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3 years ago

Find the value of x in the figure below. Assume that the lines are parallel.

Mathematics

1 answer:

maks197457 [2]3 years ago

8 0

Answer:

x = 30 degrees

Step-by-step explanation:

Since the lines are parallel, these angles can be seen as vertical angles, which are always the same as their opposite. Therefore,

75 = 2x + 15

To solve this, you would subtract 15 from both sides, getting you closer to finding x.

75 = 2x + 15

-15 - 15

60 = 2x

Lastly, you would divide both sides to get your value for x.

60 = 2x

/2 /2

30 = x

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$D = \left\{ (x, y) : 0 \le y \le \dfrac{x^2}2 \text{ and } 0 \le x \le 2 \right\}$

So, the line integral reduces to the double integral,

$\displaystyle \frac12 \int_0^2 \int_0^{\frac{x^2}2} x^{-\frac12} - y^{-\frac12} \, dy \, dx$

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$\displaystyle = \frac14 \int_0^2 x^{\frac32} - 2\sqrt 2 \, x \, dx$

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2 years ago

The summer income of the 3,408 students at Centennial High School last year was

Olin [163]

You want to find

P(1000 < X < 3000)

where X is normally distributed with mean 1751 and standard deviation 421. Transform X to Z, so that it follows the standard normal distribution with mean 0 and standard deviation 1 using the relation

X = 1751 + 421Z ==> Z = (X - 1751)/421

Then

P(1000 < X < 3000) = P((1000 - 1751)/421 < (X - 1751)/421 < (3000 - 1751)/421)

… ≈ P(-1.783 < Z < 2.967)

… ≈ P(Z < 2.967) - P(Z < -1.783)

… ≈ 0.9985 - 0.0373

… ≈ 0.9612

so that approximately 96.1% of the students fall in this income range.

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Step-by-step explanation:

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