Answer:
The second option
Step-by-step explanation:
Please find attached the complete question in the attached image
the proportion of students that like the silver calculator is 0.4 while the proportion of students that like the black calculator is 0.6. More students like the black calculator
the proportion of students that prefer the black model 77 calculator is 0.3 while the proportion of students that prefer the silver model 55 is 0.25. More students prefer the black model 77 calculator
the proportion of students that prefer the model 66 calculator is 0.15 while the proportion of students that prefer the model 55 calculator is 0.35. More students prefer the model 55
the fewest student prefer the silver model 66 calculator because it has the lowest proportion
Write them out as a fraction then reduce them. If theyre the same then its proportional.
25/45 can be cancelled down to 5/9
15/27 can be cancelled down to 3/9
So no theyre not.
150 / 200 = 0.75
0.75 = 75%
150 of anything is 75% of 200 of the same thing.
Step-by-step explanation:

We start with Left hand side
We know that csc(x) = 1/ sin(x)
So csc(2x) is replaced by 1/sin(2x)

Also we use identity
sin(2x) = 2 sin(x) cos(x)

4 divide by 2 is 2
Now we multiply top and bottom by sin(x) because we need tan(x) in our answer



We know that sinx/ cosx = tan(x)
Also 1/ sin(x)= csc(x)
so it becomes 2csc^2(x) tan(x) , Right hand side
Hence verified
There is no image but I am happy to help if you attach one