4) (a) For these problems, you should take time to familiarize yourself with common fractions that appear on the unit circle. 
does not appear in the unit circle unless you take the quotient 1/2 divided by sqrt(3)/2 which gives you 1/sqrt(3) which is the same as sqrt(3)/3. So our numerator is 1/2 and our denominator is sqrt(3)/2.
And remember tangent is just sin/cos. So what degree has sinx as 1/2 and and cosx as sqrt(3)/2? Well, 30 degrees does, but 30 degrees is not within the range we are given. That means they are looking for a sinx that gives us -1/2 and a cosx that gives us -sqrt(3)/2 and that is 210 degrees.
And 210 degrees in radians is 7pi/6.
I hoped that made sense.
(b) This is a lot easier. What angle gives us a cos x of -sqrt(3)/2? According to the unit circle, 150 degrees and 210 degrees does. They usually want these in radians, so the answer is 5pi/6 and 7pi/6, respectively.
5) What quadrant is radian measure 5 in?
Well 2pi or roughly 6.28 is a full circle. And 5 is slightly less than 6.28, so it is probably in quadrant IV.
But to be sure let's change 5 radian to degrees:
5 * 180/pi = 900/pi = 286.48 degrees
286.48 degrees is definitely in Q4, so we are correct.
Answer:
yes, we can reject the hypothesis
Step-by-step explanation:
The null hypothesis
H0 = mean weekly food budget for all households in this community is $98
Let´s find z
z= (x – mean) / standard deviation / √sample size
z = (100 – 98) / 10 / √100
z = 2
Using a Z table we can find probability
P (z>2) = 0.0228
Since P < α , results are significant and we can reject the hypothesis
This is what is called a literal equation. Solve it for m just like you would solve any equation for x. Isolate the term with the variable you're looking for. Do this by subtracting 4cm from both sides to give you g - 4cm = -3m. Now we need to divide by -3 to get m alone:
. Or we could lose the negative on the 3 in the denominator like this:
and
. There you go! Any one of those last three would work. It just depends upon how your teacher wants you to express your answer.
Lines are perpendicular if crossed at 90 degrees
You carry the 7 add the 6 put a little bit of whip cream and you got a cake ta da
