$ portion means "x is a real number"

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Answer:

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Step-by-step explanation:

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