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2 years ago

If p(a) = 0.50, p(b) = 0.60, and p(a intersection

1 answer:

5 0

Use the identity P(A ∪ B) = P(A)+P(B)-P(A ∩ B)

P(A)=0.50
P(B)=0.60
P(A ∪ B) = 0.30
=>
P(A ∪ B) = P(A)+P(B)-P(A ∩ B)
=(0.50+0.60)-0.30
=0.80

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PLEASE HELP ME GIVING 30 POINTS!!!

kramer

Using trigonometric identities, it is found that the sine and the tangent of the angle are given as follows:

$\sin{\theta} = \frac{1}{2}$ .

$\tan{\theta} = -\frac{\sqrt{3}}{3}$

<h3>How do we find the sine of an angle given the cosine?</h3>

We use the following identity:

$\sin^{2}{\theta} + \cos^{2}{\theta} = 1$

In this problem, the cosine is:

$\cos{\theta} = -\frac{\sqrt{3}}{2}$

Hence the sine is found as follows:

$\sin^{2}{\theta} + \left(-\frac{\sqrt{3}}{2}\right)^2 = 1$

$\sin^{2}{\theta} + \frac{3}{4} = 1$

$\sin^{2}{\theta} = \frac{1}{4}$

$\sin{\theta} = \pm \sqrt{\frac{1}{4}}$

Second quadrant, so the sine is positive, hence:

$\sin{\theta} = \frac{1}{2}$

<h3>What is the tangent of an angle?</h3>

The tangent is given by the <u>sine divided by the cosine</u>, hence:

$\tan{\theta} = \frac{\sin{\theta}}{\cos{\theta}}$

Hence:

$\tan{\theta} = \frac{\frac{1}{2}}{-\frac{\sqrt{3}}{2}}$

$\tan{\theta} = -\frac{1}{\sqrt{3}} \times \frac{\sqrt{3}}{\sqrt{3}}$

$\tan{\theta} = -\frac{\sqrt{3}}{3}$

More can be learned about trigonometric identities at brainly.com/question/7331447

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5 0

1 year ago

If y = 5x + 9 were changed to y = 5x + 6, how would the graph of the new function compare with the first one?

Talja [164]

The inital value would be different. in 5x+9 it would cross the yaxis at 9 and the other at 6

5 0

3 years ago

Read 2 more answers

2.<br> A cube has a volume of 7 to the third cubic centimeters. What is its surface area?<br> الم

Marizza181 [45]

Answer:

294

Step-by-step explanation:

since the area is 7^3, the cube's side length is 7

SA = 6*7^2 = 294

7 0

2 years ago

1 litre is approximately 1.75 pints, 1 gallon = 8 pints, calculate the approcimate number of gallons that are equal to 48000cm3

Umnica [9.8K]

Answer:

$10.5\ gal$

Step-by-step explanation:

we know that

$1,000\ cm^{3} =1\ l$

$1\ l=1.75\ pints$

$1\ gal=8\ pints$

we have

$48,000\ cm^{3}$

step 1

Convert to liters

$48,000\ cm^{3}=48,000/1,000=48\ l$

step 2

Convert to pints

$48\ l=48*1.75=84\ pints$

step 3

Convert to gallons

$84\ pints=84/8=10.5\ gal$

7 0

3 years ago

Two angles are supplementary. One angle has a measure that is five less than four times the other. What is the measure of the la

sattari [20]

Answer:

Step-by-step explanation:

4x-5+x=180. Add 5 to both sides

5x=185. Divide by 6

X=37

180-37=143

143

4 0

3 years ago