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timurjin [86]
3 years ago
10

Find radius of a circle whose arclength is 57.1 meters and central angle of 1.46 radians

Mathematics
1 answer:
max2010maxim [7]3 years ago
3 0
Hint:  \bf s=r\theta\implies \cfrac{s}{\theta}=r\qquad 
\begin{cases}
s=\textit{arc's length}\\
\theta=\textit{central angle, in radians}\\
r=radius
\end{cases}
You might be interested in
A university wants to compare out-of-state applicants' mean SAT math scores (?1) to in-state applicants' mean SAT math scores (?
nordsb [41]

Answer:

d. Yes, because the confidence interval does not contain zero.

Step-by-step explanation:

We are given that the university looks at 35 in-state applicants and 35 out-of-state applicants. The mean SAT math score for in-state applicants was 540, with a standard deviation of 20.

The mean SAT math score for out-of-state applicants was 555, with a standard deviation of 25.

Firstly, the Pivotal quantity for 95% confidence interval for the difference between the population means is given by;

                P.Q. =  \frac{(\bar X_1-\bar X_2)-(\mu_1-\mu_2)}{s_p\sqrt{\frac{1}{n_1} +\frac{1}{n_2} } }  ~ t__n__1-_n__2-2

where, \bar X_1 = sample mean SAT math score for in-state applicants = 540

\bar X_2 = sample mean SAT math score for out-of-state applicants = 555

s_1 = sample standard deviation for in-state applicants = 20

s_2 = sample standard deviation for out-of-state applicants = 25

n_1 = sample of in-state applicants = 35

n_2 = sample of out-of-state applicants = 35

Also, s_p=\sqrt{\frac{(n_1-1)s_1^{2} +(n_2-1)s_2^{2} }{n_1+n_2-2} } = \sqrt{\frac{(35-1)\times 20^{2} +(35-1)\times 25^{2} }{35+35-2} }  = 22.64

<em>Here for constructing 95% confidence interval we have used Two-sample t test statistics.</em>

So, 95% confidence interval for the difference between population means (\mu_1-\mu_2) is ;

P(-1.997 < t_6_8 < 1.997) = 0.95  {As the critical value of t at 68 degree

                                         of freedom are -1.997 & 1.997 with P = 2.5%}  

P(-1.997 < \frac{(\bar X_1-\bar X_2)-(\mu_1-\mu_2)}{s_p\sqrt{\frac{1}{n_1} +\frac{1}{n_2} } } < 1.997) = 0.95

P( -1.997 \times {s_p\sqrt{\frac{1}{n_1} +\frac{1}{n_2} } } < {(\bar X_1-\bar X_2)-(\mu_1-\mu_2)} < 1.997 \times {s_p\sqrt{\frac{1}{n_1} +\frac{1}{n_2} } } ) = 0.95

P( (\bar X_1-\bar X_2)-1.997 \times {s_p\sqrt{\frac{1}{n_1} +\frac{1}{n_2} } } < (\mu_1-\mu_2) < (\bar X_1-\bar X_2)+1.997 \times {s_p\sqrt{\frac{1}{n_1} +\frac{1}{n_2} } } ) = 0.95

<u>95% confidence interval for</u> (\mu_1-\mu_2) =

[ (\bar X_1-\bar X_2)-1.997 \times {s_p\sqrt{\frac{1}{n_1} +\frac{1}{n_2} } } , (\bar X_1-\bar X_2)+1.997 \times {s_p\sqrt{\frac{1}{n_1} +\frac{1}{n_2} } } ]

=[(540-555)-1.997 \times {22.64 \times \sqrt{\frac{1}{35} +\frac{1}{35} } },(540-555)+1.997 \times {22.64 \times \sqrt{\frac{1}{35} +\frac{1}{35} } }]

= [-25.81 , -4.19]

Therefore, 95% confidence interval for the difference between population means SAT math score for in-state and out-of-state applicants is [-25.81 , -4.19].

This means that the mean SAT math scores for in-state students and out-of-state students differ because the confidence interval does not contain zero.

So, option d is correct as Yes, because the confidence interval does not contain zero.

6 0
3 years ago
Donald is 38 years younger than Natalie. 5 years ago, Natalie's age was 3 times Donald's age. How old is Donald now?
Svetlanka [38]

9514 1404 393

Answer:

  24

Step-by-step explanation:

Let d represent Donald's age now. Then Natali's age now is d+38. The age relationship 5 years ago was ...

  (d+38) -5 = 3(d -5)

  d +33 = 3d -15 . . . . . eliminate parentheses

  48 = 2d . . . . . . . . . . . add 15-d

  24 = d . . . . . . . . . . . . . divide by 2

Donald is 24 years old now.

_____

<em>Alternate solution</em>

You can also work this by considering that 5 years ago, Natalie's age was more than Donald's age by twice Donald's age then. Hence Donald was 38/2 = 19 at that time. Now, Donald is 19+5 = 24.

4 0
3 years ago
Write --X2 = 15 in standard form.
drek231 [11]
I’m assuming this is -x^2 = 15
standard form: -x^2 - 15 = 0
8 0
3 years ago
Which complex number is a distance of sqrt17 from the origin on the complex plane?
lions [1.4K]

Let z=x+iy be a complex number. The distance from this complex number to the origin is

\sqrt{(x-0)^2+(y-0)^2}=\sqrt{x^2+y^2}.

Consider all options:

A. z=2+15i, then \sqrt{2^2+15^2}=\sqrt{229}.

B. z=17+i, then \sqrt{17^2+1^2}=\sqrt{290}.

C. z=20-3i, then \sqrt{20^2+(-3)^2}=\sqrt{409}.

D. z=4-i, then \sqrt{4^2+(-1)^2}=\sqrt{17}.

Answer: correct choice is D.

4 0
4 years ago
The function D(t) defines a traveler’s distance from home, in miles, as a function of time, in hours. Which times and distances
Neporo4naja [7]

Answer:

B, D, E

Step-by-step explanation:

7 0
3 years ago
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