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2 years ago

Helppp!!!! please!!!

Mathematics

1 answer:

lara31 [8.8K]2 years ago

7 0

Answer:

I. (x - 6)² + (y + 7)² = 121

Step-by-step explanation:

Given a circle with coordinates of the center as (6, -7), and with a diameter of 22, equation of the circle is given below using the standard equation formula of a circle:

Formula => (x - a)² + (y - b)² = r²

Where,

a = 6

b = -7

r = radius of circle = ½ of diameter = ½ of 22 = 11

Thus, plug in the above values into the standard equation formula:

(x - 6)² + (y - (-7))² = 11²

(x - 6)² + (y + 7)² = 121

<em>Our answer, which is the equation of the circle is I. (x - 6)² + (y + 7)² = 121</em>

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Answer:

1) $z=\frac{4000-4500}{2500}=-0.2$

That means 0.2 deviations below the mean

2) $z=\frac{600-500}{200}=0.5$

That means 0.5 deviations above the mean

3) $z=\frac{750-850}{100}=-1$

That means 1 deviations below the mean

4) For this case the lowest instrument compared to the other instruments of the same type is the drum set since have the lowest z score z =-1

5) For this case the highest instrument compared to the other instruments of the same type is guitar since have the highest z score z =0.5

Step-by-step explanation:

They plan to purchase a piano costing $4,000, a guitar costing $600, and a drum set costing $750.

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

Part 1

Let X the random variable that represent the cost of for a piano, and for this case we know this

Where $\mu=4500$ and $\sigma=2500$

And the best way to solve this problem is using the normal standard distribution and the z score given by:

$z=\frac{x-\mu}{\sigma}$

If we replace the formula for X= 4000 we got:

$z=\frac{4000-4500}{2500}=-0.2$

That means 0.2 deviations below the mean

Part 2

Let X the random variable that represent the cost of for a guitar, and for this case we know this

Where $\mu=500$ and $\sigma=200$

And the best way to solve this problem is using the normal standard distribution and the z score given by:

$z=\frac{x-\mu}{\sigma}$

If we replace the formula for X= 600 we got:

$z=\frac{600-500}{200}=0.5$

That means 0.5 deviations above the mean

Part 3

Let X the random variable that represent the cost of for drum set, and for this case we know this

Where $\mu=850$ and $\sigma=100$

And the best way to solve this problem is using the normal standard distribution and the z score given by:

$z=\frac{x-\mu}{\sigma}$

If we replace the formula for X= 750 we got:

$z=\frac{750-850}{100}=-1$

That means 1 deviations below the mean

Part 4

For this case the lowest instrument compared to the other instruments of the same type is the drum set since have the lowest z score z =-1

Part 5

For this case the highest instrument compared to the other instruments of the same type is guitar since have the highest z score z =0.5

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2 years ago