The answer is D. You can't make an equation out of this!
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Let's say we had a sample of 100 people. We'll split them into two equal groups of 50 each. The two groups will be the treatment and control groups. The treatment group, aka experimental group, is where the actual drug is given. The control group is where the fake drug is given. People in the control group must not know the pill is fake. For more info, check out the placebo effect. In short, this is when a person takes a fake pill and thinks they get better, and that positive mentality helps them actually get better.
If both the treatment and control groups improve (on average) together, then that means the fake pill is just as good as the real thing. Consequently, it means the real pill isn't effective at all. If on the other hand the experimental group does better overall compared to the control group, then we can see that the real pill is doing what it's intended to do. Of course, there are a lot of complicated factors involved, as there is with anything dealing with medicine. I haven't mentioned anything about side effects or things of that nature. In this simplified viewpoint of the world, we're only considering the one factor of whether or not the drug clears up the psoriasis on the skin.
To make things fair, it's best to randomly generate numbers so that you randomly assign people into each group. That way you have representative samples. Also, when drawing the sample of 100 people, make sure that's as random as possible to help represent the population as best as possible. The fact that the people in the control group not knowing that they are taking the fake pill means we have a single blind experiment. A double blind experiment is when even the researchers are not sure who is taking the real pill vs the fake pill. Double blind experiments are encouraged to prevent the researcher's bias from affecting the results.
To keep participants from knowing whether or not they are in the control group, the common solution is to provide a sugar pill. The pill will not cause any side effects and will not cause any improvements to health. It's simply sugar. To the participant, it seems like the real thing since they can't taste the difference or detect anything seems different.
9u means you're multiplying 9 into that vector, both components. Same with the 2v. 9*3 = 27 and 9*-1 = -9, so your new vector u is <27, -9>. Now let's do v. 2* -6 (twice) = -12, so your new v vector is <-12, -12>. Add those together now, first components of each and second components of each. 27 + (-12) = 15; -9+(-12)=-21. So the addition of those gives us a final vector with a displacement of <15, -21>
This can be written as:
"No greater than" does not necessarily mean less than, but it just means it cannot go over. So equal to or less than.
"The difference of a number and 2" can be represented as "n - 2"
If you were to solve this inequality, you would end up getting:
or
Hope this helps! :)
