Answer:You'll find that x = 671 miles
Step-by-step explanation:
Setting up and solving an equation of ratios is one of the fastest ways in which to solve this kind of probelm.
183 miles 3 hrs
-------------- = ------------
x 11 hrs
A central angle means an angle that is at the center of a circle and whose legs are intersecting the circle.
<h3>What is a central angle?</h3>
Your information is incomplete as the data is not given. Therefore, an overview will be given.
Central angles are shaped by an arc between the two points. When a central angle and the inscribed angle intercept the same arc, then the central angle would be the double of the inscribed angles while the inscribed angle will be half of the central angle.
Learn more about central angle on:
brainly.com/question/19758686
Answer: There are
children at the circus show.
Step-by-step explanation:
Let be "x" the total number of spectators at the circus show and "c" the number of children at the circus show.
Knowing that
of the spectators are men, we can find the remaining:
![x-\frac{1}{4}x=\frac{3}{4}x](https://tex.z-dn.net/?f=x-%5Cfrac%7B1%7D%7B4%7Dx%3D%5Cfrac%7B3%7D%7B4%7Dx)
Since
of the remaining number of spectaros are women and there are a total of 132 women, we can write the following equation:
![(\frac{2}{5})(\frac{3}{4}x)=132](https://tex.z-dn.net/?f=%28%5Cfrac%7B2%7D%7B5%7D%29%28%5Cfrac%7B3%7D%7B4%7Dx%29%3D132)
Solving for "x", we get:
![x=(132)(\frac{20}{6})\\\\x=440](https://tex.z-dn.net/?f=x%3D%28132%29%28%5Cfrac%7B20%7D%7B6%7D%29%5C%5C%5C%5Cx%3D440)
Therefore, we get that "c" is:
![c=440-\frac{1}{4}(440)-132\\\\c=198](https://tex.z-dn.net/?f=c%3D440-%5Cfrac%7B1%7D%7B4%7D%28440%29-132%5C%5C%5C%5Cc%3D198)
17 Answer: 205
<u>Step-by-step explanation:</u>
![\{1\dfrac{2}{3}+1\dfrac{5}{6}+2+...+8\dfrac{1}{3}\}\implies a_1=1\dfrac{2}{3},\ d=\dfrac{1}{6}\\\\\\a_n=a_1+d(n-1)\qquad solve\ for\ n\\\\8\dfrac{1}{3}=1\dfrac{2}{3}+\dfrac{1}{6}(n-1)\\\\\\\dfrac{25}{3}=\dfrac{5}{3}+\dfrac{1}{6}n-\dfrac{1}{6}\\\\\\\dfrac{50}{6}=\dfrac{10}{6}+\dfrac{1}{6}n-\dfrac{1}{6}\\\\\\\dfrac{41}{6}=\dfrac{1}{6}n\\\\\\\dfrac{41}{6}\cdot 6=n\\\\41=n](https://tex.z-dn.net/?f=%5C%7B1%5Cdfrac%7B2%7D%7B3%7D%2B1%5Cdfrac%7B5%7D%7B6%7D%2B2%2B...%2B8%5Cdfrac%7B1%7D%7B3%7D%5C%7D%5Cimplies%20a_1%3D1%5Cdfrac%7B2%7D%7B3%7D%2C%5C%20d%3D%5Cdfrac%7B1%7D%7B6%7D%5C%5C%5C%5C%5C%5Ca_n%3Da_1%2Bd%28n-1%29%5Cqquad%20solve%5C%20for%5C%20n%5C%5C%5C%5C8%5Cdfrac%7B1%7D%7B3%7D%3D1%5Cdfrac%7B2%7D%7B3%7D%2B%5Cdfrac%7B1%7D%7B6%7D%28n-1%29%5C%5C%5C%5C%5C%5C%5Cdfrac%7B25%7D%7B3%7D%3D%5Cdfrac%7B5%7D%7B3%7D%2B%5Cdfrac%7B1%7D%7B6%7Dn-%5Cdfrac%7B1%7D%7B6%7D%5C%5C%5C%5C%5C%5C%5Cdfrac%7B50%7D%7B6%7D%3D%5Cdfrac%7B10%7D%7B6%7D%2B%5Cdfrac%7B1%7D%7B6%7Dn-%5Cdfrac%7B1%7D%7B6%7D%5C%5C%5C%5C%5C%5C%5Cdfrac%7B41%7D%7B6%7D%3D%5Cdfrac%7B1%7D%7B6%7Dn%5C%5C%5C%5C%5C%5C%5Cdfrac%7B41%7D%7B6%7D%5Ccdot%206%3Dn%5C%5C%5C%5C41%3Dn)
