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3 years ago

The probability distribution for a

Mathematics

1 answer:

Tpy6a [65]3 years ago

3 0

Answer:

$P(x \le -3) =0.30$

Step-by-step explanation:

Given

The attached probability distribution of x

Required

Find $P(x \le -3)$

To do this, we consider all values of x less than or equal to-3.

So, we have:

$P(x \le -3) =P(x=-5) + P(x = -3)$

From the table:

$P(x=-5) = 0.17$

$P(x = -3) = 0.13$

So, the equation becomes

$P(x \le -3) =P(x=-5) + P(x = -3)$

$P(x \le -3) =0.17 + 0.13$

$P(x \le -3) =0.30$

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What is the exact value of sin(theta + beta)?

NISA [10]

Answer: $\frac{-3\sqrt{13}+4\sqrt{3}}{20}$

This is the single fraction of -3*sqrt(13)+4*sqrt(3) up top all over 20.

sqrt = square root

=======================================================

Explanation:

Angle theta is between pi and 3pi/2. This places the angle in quadrant Q3 where both cosine and sine are negative

Use the pythagorean trig identity to get the following:

$\sin^2 \theta + \cos^2 \theta = 1\\\\\sin^2 \theta + \left(-\frac{\sqrt{3}}{4}\right)^2 = 1\\\\\sin^2 \theta + \frac{3}{16} = 1\\\\\sin^2 \theta = 1 - \frac{3}{16}\\\\\sin^2 \theta = \frac{16}{16} - \frac{3}{16}\\\\\sin^2 \theta = \frac{16-3}{16}\\\\\sin^2 \theta = \frac{13}{16}\\\\\sin \theta = -\sqrt{\frac{13}{16}} \ \text{ ... sine is negative in Q3}\\\\\sin \theta = -\frac{\sqrt{13}}{\sqrt{16}}\\\\\sin \theta = -\frac{\sqrt{13}}{4}\\\\$

Angle beta is in Q1 where sine and cosine are positive.

Draw a right triangle with legs 3 and 4. The hypotenuse is 5 through the pythagorean theorem. In other words, we have a 3-4-5 right triangle.

Since $\tan \beta = \frac{3}{4}$ , this means $\sin \beta = \frac{3}{5} \ \text{ and } \ \cos \beta = \frac{4}{5}$

Use these ideas:

sin = opposite/hypotenuse
cos = adjacent/hypotenuse
tan = opposite/adjacent

In this case we have: opposite = 3, adjacent = 4, hypotenuse = 5.

-------------------------------------

To recap:

$\cos \theta = -\frac{\sqrt{3}}{4}\\\\\sin \theta = -\frac{\sqrt{13}}{4}\\\\\cos \beta = \frac{3}{5}\\\\\sin \beta = \frac{4}{5}\\\\$

They lead to this

$\sin\left(\theta + \beta\right) = \sin \theta * \cos \beta - \cos \theta * \sin \beta\\\\\sin\left(\theta + \beta\right) = -\frac{\sqrt{13}}{4} * \frac{3}{5} - \left(-\frac{\sqrt{3}}{4}\right) * \frac{4}{5}\\\\\sin\left(\theta + \beta\right) = -\frac{3\sqrt{13}}{20}+\frac{4\sqrt{3}}{20}\\\\\sin\left(\theta + \beta\right) = \frac{-3\sqrt{13}+4\sqrt{3}}{20}\\\\$

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2 years ago

The lowest elevation in Long Beach, California, is 7 ¾ feet below sea level. The elevation of Death Valley is about 40 times low

FinnZ [79.3K]

Answer:

The elevation of Death Valley = 31/160 feet

Step-by-step explanation: Since

The lowest elevation in Long Beach, California, is 7 ¾ feet

Let say L = 7 ¾ feet

The elevation of Death Valley is about 40 times lower than the elevation of Long Beach

That is D = 1/40 of L

D = 1/40 × 31/4

D = 31/160 feet

The elevation of Death Valley is 31/160 feet

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