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nikdorinn [45]
1 year ago
12

8 ABC please trig assignment

Mathematics
1 answer:
Papessa [141]1 year ago
6 0

Using equivalent angles, the solutions are given as follows:

a) x = \frac{15\pi}{23}.

b) x = \frac{9\pi}{62}, x = \frac{53\pi}{62}.

c) x = \frac{3\pi}{8}, \frac{11\pi}{8}

<h3>What are equivalent angles?</h3>

Each angle on the second, third and fourth quadrants will have an equivalent on the first quadrant.

For item a, we have to find the equivalent angle on the 2nd quadrant, where the sine is also positive.

Hence:

\pi - \frac{8\pi}{23} = \frac{23\pi}{23} - \frac{8\pi}{23} = \frac{15\pi}{23}

Hence x = \frac{15\pi}{23}.

For item b, if two angles are complementary, the sine of one is the cosine of the other.

Complementary angles add to 90º = 0.5pi, hence:

x + \frac{11\pi}{31} = \frac{\pi}{2}

x = \frac{31\pi}{62} - \frac{22\pi}{62}

x = \frac{9\pi}{62}

The equivalent angle on the second quadrant is:

\pi - \frac{9\pi}{62} = \frac{62\pi}{62} - \frac{9\pi}{62} = \frac{53\pi}{62}

Hence the solutions are:

x = \frac{9\pi}{62}, x = \frac{53\pi}{62}

For item c, the angles are also complementary, hence:

x + \frac{\pi}{8} = \frac{\pi}{2}

x = \frac{4\pi}{8} - \frac{\pi}{8}

x = \frac{3\pi}{8}

The tangent is also positive on the third quadrant, hence the equivalent angle is:

x = \pi + \frac{3\pi}{8} = \frac{8\pi}{8} + \frac{3\pi}{8} = \frac{11\pi}{8}

Hence the solutions are:

x = \frac{3\pi}{8}, \frac{11\pi}{8}

More can be learned about equivalent angles at brainly.com/question/28163477

#SPJ1

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Answer:

(a) The probability that the store’s revenues were at least $9,000 is 0.0233.

(b) The revenue of the store on the worst 1% of such days is $7,631.57.

Step-by-step explanation:

According to the Central Limit Theorem if we have a population with mean μ and standard deviation σ and we take appropriately huge random samples (n ≥ 30) from the population with replacement, then the distribution of the sum of values of X, i.e ∑X, will be approximately normally distributed.  

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As the sample size is quite large, i.e. <em>n</em> = 310 > 30, the central limit theorem can be applied to approximate the sampling distribution of the store’s revenues for Sundays by a normal distribution.

(a)

Compute the probability that the store’s revenues were at least $9,000 as follows:

P(S\geq 9000)=P(\frac{S-\mu_{X}}{\sigma_{X}}\geq \frac{9000-(27\times310)}{\sqrt{310}\times 18})\\\\=P(Z\geq 1.99)\\\\=1-P(Z

Thus, the probability that the store’s revenues were at least $9,000 is 0.0233.

(b)

Let <em>s</em> denote the revenue of the store on the worst 1% of such days.

Then, P (S < s) = 0.01.

The corresponding <em>z-</em>value is, -2.33.

Compute the value of <em>s</em> as follows:

z=\frac{s-\mu_{X}}{\sigma_{X}}\\\\-2.33=\frac{s-8370}{316.923}\\\\s=8370-(2.33\times 316.923)\\\\s=7631.56941\\\\s\approx \$7,631.57

Thus, the revenue of the store on the worst 1% of such days is $7,631.57.

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