![\text{Now use the sum formula:}\\\\S_n=\dfrac{a_1+a_n}{2}\cdot n\\\\\\S_{41}=\dfrac{1\dfrac{2}{3}+8\dfrac{1}{3}}{2}\cdot 41\\\\\\.\quad =\dfrac{10}{2}\cdot 41\\\\\\.\quad =5\cdot 41\\\\.\quad =\large\boxed{205}](https://tex.z-dn.net/?f=%5Ctext%7BNow%20use%20the%20sum%20formula%3A%7D%5C%5C%5C%5CS_n%3D%5Cdfrac%7Ba_1%2Ba_n%7D%7B2%7D%5Ccdot%20n%5C%5C%5C%5C%5C%5CS_%7B41%7D%3D%5Cdfrac%7B1%5Cdfrac%7B2%7D%7B3%7D%2B8%5Cdfrac%7B1%7D%7B3%7D%7D%7B2%7D%5Ccdot%2041%5C%5C%5C%5C%5C%5C.%5Cquad%20%3D%5Cdfrac%7B10%7D%7B2%7D%5Ccdot%2041%5C%5C%5C%5C%5C%5C.%5Cquad%20%3D5%5Ccdot%2041%5C%5C%5C%5C.%5Cquad%20%3D%5Clarge%5Cboxed%7B205%7D)
18 Answer: 1968
<u>Step-by-step explanation:</u>
![a_1=-6,\ d=2,\ n=48, \quad \text{solve for }a_{48}\\\\a_{n}=a_1+d(n-1)\\\\a_{48}=-6+2(48-1)\\\\.\quad =-6+2(47)\\\\.\quad =-6+94\\\\.\quad =88](https://tex.z-dn.net/?f=a_1%3D-6%2C%5C%20d%3D2%2C%5C%20n%3D48%2C%20%5Cquad%20%5Ctext%7Bsolve%20for%20%7Da_%7B48%7D%5C%5C%5C%5Ca_%7Bn%7D%3Da_1%2Bd%28n-1%29%5C%5C%5C%5Ca_%7B48%7D%3D-6%2B2%2848-1%29%5C%5C%5C%5C.%5Cquad%20%3D-6%2B2%2847%29%5C%5C%5C%5C.%5Cquad%20%3D-6%2B94%5C%5C%5C%5C.%5Cquad%20%3D88)
![\text{Now use the sum formula:}\\\\S_n=\dfrac{a_1+a_n}{2}\cdot n\\\\\\S_{48}=\dfrac{-6+88}{2}\cdot 48\\\\\\.\quad =\dfrac{82}{2}\cdot 48\\\\\\.\quad =41\cdot 48\\\\.\quad =\large\boxed{1968}](https://tex.z-dn.net/?f=%5Ctext%7BNow%20use%20the%20sum%20formula%3A%7D%5C%5C%5C%5CS_n%3D%5Cdfrac%7Ba_1%2Ba_n%7D%7B2%7D%5Ccdot%20n%5C%5C%5C%5C%5C%5CS_%7B48%7D%3D%5Cdfrac%7B-6%2B88%7D%7B2%7D%5Ccdot%2048%5C%5C%5C%5C%5C%5C.%5Cquad%20%3D%5Cdfrac%7B82%7D%7B2%7D%5Ccdot%2048%5C%5C%5C%5C%5C%5C.%5Cquad%20%3D41%5Ccdot%2048%5C%5C%5C%5C.%5Cquad%20%3D%5Clarge%5Cboxed%7B1968%7D)
19 Answer: -116
<u>Step-by-step explanation:</u>
![\{3, -2, -7, ...\}\\a_1=3,\ d=-5,\ n=8, \quad \text{solve for }a_{8}\\\\a_{n}=a_1+d(n-1)\\\\a_{8}=3-5(8-1)\\\\.\quad =3-5(7)\\\\.\quad =3-35\\\\.\quad =-32\\\\\text{Now use the sum formula:}\\\\S_8=\dfrac{a_1+a_8}{2}\cdot 8\\\\\\S_{8}=\dfrac{3-32}{2}\cdot 8\\\\\\.\quad =\dfrac{-29}{2}\cdot 8\\\\\\.\quad =-29\cdot 4\\\\.\quad =\large\boxed{-116}](https://tex.z-dn.net/?f=%5C%7B3%2C%20-2%2C%20-7%2C%20...%5C%7D%5C%5Ca_1%3D3%2C%5C%20d%3D-5%2C%5C%20n%3D8%2C%20%5Cquad%20%5Ctext%7Bsolve%20for%20%7Da_%7B8%7D%5C%5C%5C%5Ca_%7Bn%7D%3Da_1%2Bd%28n-1%29%5C%5C%5C%5Ca_%7B8%7D%3D3-5%288-1%29%5C%5C%5C%5C.%5Cquad%20%3D3-5%287%29%5C%5C%5C%5C.%5Cquad%20%3D3-35%5C%5C%5C%5C.%5Cquad%20%3D-32%5C%5C%5C%5C%5Ctext%7BNow%20use%20the%20sum%20formula%3A%7D%5C%5C%5C%5CS_8%3D%5Cdfrac%7Ba_1%2Ba_8%7D%7B2%7D%5Ccdot%208%5C%5C%5C%5C%5C%5CS_%7B8%7D%3D%5Cdfrac%7B3-32%7D%7B2%7D%5Ccdot%208%5C%5C%5C%5C%5C%5C.%5Cquad%20%3D%5Cdfrac%7B-29%7D%7B2%7D%5Ccdot%208%5C%5C%5C%5C%5C%5C.%5Cquad%20%3D-29%5Ccdot%204%5C%5C%5C%5C.%5Cquad%20%3D%5Clarge%5Cboxed%7B-116%7D)