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2 years ago

Please help me with this thanks!!

Mathematics

2 answers:

klasskru [66]2 years ago

6 0

Answer: 47°

Step-by-Step Explanation:

In a Triangle the Sum of all the Angles equal to 180° (Angle Sum Property)

Therefore,
x + 78 + 55 = 180
x + 133 = 180
x = 180 - 133
=> x = 47

Hence, ∠x = 47°

amm18122 years ago

3 0

Answer:

x° = 47°

Step-by-step explanation:

The sum of the measurements of three interior Angles in a triangle is 180°.This is known as angle sum property.Same case is here.

78°,55° and x° are interior angles here.

So,

$78{}^{ \circ} + 55 {}^{ \circ} + x {}^{ \circ} = 180 {}^{ \circ}$

Solving for x°,

$133 {}^{ \circ} + x {}^{ \circ} = 180 {}^{ \circ}$
$x {}^{ \circ} = 180 {}^{ \circ} - 133 {}^{ \circ}$
$x {}^{ \circ} = \boxed{47 {}^{ \circ} }$

Hence,the value of x° is 47°.

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Consider a binomial experiment with n = 10 and p = 0.10. (a) Compute f(0). If required, round your answer to four decimal places

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Answer:

(a) The value of f (0) is 0.3487.

(b) The value of f (2) is 0.1937.

(d) The value of P (X ≥ 1) is 0.6513.

(e) The value of E (X) is 1.

(f) The value of V (X) is 0.9 and σ is 0.9487.

Step-by-step explanation:

The random variable X follows a Binomial distribution with parameter n = 10 and p = 0.10.

The probability mass function of X is:

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(a)

Compute the value of f (0) as follows:

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Thus, the value of f (0) is 0.3487.

(b)

Compute the value of f (2) as follows:

f (2) = P (X = 2)

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(c)

Compute the value of P (X ≤ 2) as follows:

P (X ≤ 2) = P (X = 0) + P (X = 1) + P (X = 2)

$=\sum\limits^{0}_{2} {{10\choose x}0.10^{x}(1-0.10)^{10-x}}\\=0.3487+0.3874+0.1937\\=0.9298$

Thus, the value of P (X ≤ 2) is 0.9298.

(d)

Compute the value of P (X ≥ 1) as follows:

P (X ≥ 1) = 1 - P (X < 1)

= 1 - P (X = 0)

= 1 - 0.3487

= 0.6513

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(e)

Compute the expected value of X as follows:

$E(X)=n\times p$

$=10\times 0.10\\=1$

Thus, the value of E (X) is 1.

(f)

Compute the variance of X as follows:

$V(X)=np(1-p)$

$=10\times 0.10\times (1-0.10)\\=0.90$

Compute the standard deviation of X as follows:

$SD(X)=\sqrt{V(X)}$

$=\sqrt{0.90}\\=0.94868\\\approx0.9487$

Thus, the value of V (X) is 0.9 and σ is 0.9487.

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