For this type of question, we have to take out the percentage of each candidate:
For Arthur
85 from 95
Convert 95 to 100
That means that we have to add 5, do the same thing with 85. Add 5 to 85 and you get 90. That means Arthur got 90% For Miguel 64 from 76. Covert 76 to 100. That means we have to add 24. Do the same thing with 64. Add 24 + 64. It equals 88% Miguel got 88%
We obtain the joint PMF directly from the joint MGF:
![\implies\mathrm{Pr}[X=x,Y=y]=\begin{cases}0.1&\text{for }x=y=0\\0.2&\text{for }x=1,y=0\\0.3&\text{for }x=0,y=1\\0.4&\text{for }x=y=1\\0&\text{otherwise}\end{cases}](https://tex.z-dn.net/?f=%5Cimplies%5Cmathrm%7BPr%7D%5BX%3Dx%2CY%3Dy%5D%3D%5Cbegin%7Bcases%7D0.1%26%5Ctext%7Bfor%20%7Dx%3Dy%3D0%5C%5C0.2%26%5Ctext%7Bfor%20%7Dx%3D1%2Cy%3D0%5C%5C0.3%26%5Ctext%7Bfor%20%7Dx%3D0%2Cy%3D1%5C%5C0.4%26%5Ctext%7Bfor%20%7Dx%3Dy%3D1%5C%5C0%26%5Ctext%7Botherwise%7D%5Cend%7Bcases%7D)
Then
![\mathrm{Pr}[X=Y]=\mathrm{Pr}[X=Y=0]+\mathrm{Pr}[X=Y=1]=0.1+0.4=\boxed{0.5}](https://tex.z-dn.net/?f=%5Cmathrm%7BPr%7D%5BX%3DY%5D%3D%5Cmathrm%7BPr%7D%5BX%3DY%3D0%5D%2B%5Cmathrm%7BPr%7D%5BX%3DY%3D1%5D%3D0.1%2B0.4%3D%5Cboxed%7B0.5%7D)
They think this because younger drivers are less experienced.
Answer: Choice C) 2
----------------------------------------------
Explanation:
Using the law of sines, we get
sin(B)/b = sin(C)/c
sin(18)/7 = sin(C)/11
0.0441452849107 = sin(C)/11
11*0.0441452849107 = sin(C)
0.4855981340177 = sin(C)
sin(C) = 0.4855981340177
C = arcsin(0.4855981340177) or C = 180-arcsin(0.4855981340177)
C = 29.0516679549861 or C = 150.948332045013
There are two possibilities for angle C because of something like sin(30) = sin(150) = 1/2 = 0.5
Those approximate values of C round to
C = 29.05 and C = 150.95
If C = 29.05, then angle A is
A = 180-B-C
A = 180-18-29.05
A = 132.95
Making this triangle possible since angle A is a positive number
If C = 150.95, then angle A is
A = 180-B-C
A = 180-18-150.95
A = 11.05
making this triangle possible since angle A is a positive number
There are two distinct triangles that can be formed.
One triangle is with the angles: A = 132.95, B = 18, C = 29.05
The other triangle is with the angles: A = 11.05, B = 18, C = 150.95
The decimal values are approximate
Answer:
135 cubes because if you multiply all the sides you get 2 7/64 so then you multiply that with 1/4 and you get 135/256. Just use the top number. I hope this helps!
