What is 0.426 divided by 0.2

Find sin 0, where is the angle shown. Give an exact value, not a decimal approximation.

Nata [24]

Answer:

$\displaystyle \sin\theta=\frac{12}{13}$

Step-by-step explanation:

Recall that in a right triangle, sine is the ratio of the opposite side to the hypotenuse:

$\displaystyle \sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$

We are actually not given the opposite side in this case. However, since we know the hypotenuse and the adjacent side, we can use the Pythagorean Theorem to find the opposite side. So:

$a^2+b^2=c^2$

Let a be the adjacent side and b be the opposite side. c will be the hypotenuse.

Substitute:

$(5)^2+b^2=(13)^2$

Solve for b:

$b=\sqrt{169-25}=\sqrt{144}=12$

So, the opposite side measures 12.

Then sine will be:

$\displaystyle \sin\theta=\frac{12}{13}$

3 0

3 years ago

How could you use the distributive property to rewrite -18+(-27)

anastassius [24]

Answer:

Here are just three examples I came up with:

-9(2 + 3)

or

-3(6 + 9)

or

-(18 + 27)

Step-by-step explanation:

To come up with these expressions, I found common factors between the numbers -18 and -27.
Then, I factored the numbers with the common factor (the common number is the number outside of the parentheses.)
When you distribute any of the expressions above, you will find they they can be simplified to -18 - 27, which is the same as -18 + (-27).

3 0

3 years ago

Read 2 more answers

Use what you know about the sum of the angles in a triangle together with the properties of supplementary angles to calculate th

Len [333]

Answer:

a = 35°; b = 50°; c = 85°; d = 30°

Step-by-step explanation:

a = 35° because a + 80 + 65 = 180.

b = 50° because b+ 35 + 95 = 180.

c = 85° because c + 95 = 180.

d = 30° because d + 85 + 65 = 180.

5 0

3 years ago

What is the measurement of ABC?

JulsSmile [24]

Answer:

118°

Step-by-step explanation:

because 28 + 90 = 118

4 0

2 years ago

The mayor of a town saw an article that claimed the national unemployment rate is 8%. They wondered if this held true in their t

mash [69]

Answer:

Z = $\frac{0.11-0.08}{\sqrt{0.08*0.92/200} }$ = 1.6

we reject the Null hypothesis

Step-by-step explanation:

The correct test statistic

Assume :

Null Hypothesis : H_0 : p = 0.08

Alternative hypothesis : H_a : p ≠ 0.08

p = proportion of residents that are unemployed

x = unemployed residents = 22

n = sample size = 200

To get the sample of the population that is unemployed we use this equation

$p = \frac{X}{n}$ = 22 / 200 = 0.11

now we apply the test of of significance of single proportion

= Z = $\frac{p - P}{\sqrt{pq/n} }$

therefore Z = $\frac{0.11-0.08}{\sqrt{0.08*0.92/200} }$ = 1.6

Therefore we reject the Null hypothesis

3 0

3 years ago