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Vikki [24]
3 years ago
5

A cellular phone network uses towers to

Mathematics
1 answer:
kirill [66]3 years ago
6 0

Answer:

Both (6,\, 0) and (8,\, 2) are inside this circular area.

(6 - 5)^{2} + (0 - 1)^{2} = 2 < 22.

(8 - 5)^{2} + (2 - 1)^{2} = 10 < 22.

Step-by-step explanation:

Equation for a circle in 2D, with center (a,\, b) and radius r:

(x - a)^{2} + (y - b)^{2} = r^{2}.

Compare this expression with the one from this question:

(x - 5)^{2} + (y - 1)^{2} = 22 = \left(\sqrt{22}\right)^{2}.

Hence: a = 5, b = 1, and r = \sqrt{22}.

Therefore, \! (5,\, 1) and \sqrt{22} would be the center and the radius of the circle (x - 5)^{2} + (y - 1)^{2} = 22.

A point is inside a circle if and only the Euclidean distance between that point and the center of that circle is smaller than the radius of the circle. That is the same as requiring that the square of the Euclidean distance between these two points to be smaller than the square of the radius of the circle.

Formula for the Euclidean distance between (x_1,\, y_1) and (x_2,\, y_2):

\displaystyle \sqrt{(x_1 - x_2)^{2} + (y_1 - y_2)^{2}}.

The square of the Euclidean distance between these two points would be:

\displaystyle (x_1 - x_2)^{2} + (y_1 - y_2)^{2}.

Calculate the square of the distance between (6,\, 0) and the center of the circle, (5,\, 1).

(6 - 5)^{2} + (0 - 1)^{2} = 2.

The square of this distance is smaller than 22, the square of the radius of this circle. Hence, the point (6,\, 0) is inside this circle.

Similarly, calculate the square of the distance between (8,\, 2) and the center of the circle, (5,\, 1).

(8 - 5)^{2} + (2 - 1)^{2} = 10.

The square of this distance is smaller than 22, the square of the radius of this circle. Hence, the point (8,\, 2) is also inside this circle.

Notice that the point (x,\, y) is on the 2D circle (x - a)^{2} + (y - b)^{2} = r^{2} if and only if x and y satisfy the equation of that circle.

On the other hand, (x,\, y) is inside this circle if and only x and y satisfy the inequality (x - a)^{2} + (y - b)^{2} < r^{2}.

Both (6,\, 0) and (8,\, 2) satisfy the inequality (x - 5)^{2} + (y - 1)^{2} < 22. Hence, both points are inside the circle (x - 5)^{2} + (y - 1)^{2} = 22.

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Alex Ar [27]

Answer:

b) 6.68%

Step-by-step explanation:

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the z-score of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

The mean score on the scale is 50. The distribution has a standard deviation of 10.

This means that \mu = 50, \sigma = 10

Matthew scores a 65. What percentage of people could be expected to score the same as Matthew or higher on this scale?

The proportion is 1 subtracted by the p-value of Z when X = 65. So

Z = \frac{X - \mu}{\sigma}

Z = \frac{65 - 50}{10}

Z = 1.5

Z = 1.5 has a p-value of 0.9332.

1 - 0.9332 = 0.0668

0.0668*100% = 6.68%

So the correct answer is given by option b.

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3 years ago
Analyze the graph of the function f(x) to complete the statement.
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Step-by-step explanation:

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3 years ago
What is the volume of a cone with a diameter of 16 centimeters and a height of 15 centimeters?
AleksAgata [21]

Answer:

The correct answer is 8cm.

Step-by-step explanation:

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Answer:

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Step-by-step explanation:

-5x + 4y = 2

9x - 4y = 6

Sum both eq.

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then:

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