Answer:
x = 14
Step-by-step explanation.
First I would use sine to find x's value. So ----> sin(30) = 7/x ----> x sin(30) = 7 ----> x = 7/sin(30) = 14.
You Can also find that x is equal to 14 by applying the 30, 60, 90, triangle rule. Becuase '7' opposes the 30 degree angle it is 1/2 the hypotenuse, if thats the case just multiply the 7 by 2 and you have the hypotenuse length.
Answer:
a) For this case we can use the fact that 
And for this case since we ar einterested on
and we know that the if we are below the y axis the sine would be negative then:

b) From definition we can use the fact that
and we got this:

We can use the notabl angle
and we know that :

Then we know that
correspond to 225 degrees and that correspond to the III quadrant, and we know that the sine and cosine are negative on this quadrant. So then we have this:

Step-by-step explanation:
For this case we can use the notable angls given on the picture attached.
Part a
For this case we can use the fact that 
And for this case since we ar einterested on
and we know that the if we are below the y axis the sine would be negative then:

Part b
From definition we can use the fact that
and we got this:

We can use the notabl angle
and we know that :

Then we know that
correspond to 225 degrees and that correspond to the III quadrant, and we know that the sine and cosine are negative on this quadrant. So then we have this:

Answer: 0.34
Explanation: First, you add all of the probabilities together to find the total probability when Dr. Green is missing. (You will get 0.66.) Next, you will need to subtract this from 1.00. 1 - 0.66 = 0.34. 0.34 is your final answer.
$24.00. 6,000 divided by 500 is 12 times the $2 per 500 is $24