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Mnenie [13.5K]
3 years ago
9

The distance between two points needs to be measured, in meters. The true distance between the points is 10 meters, but due to m

easurement error we can’t measure the distance exactly. Instead, we will observe a value of 10+???? , where the error ???? is distributed (0,0.04) . Find the probability that the observed distance is within 0.4 meters of the true distance. Give an approximate numerical answer.
Mathematics
1 answer:
luda_lava [24]3 years ago
7 0

Answer:

The probability that the observed distance is within 0.4 meters is 0.955

Step-by-step explanation:

Margin of error (ME) from the mean can be calculated using the formula

ME=z×s where

  • z is the corresponding statistic of the probability that the observed distance is within 0.4 meters
  • s is the standard deviation of the observed error

Error is distributed as N(0,0.04) means that measurements have <em>standard deviation</em> 0.2, square root of 0.04.

<em>Margin of error</em> is given as 0.4 meters.

Thus 0.4=z×0.2  gives z=2 and the corresponding p-value is 0.045, which means that the probability of observing a margin of error 0.4 is 1-0.045=0.955.

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What is the product of 3.45 x<br> (1.93 x 10^4)
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66,585

Step-by-step explanation:

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Always use pemdas and hope this helped!

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2 years ago
What is m&lt;9 = 130 degrees, What is m&lt;4
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3 years ago
A television screen's width is 1.778 times its height. If its
Nana76 [90]

Answer:

Let a, b, and c be the height, width, and the diagonal of the screen respectively

Since they form a triangle and the angle between a and b is 90 degrees, according to the Pythagorean Theorem a^2 + b^2 = c^2

Let's assume that the aspect ratio is 16:9. Therefore b/a = 16/9

Now we have a system of two equations with two unknowns. We need to express everything in terms of a single unknown, so let's express a in terms of b.

Since, b/a = 16/9, by cross multiplying 16a = 9b. Therefore a=9b/16.

Now we can subsitute 9b/16 for a in the first equation

a^2+b^2=c^2 becomes (9b/16)^2 + b^2 = c^2

Squaring the nominator and the denominator of the fraction yields

81b^2/256 + b^2 = c^2

To perform the addition, we need to express b^2 as a fraction with denominator 256 which is 256b^2/256, Now we have

81b^2/256 + 256b^2/256 = c^2

Adding fractions with the same denominators is now easy and produces

337b^2/256 = c^2

Cross multiply to get

337b^2 = 256c^2

Divide both sides by 337 to get b^2

b^2=256c^2/337

Take the square root of both sides to get b

b = sqrt(256c^2/337)

Lots of complicated Pythagorean responses. This is much simpler to answer with Trigonometry.

TLDR; just multiply the diagonal by the following two coefficients, and add the bezel width, to get the width and height:

w = diag x 0.872 + 2 x bw

h = diag x 0.49 + 2 x bw

(Where diag is the diagonal size of the screen and bw is the bezel width)

Thats all you need to know to do this.

Now here’s the Teig behind it:

First, calculate the angle of the diagonal relative to the base, using tangent, which yields ::

a = tan(9/16)

This will give you an angle of 0.512 radians (or roughly 30 degrees).

Next, calculate the ratio of the height relative to the hypotenuse (the diagonal length) using arc-sine, which yields the relative proportion of opposite length over the hypotenuse for a given angle:

h = asin(0.512)

The result will be roughly h = 0.49, or 49% of the diagonal.

Finally, get the ratio of eidth to hypotenuse using arc-cosine:

w = acos(0.512)

The result is roughly w = 0.872, or 87.2% of the diagonal.

that’s all the math! Enjoy!

6 0
3 years ago
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