Answer:
Option A ![sin(A)=\frac{9}{15}](https://tex.z-dn.net/?f=sin%28A%29%3D%5Cfrac%7B9%7D%7B15%7D)
Step-by-step explanation:
we know that
![tan(A)=sin(A)/cos(A)](https://tex.z-dn.net/?f=tan%28A%29%3Dsin%28A%29%2Fcos%28A%29)
Solve for sin(A)
![sin(A)=tan(A)cos(A)](https://tex.z-dn.net/?f=sin%28A%29%3Dtan%28A%29cos%28A%29)
we have
![tan(A)=\frac{9}{12}](https://tex.z-dn.net/?f=tan%28A%29%3D%5Cfrac%7B9%7D%7B12%7D)
![cos(A)=\frac{12}{15}](https://tex.z-dn.net/?f=cos%28A%29%3D%5Cfrac%7B12%7D%7B15%7D)
substitute
![sin(A)=\frac{9}{12}(\frac{12}{15})](https://tex.z-dn.net/?f=sin%28A%29%3D%5Cfrac%7B9%7D%7B12%7D%28%5Cfrac%7B12%7D%7B15%7D%29)
![sin(A)=\frac{9}{15}](https://tex.z-dn.net/?f=sin%28A%29%3D%5Cfrac%7B9%7D%7B15%7D)
From the table we see that 48 of the 165 shirts are red mediums, so the probability is
48/165 = 29.1 %
idk if this helps or not sorry if ot dose not help
Answer:
![y=-\frac{5}{6} + 7](https://tex.z-dn.net/?f=y%3D-%5Cfrac%7B5%7D%7B6%7D%20%2B%207)
Step-by-step explanation:
Slope-intercept formula requires us to isolate the y variable. We can do this in just a couple of steps.
1) Move 5x from the left to the right side by subtracting 5x from both sides. This cancels out the 5x on the left side, and remember, what we do to one side we must do to the other to keep the equation balanced.
![6y=-5x+42](https://tex.z-dn.net/?f=6y%3D-5x%2B42)
2) Divide both sides by 6. Again, we are cancelling out the 6 on the left but we must also divide on the right. This would mean dividing -5 and 42 by 6 to get:
![y=-\frac{5}{6} + 7](https://tex.z-dn.net/?f=y%3D-%5Cfrac%7B5%7D%7B6%7D%20%2B%207)
Answer:
![\large \boxed{\text{7.428 in}}](https://tex.z-dn.net/?f=%5Clarge%20%5Cboxed%7B%5Ctext%7B7.428%20in%7D%7D)
Step-by-step explanation:
![\begin{array}{rcl}D & = & 0.145 r^{2}\\8 & = & 0.145 r^{2}\\55.17 & = & r^{2}\\r & = & \sqrt{55.17}\\& = & \textbf{7.428 in}\\\end{array}\\\text{The radius is $\large \boxed{\textbf{7.428 in}}$ when the depth is 8 in.}](https://tex.z-dn.net/?f=%5Cbegin%7Barray%7D%7Brcl%7DD%20%26%20%3D%20%26%200.145%20r%5E%7B2%7D%5C%5C8%20%26%20%3D%20%26%200.145%20r%5E%7B2%7D%5C%5C55.17%20%26%20%3D%20%26%20r%5E%7B2%7D%5C%5Cr%20%26%20%3D%20%26%20%5Csqrt%7B55.17%7D%5C%5C%26%20%3D%20%26%20%5Ctextbf%7B7.428%20in%7D%5C%5C%5Cend%7Barray%7D%5C%5C%5Ctext%7BThe%20radius%20is%20%24%5Clarge%20%5Cboxed%7B%5Ctextbf%7B7.428%20in%7D%7D%24%20when%20the%20depth%20is%208%20in.%7D)
The graph shows the profile of your parabolic listening device,
A) The hypotenuse is the longest side of the triangle .In the figure EG is the hypotenuse.The given angle is <G=40 degrees.The side adjacent is FG= 10 units.
The question is asking us to find the trigonometry ratio which will help us find EG.We can use cos as cos is ratio of adjacent and hypotenuse.
![cos 40=\frac{10}{Hypotenuse EG.}](https://tex.z-dn.net/?f=cos%2040%3D%5Cfrac%7B10%7D%7BHypotenuse%20EG.%7D)
B) Cos 40 =0.766.
Substituting tan40 value we have:
![0.766=\frac{10}{EG}](https://tex.z-dn.net/?f=0.766%3D%5Cfrac%7B10%7D%7BEG%7D)
EG=13.05.
C)Sum of angles in triangle is 180.
<E+<F+<G=180
<E+90+40=180
<E+130=180
<E=50 degrees.
D) ![Tan 40=\frac{EF}{10}](https://tex.z-dn.net/?f=Tan%20%2040%3D%5Cfrac%7BEF%7D%7B10%7D)
EF=8.39
E) Area of triangle EFG= ![\frac{1}{2}x base x height.](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7Dx%20base%20x%20height.)
A rea of the triangle = ![\frac{1}{2}x8.39x13.05](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7Dx8.39x13.05)
Area= 54.75 square units.