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SVETLANKA909090 [29]

3 years ago

5

The sum of the interior angles of a polygon is 9360 degrees, how many sides does the polygon have?

2 answers:

Norma-Jean [14]3 years ago

5 0

(n - 2) × 180 = 9360

180n - 360 = 9360
• Add 360 on both sides to remove the 360

180n = 900
• Divide both sides with 180 to get only the n aka number of sides

n = 5

ValentinkaMS [17]3 years ago

3 0

5. hope it helped love :)

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X and y are normal random variables with e(x) = 2, v(x) = 5, e(y) = 6, v(y) = 8 and cov(x,y)=2. determine the following: e(3x 2y

andriy [413]

The result for the given normal random variables are as follows;

a. E(3X + 2Y) = 18

b. V(3X + 2Y) = 77

c. P(3X + 2Y < 18) = 0.5

d. P(3X + 2Y < 28) = 0.8729

<h3>What is normal random variables?</h3>

Any normally distributed random variable having mean = 0 and standard deviation = 1 is referred to as a standard normal random variable. The letter Z will always be used to represent it.

Now, according to the question;

The given normal random variables are;

E(X) = 2, V(X) = 5, E(Y) = 6, and V(Y) = 8.

Part a.

Consider E(3X + 2Y)

$\begin{aligned}E(3 X+2 Y) &=3 E(X)+2 E(Y) \\&=(3) (2)+(2)(6 )\\&=18\end{aligned}$

Part b.

Consider V(3X + 2Y)

$\begin{aligned}V(3 X+2 Y) &=3^{2} V(X)+2^{2} V(Y) \\&=(9)(5)+(4)(8) \\&=77\end{aligned}$

Part c.

Consider P(3X + 2Y < 18)

A normal random variable is also linear combination of two independent normal random variables.

$3 X+2 Y \sim N(18,77)$

Thus,

$P(3 X+2 Y < 18)=0.5$

Part d.

Consider P(3X + 2Y < 28)

$Z=\frac{(3 X+2 Y-18)}{\sqrt{77}}$

$\begin{aligned} P(3X + 2Y < 28)&=P\left(\frac{3 X+2 Y-18}{\sqrt{77}} < \frac{28-18}{\sqrt{77}}\right) \\&=P(Z < 1.14) \\&=0.8729\end{aligned}$

Therefore, the values for the given normal random variables are found.

To know more about the normal random variables, here

brainly.com/question/23836881

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The correct question is-

X and Y are independent, normal random variables with E(X) = 2, V(X) = 5, E(Y) = 6, and V(Y) = 8. Determine the following:

a. E(3X + 2Y)

b. V(3X + 2Y)

c. P(3X + 2Y < 18)

d. P(3X + 2Y < 28)

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2 years ago

Rewrite the equation y^2 – 4y – 2x – 4 = 0 in standard form.

patriot [66]

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(y - 2)² = 2x + 8

<u> -8 </u> <u> -8 </u>

(y - 2)² - 8 = 2x

$\frac{(y - 2)^{2}}{2} - \frac{8}{2} = \frac{2x}{2}$

$\frac{1}{2}$ (y - 2)² - 4 = x

x = $\frac{1}{2}$ (y - 2)² - 4

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