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3 years ago

Given two complementary angles, 3x and (x - 2). Find the value of x.

Mathematics

1 answer:

ohaa [14]3 years ago

6 0

Answer:

x = 23°

Step-by-step explanation:

Note: Complementary angles measure 90°

3x + (x - 2)° = 90°

=> 3x + x - 2° = 90°

=> 4x - 2° = 90°

Add the additive inverse of -2 to both sides of the equation

i.e 4x - 2° + 2° = 90° + 2°

=> 4x = 92°

Divide both sides of the equation by the coefficient of x which is 4

=> 4x/4 = 92°/4

x = 23°

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Answer:

a)0.067

b)0.111

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Step-by-step explanation:

We are given the following information in the question:

Mean, μ = $385

Standard Deviation, σ = $110

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$z_{score} = \displaystyle\frac{x-\mu}{\sigma}$

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c))P(domestic airfare is between $300 and $500)

$P(300 \leq x \leq 500) = P(\displaystyle\frac{300 - 385}{110} \leq z \leq \displaystyle\frac{500-385}{110}) = P(-0.77 \leq z \leq 1.04)\\\\= P(z \leq 1.04) - P(z < -0.77)\\= 0.851 - 0.239 = 0.612 = 61.2\%$

$P(300 \leq x \leq 500) = 61.2\%$

d) P(X=x) = 0.03

We have to find the value of x such that the probability is 0.03.

P(X > x)

$P( X > x) = P( z > \displaystyle\frac{x - 385}{110})=0.03$

$= 1 -P( z \leq \displaystyle\frac{x - 385}{110})=0.03$

$=P( z \leq \displaystyle\frac{x - 385}{110})=0.997$

Calculation the value from standard normal z table, we have,

$\displaystyle\frac{x - 385}{110} = 2.748\\x = 687.28$

Hence, the domestic fares must be $687.28 or greater for them to lie in the highest 3%.

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