Which is the graph of f(x) = (2)-x?

In a circle with a radius of 27 2/5 in., an arc is intercepted by a central angle of 7π/4 radians. What is the arc length? Use

nexus9112 [7]

$\bf \textit{arc's length}\\\\
s=r\theta \quad 
\begin{cases}
r=radius\\
\theta =angle~in\\
\qquad radians\\
------\\
r=27\frac{2}{5}\\
\theta =\frac{7\pi }{4}
\end{cases}\implies s=27\frac{2}{5}\cdot \cfrac{7\pi }{4}\implies s=\cfrac{27\cdot 5+2}{5}\cdot \cfrac{7\pi }{4}
\\\\\\
s=\cfrac{137}{5}\cdot \cfrac{7\pi }{4}\implies s=\cfrac{959\pi }{20}$

5 0

3 years ago

Read 2 more answers

According to the U.S. Bureau of Labor Statistics, 20% of all people 16 years of age or older do volunteer work. In this age grou

Murljashka [212]

Answer:

1. P(X≥35) = 0.0183

2. P(X≤21) = 0.0183

3. P(0.18<p<0.25) = 0.7915

Step-by-step explanation:

We have the proportion for women: pw=0.22, and the proportion for men: pm=0.19.

1. We have a sample of 140 woman and we have to calculate the probability of getting 35 or more who do volunteer work.

This is equivalent to a proportion of

$p=X/n=35/140=0.25$

The standard error of the proportion is:

$\sigma_p=\sqrt{\dfrac{p(1-p)}{n}}=\sqrt{\dfrac{0.22*0.78}{300}}\\\\\\ \sigma_p=\sqrt{0.0006}=0.0239$

We calculate the z-score as:

$z=\dfrac{p-p_w}{\sigma_p}=\dfrac{0.25-0.22}{0.0239}=\dfrac{0.03}{0.0239}=0.8198$

Then, the probability of having 35 women or more who do volunteer work in this sample of 140 women is:

$P(X>35)=P(p>0.25)=P(z>2.0906)=0.0183$

2. We have to calculate the probability of having 21 or fewer women in the group who do volunteer work.

The proportion is now:

$p=X/n=21/140=0.15$

We can calculate then the z-score as:

$z=\dfrac{p-p_w}{\sigma_p}=\dfrac{0.15-0.2}{0.0239}=\dfrac{-0.05}{0.0239}=-2.0906$

Then, the probability of having 21 women or less who do volunteer work in this sample of 140 women is:

$P(X$

3. For the sample with men and women, we use the proportion for both, which is π=0.2.

The sample size is n=300.

Then, the standard error of the proportion is:

$\sigma_p=\sqrt{\dfrac{p(1-p)}{n}}=\sqrt{\dfrac{0.2*0.8}{300}}\\\\\\ \sigma_p=\sqrt{0.0005}=0.0231$

We can calculate the z-scores for p1=0.18 and p2=0.25:

$z_1=\dfrac{p_1-\pi}{\sigma_p}=\dfrac{0.18-0.2}{0.0231}=\dfrac{-0.02}{0.0231}=-0.8660\\\\\\z_2=\dfrac{p_2-\pi}{\sigma_p}=\dfrac{0.25-0.2}{0.0231}=\dfrac{0.05}{0.0231}=2.1651$

We can now calculate the probabilty of having a proportion within 0.18 and 0.25 as:

$P=P(0.18$

5 0

4 years ago

1) Would this be Mal, Lised Or B'Hon?<br><br> 2) Would it be 1560, 1650 or 1700

Fiesta28 [93]

1) The MST will have 3 connections to Mal, more than any other node.

2) The sum of weights is 250 +3*300 +500 = 1650.
.. (You can rule out 1560 as a choice because no weight ends in 10 or 60. This is simply test-taking savvy, not math.)

4 0

4 years ago

Rewrite the expression in the form a^n. (a^2/3)^-1

Slav-nsk [51]

Answer:

a^(-2/3)

Step-by-step explanation:

(a^2/3)^-1

We know x^y^z = x^(y*z)

a^(2/3*-1)

a^(-2/3)

8 0

3 years ago

Which set of real numbers BEST describes the solution set for the inequality?3x 1 =<5

Deffense [45]

<span>B. all real numbers greater than or equal to 2</span>

3 0

3 years ago