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3 years ago

Find the coordinates of the midpoint of a segment with endpoints at (-11,34) and (47,0).

Mathematics

1 answer:

34kurt3 years ago

7 0

The point (-11,34) has the coordinates x = -11 and y = 34

The point (47,0) has the coordinates x = 47 and y = 0

Let's focus on just the x coordinates of each point for now. Those values are -11 and 47. Add them up to get -11+47 = 36. Then divide by two to end up with 36/2 = 18

The x coordinate of the midpoint is x = 18

Repeat those steps for the y coordinates. First add them up: 34+0 = 34. Then divide by two: 34/2 = 17

The y coordinate of the midpoint is y = 17

<h3>Therefore the midpoint is located at (x,y) = (18,17)</h3>

--------------------------

side note:

If you want, you can use the formulas

xm = (x1+x2)/2

ym = (y1+y2)/2

where (x1,y1) and (x2,y1) are the two endpoints and (xm, ym) is the midpoint. Though this method may be a bit confusing.

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3 years ago

Terri Vogel, an amateur motorcycle racer, averages 129.71 seconds per 2.5 mile lap (in a 7 lap race) with a standard deviation o

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(a) The percent of her laps that are completed in less than 130 seconds is 55%.

(b) The fastest 3% of her laps are under 125.42 seconds.

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The random variable X is defined as the number of seconds for a randomly selected lap.

The random variable X is normally distributed with mean, μ = 129.71 seconds and standard deviation, σ = 2.28 seconds.

Thus, $X\sim N(129.71,\ 2.28^{2})$ .

(a)

Compute the probability that a lap is completes in less than 130 seconds as follows:

$P(X$

$=P(Z$

The percentage is, 0.55 × 100 = 55%.

Thus, the percent of her laps that are completed in less than 130 seconds is 55%.

(b)

Let x represents the 3rd percentile.

That is, P (X < x) = 0.03.

⇒ P (Z < z) = 0.03

The value of z for the above probability is:

z = -1.88

Compute the value of x as follows:

$z=\frac{x-\mu}{\sigma}\\-1.88=\frac{x-129.71}{2.28}\\x=129.71-(1.88\times 2.28)\\x=125.4236\\x\approx 125.42$

Thus, the fastest 3% of her laps are under 125.42 seconds.

(c)

Let x₁ and x₂ be the values between which the middle 80% of the distribution lie.

That is,

$P(x_{1}$

The value of z for the above probability is:

z = 1.28

Compute the values of x₁ and x₂ as follows:

$-z=\frac{x_{1}-\mu}{\sigma}\\-1.28=\frac{x_{1}-129.71}{2.28}\\x_{1}=129.71-(1.28\times 2.28)\\x=126.7916\\x\approx 126.80$ $z=\frac{x_{2}-\mu}{\sigma}\\1.28=\frac{x_{2}-129.71}{2.28}\\x_{2}=129.71+(1.28\times 2.28)\\x=132.6284\\x\approx 132.63$

Thus, the middle 80% of her laps are from 126.80 seconds to 132.63 seconds.

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3 years ago

Find the coordinates of the midpoint of a segment with endpoints at (-11,34) and (47,0).​

Find the coordinates of the midpoint of a segment with endpoints at (-11,34) and (47,0).