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3 years ago

Find the value of x from the given figure:

Mathematics

2 answers:

zubka84 [21]3 years ago

7 0

Answer:

60°

Step-by-step explanation:

2x and x are linear pair,

=> 2x + x = 180

=> 3x = 180

=> x = 180/3

=> x = 60°

=>2x =120°

Fiesta28 [93]3 years ago

3 0

Answer:

x = 60

Step-by-step explanation:

x + 2x = 180 {linear pair}

Combine like terms

3x = 180

Divide both sides by 3

x = 180/3

x = 60

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Suppose the proportion X of surface area in a randomly selected quadrat that is covered by a certain plant has a standard beta d

dem82 [27]

Answer:

(a) The value of E (X) is 4/7.

The value of V (X) is 3/98.

(b) The value of P (X ≤ 0.5) is 0.3438.

Step-by-step explanation:

The random variable X is defined as the proportion of surface area in a randomly selected quadrant that is covered by a certain plant.

The random variable X follows a standard beta distribution with parameters α = 4 and β = 3.

The probability density function of X is as follows:

$f(x) = \frac{x^{\alpha-1}(1-x)^{\beta-1}}{B(\alpha,\beta)} ; \hspace{.3in}0 \le x \le 1;\ \alpha, \beta > 0$

Here, B (α, β) is:

$B(\alpha,\beta)=\frac{(\alpha-1)!\cdot\ (\beta-1)!}{((\alpha+\beta)-1)!}$

$=\frac{(4-1)!\cdot\ (3-1)!}{((4+3)-1)!}\\\\=\frac{6\times 2}{720}\\\\=\frac{1}{60}$

So, the pdf of X is:

$f(x) = \frac{x^{4-1}(1-x)^{3-1}}{1/60}=60\cdot\ [x^{3}(1-x)^{2}];\ 0\leq x\leq 1$

(a)

Compute the value of E (X) as follows:

$E (X)=\frac{\alpha }{\alpha +\beta }$

$=\frac{4}{4+3}\\\\=\frac{4}{7}$

The value of E (X) is 4/7.

Compute the value of V (X) as follows:

$V (X)=\frac{\alpha\ \cdot\ \beta}{(\alpha+\beta)^{2}\ \cdot\ (\alpha+\beta+1)}$

$=\frac{4\cdot\ 3}{(4+3)^{2}\cdot\ (4+3+1)}\\\\=\frac{12}{49\times 8}\\\\=\frac{3}{98}$

The value of V (X) is 3/98.

(b)

Compute the value of P (X ≤ 0.5) as follows:

$P(X\leq 0.50) = \int\limits^{0.50}_{0}{60\cdot\ [x^{3}(1-x)^{2}]} \, dx$

$=60\int\limits^{0.50}_{0}{[x^{3}(1+x^{2}-2x)]} \, dx \\\\=60\int\limits^{0.50}_{0}{[x^{3}+x^{5}-2x^{4}]} \, dx \\\\=60\times [\dfrac{x^4}{4}+\dfrac{x^6}{6}-\dfrac{2x^5}{5}]\limits^{0.50}_{0}\\\\=60\times [\dfrac{x^4\left(10x^2-24x+15\right)}{60}]\limits^{0.50}_{0}\\\\=[x^4\left(10x^2-24x+15\right)]\limits^{0.50}_{0}\\\\=0.34375\\\\\approx 0.3438$

Thus, the value of P (X ≤ 0.5) is 0.3438.

8 0

3 years ago

Helppppppp please first is brainliest

Ad libitum [116K]

The answer is C my boi

6 0

3 years ago

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Assume that lines that appear to be tangent are tangent. O is the center of the circle. In degrees, what is the value of x?

Nastasia [14]

9514 1404 393

Answer:

145

Step-by-step explanation:

In this geometry, the central angle (x°) and the external angle (35°) are supplementary.

x° = 180° -35°

x = 145

4 0

3 years ago

A line has this equation: y= -9x-2

tia_tia [17]

Answer:

y = - 9x + 15

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = - 9x - 2 ← is in slope- intercept form

with slope m = - 9

Parallel lines have equal slopes, thus

y = - 9x + c ← is the partial equation

To find c substitute (2, - 3) into the partial equation

- 3 = - 18 + c ⇒ c = - 3 + 18 = 15

y = - 9x + 15 ← equation of parallel line

8 0

3 years ago

14. A plane traveled from California and back. It took one hour longer on the way out than it did on the way back. The plane's a

kow [346]

Answer:

C. 7 hours

Step-by-step explanation:

Let the time for the trip out be represented by t. Then the time for the return trip is t-1. The distance was the same for both trips, so we have ...

distance = speed × time

300t = 350(t -1)

300t = 350t -350 . . . . eliminate parentheses

350 = 50t . . . . . . . . . . add 350-300t

7 = t . . . . . . divide by 50

The trip out took 7 hours.

8 0

3 years ago

Find the value of x from the given figure:​

Find the value of x from the given figure: