You drive 720 miles in eight hours. How many Miles do you drive in one hour?

Ethan is watching a satellite launch from an observation spot 1 mile away. Find the angle of elevation from Ethan to the satelli

Thepotemich [5.8K]

Answer:

$\theta=80.53^{\circ}$

Step-by-step explanation:

From the attached figure, AB is the height of the satellite and the distance between Ethan and the ground is 1 mile.

We can find the angle of elevation from Ethan to the satellite using trigonometry as follows :

$\tan\theta=\dfrac{P}{B}\\\\\tan\theta=\dfrac{6}{1}\\\\\theta=\tan^{-1}(6)\\\\\theta=80.53^{\circ}$

So, the angle of elevation is 80.53 degrees.

3 0

3 years ago

What is the probability that a random person who tests positive for a certain blood disease actually has the disease, if we know

xeze [42]

Answer:

Step-by-step explanation:

Hello!

Any medical test used to detect certain sicknesses have several probabilities associated with their results.

Positive (test is +) ⇒ P(+)

True positive (test is + and the patient is sick) ⇒ P(+ ∩ S)

False-positive (test is + but the patient is healthy) ⇒P(+ ∩ H)

Negative (test is -) ⇒ P(-)

True negative (test is - and the patient is healthy) ⇒ P(- ∩ H)

False-negative (test is - but the patient is sick) ⇒ P(- ∩ S)

The sensibility of the test is defined as the capacity of the test to detect the sickness in sick patients (true positive rate).

⇒ P(+/S) = P(+ ∩ S)

P(S)

The specificity of the test is the capacity of the test to have a negative result when the patients are truly healthy (true negative rate)

⇒ P(-/H) = P(- ∩ H)

P(H)

For this particular blood disease the following probabilities are known:

1% of the population has the disease: P(S)= 0.01

95% of those who are sick, test positive for it: P(+/S)= 0.95 (sensibility of the test)

2% of those who don't have the disease, test positive for it: P(+/H)= 0.02

The probability of a person having the blood sickness given that the test was positive is:

P(S/+)= P(+ ∩ S)

P(+)

The first step you need to calculate the intersection between both events + and S, for that you will use the information about the sickness prevalence in the population and the sensibility of the test:

P(+/S) = P(+ ∩ S)

P(S)

P(+/S)* P(S) = P(+ ∩ S)

P(+ ∩ S) = 0.95*0.01= 0.0095

The second step is to calculate the probability of the test being positive:

P(+)= P(+ ∩ S) + P(+ ∩ H)

Now we know that 1% of the population has the blood sickness, wich means that 99% of the population doesn't have it, symbolically: P(H)= 0.99

Then you can clear the value of P(+ ∩ H):

P(+/H) = P(+ ∩ H)

P(H)

P(+/H)*P(H) = P(+ ∩ H)

P(+ ∩ H) = 0.02*0.99= 0.0198

Next you can calculate P(+):

P(+)= P(+ ∩ S) + P(+ ∩ H)= 0.0095 + 0.0198= 0.0293

Now you can calculate the asked probability:

P(S/+)= P(+ ∩ S) = 0.0095 = 0.32

P(+) 0.0293

I hope it helps!

6 0

2 years ago

Let cos A = <img src="https://tex.z-dn.net/?f=1%2F%5Csqrt%7B10%7D" id="TexFormula1" title="1/\sqrt{10}" alt="1/\sqrt{10}" align=

Rzqust [24]

Umm i’m sorry but what is the question here .

This isn’t english

3 0

2 years ago

Point A' is the image of point A when point A is rotated about the origin B. What angle in the counterclockwise direction is

Elza [17]

9514 1404 393

Answer:

90° CCW

Step-by-step explanation:

The slope of BA is -1/3. The slope of BA' is 3, so the slopes are opposite reciprocals of one another. These segments are perpendicular, meaning the angle between them is 90°.

Point A' has been rotated 90° CCW about point B.

8 0

2 years ago

Omar wanted to fill his bathtub. His faucet poured water at a rate of 9 liters per minute. Omar forgot to plug the drain. So 12

vladimir1956 [14]

Answer:

162/9 = 18 minutes

Step-by-step explanation:

5 0

2 years ago