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3 years ago

If tan(theta) is 5/12 and theta is an acute angle, find sin(theta)

Mathematics

1 answer:

navik [9.2K]3 years ago

7 0

Comment

The tangent represents the sides making up the right angle in a right angle triangle. To find out the answer to what you have asked, the simplest way is to assume that you are talking about a right angle triangle.

Step One

Find the hypotenuse. Use a variation of the Pythagorean Theorem.

opposite^2 + adjacent^2 = hypotenuse^2

5^2 + 12^2 = x^2

25 + 144 = x^2

x^2 = 169

sqrt(x^2) = sqrt(169)

x = 13

Step Two

Find the sine.

When the tangent is given, the opposite in this case is 5.

That's because the opposite is always the numerator of a tangent.

Sin(theta) = 5/13 Answer

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Pls help! ill give brainless to the best answer !! what is 25% of 75? show your work.

Nana76 [90]

Answer:

18.75

Step-by-step explanation:

25% of 75 =

0.25 x 75 =

18.75

Hope that helps!

4 0

3 years ago

Read 2 more answers

Suppose that the distribution of typing speed in words per minute (wpm) for experienced typists using a new type of split keyboa

KengaRu [80]

Answer:

a. 0.5 or 50%

b. 0.496 or 49.6%

c. 0.8185 or 81.85%

d. Yes, it would be just 0.0013 or 0.13% of probability to find a typist whose speed exceeds 105 wpm

e. 0.0252 or 2.52%

f. The qualifying speed would be 47.4 wpm.

Step-by-step explanation:

a. Let's find the z-score this way:

μ = 60 σ= 15

z-score = (x - μ)/σ

z-score = (60 - 60)/15

z-score = 0

Now, let's calculate the p value for z-score = 0, using the z-table:

p (z=0) = 0.5 or 50%

b. z-score = (x - μ)/σ

z-score = (59.9 - 60)/15

z-score = -0.01

Now, let's calculate the p value for z-score = -.0.01, using the z-table:

p (z = -0.01) = 0.496 or 49.6%

If the question were less or equal than 60, a and b would have the same answer. But in this case, the question is "less than 60 wpm".

z-score = (x - μ)/σ

z-score = (45 - 60)/15

z-score = - 1

Now, let's calculate the p value for z-score = -1, using the z-table:

p (z = -1) = 0.1587

z-score = (x - μ)/σ

z-score = (90 - 60)/15

z-score = 2

Now, let's calculate the p value for z-score = 2, using the z-table:

p (z = 2) = 0.9772

In consequence,

p (-1 ≤ z ≤ 2) = 0.9772 - 0.1587 = 0.8185 or 81.85%

d. z-score = (x - μ)/σ

z-score = (105 - 60)/15

z-score = 3

Now, let's calculate the p value for z-score = 3, using the z-table:

p (z = 3) = 0.9987

In consequence,

p (z > 3) = 1 - 0.9987 = 0.0013

Yes, it would be just a 0.13% of probability to find a typist whose speed exceeds 105 wpm.

e. z-score = (x - μ)/σ

z-score = (75 - 60)/15

z-score = 1

Now, let's calculate the p value for z-score = 1, using the z-table:

p (z = 1) = 0.8413

In consequence,

p (z > 1) = 1 - 0.8413 = 0.1587

and if the two typists are independently selected, then

p = 0.1587 * 0.1587

p = 0.0252 or 2.52%

f. p = 0.2, using the z-table, the z-score is -0.84, then:

z-score = (x - μ)/σ

-0.84 = (x - 60)/15

-12.6 = x - 60

-x = -60 + 12.6

-x = - 47.4

x = 47.4

The qualifying speed would be 47.4 wpm.

8 0

3 years ago

I need help asappppppppppppp

svetoff [14.1K]

Answer: Choice [D] - "power of a power" ✅

Step-by-step explanation:

Hii, do you need to know which law you should use to simplify $\sf\bigg(x^4\bigg)^9$ ?

No problem!

The law we will use here is "power of a power".

What "power of powers" means is we raise a power to a power, which is exactly what we do here: We raise x^4 to the power of 9. To simplify our expression, we multiply the powers. ( $\boldsymbol{4\cdot9}$ )