Answer:
Step-by-step explanation:
![75 + \frac{3}{8} x = 13\frac{1}{4}\\\\75 + \frac{3}{8} x = \frac{53}{4}\\\\\frac{3}{8}x = \frac{53}{ 4} - 75\\\\\frac{3}{8}x = \frac{53-300}{4}\\\\\frac{3}{8}x = - \frac{247}{4}\\\\x = -\frac{247 \times 8}{4 \times 3} \\\\x = -\frac{494}{3}](https://tex.z-dn.net/?f=75%20%2B%20%5Cfrac%7B3%7D%7B8%7D%20x%20%3D%2013%5Cfrac%7B1%7D%7B4%7D%5C%5C%5C%5C75%20%2B%20%5Cfrac%7B3%7D%7B8%7D%20x%20%3D%20%5Cfrac%7B53%7D%7B4%7D%5C%5C%5C%5C%5Cfrac%7B3%7D%7B8%7Dx%20%3D%20%5Cfrac%7B53%7D%7B%204%7D%20-%2075%5C%5C%5C%5C%5Cfrac%7B3%7D%7B8%7Dx%20%3D%20%5Cfrac%7B53-300%7D%7B4%7D%5C%5C%5C%5C%5Cfrac%7B3%7D%7B8%7Dx%20%3D%20-%20%5Cfrac%7B247%7D%7B4%7D%5C%5C%5C%5Cx%20%3D%20-%5Cfrac%7B247%20%5Ctimes%208%7D%7B4%20%5Ctimes%203%7D%20%5C%5C%5C%5Cx%20%3D%20-%5Cfrac%7B494%7D%7B3%7D)
Answer: 26
Step-by-step explanation:
10 : 3 means for every 3 songs he kept, he deleted 10
He deleted 20
10 * 2 = 20
3 * 2 = 6
He deleted 20 songs, and kept 6.
So, he had 26 songs on his MP3 player.
20 + 6 = 26
Answer:Joanie watched 4/15 of the movie at night
Step-by-step explanation:
Let total amount of movie to watch = 1 whole since we are dealing with fractions
Amount of movie watched in the morning = 1/3
Amount watched at night = x
Amount remaining= 2/5
so that Total amount of movie to watch - Amount watched in morning and night = Amount remaining to watch
1 - ( 1/3 + x ) = 2/5
1- 2/5 = 1/3 + x
3/5 =1/3 + x
3/5 - 1/3 = x
9- 5/15 = x
x= Amount watched at night = 4/15
Answer:
If only the fittest survive in certain enviorments other animals have to evolve to live in different places
Step-by-step explanation:
Given:
In ΔWXY, x = 680 inches, w = 900 inches and ∠W=157°.
To find:
The all possible values of ∠X, to the nearest degree.
Solution:
Law of Sines:
![\dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}](https://tex.z-dn.net/?f=%5Cdfrac%7Ba%7D%7B%5Csin%20A%7D%3D%5Cdfrac%7Bb%7D%7B%5Csin%20B%7D%3D%5Cdfrac%7Bc%7D%7B%5Csin%20C%7D)
For ΔWXY,
![\dfrac{w}{\sin W}=\dfrac{x}{\sin X}=\dfrac{y}{\sin Y}](https://tex.z-dn.net/?f=%5Cdfrac%7Bw%7D%7B%5Csin%20W%7D%3D%5Cdfrac%7Bx%7D%7B%5Csin%20X%7D%3D%5Cdfrac%7By%7D%7B%5Csin%20Y%7D)
Now,
![\dfrac{w}{\sin W}=\dfrac{x}{\sin X}](https://tex.z-dn.net/?f=%5Cdfrac%7Bw%7D%7B%5Csin%20W%7D%3D%5Cdfrac%7Bx%7D%7B%5Csin%20X%7D)
![\dfrac{900}{\sin (157^\circ)}=\dfrac{680}{\sin X}](https://tex.z-dn.net/?f=%5Cdfrac%7B900%7D%7B%5Csin%20%28157%5E%5Ccirc%29%7D%3D%5Cdfrac%7B680%7D%7B%5Csin%20X%7D)
![900\sin X=680\sin (157^\circ)](https://tex.z-dn.net/?f=900%5Csin%20X%3D680%5Csin%20%28157%5E%5Ccirc%29)
![\sin X=\dfrac{680}{900}\sin (157^\circ)](https://tex.z-dn.net/?f=%5Csin%20X%3D%5Cdfrac%7B680%7D%7B900%7D%5Csin%20%28157%5E%5Ccirc%29)
![\sin X=0.295219](https://tex.z-dn.net/?f=%5Csin%20X%3D0.295219)
![X=\sin^{-1}(0.295219)](https://tex.z-dn.net/?f=X%3D%5Csin%5E%7B-1%7D%280.295219%29)
![X=17.17067](https://tex.z-dn.net/?f=X%3D17.17067)
![X\approx 17](https://tex.z-dn.net/?f=X%5Capprox%2017)
Therefore, the value of ∠X is 17 degrees.