Answer:
1) 270 degrees
2) pi/4 rad
Step-by-step explanation:
1.) For which value of theta is sine theta = negative 1?
Given
sintheta = -1
theta = arcsin(-1)
theta = -90degrees
Since sin is negative in the third and 4th quadrant
In the third quadrant, theta = 180 + 90 = 270degrees
In the fourth quadrant, theta = 360 - 90 = 270 degrees
Hence the required value of theta is 270degrees
2) Given the radius of the circle to be 1, the y axis value will also be 1 units
Opposite = 1
adjacent = 1
hyp = √1²+1²
hyp = √2
sin theta = opp/hyp
sin theta = 1/√2
theta = arccsin(1/√2)
theta = 45 degrees
Express in radians
45 degrees = pi/4 radians
Hence the required angle in the first quadrant is pi/4 rad
Answer:
5 miles
Step-by-step explanation:
This is because if you draw a line going west and label it as 4 miles, then draw another line going south and label it 3 miles, you form a right angle, right? So, the fastest way to go back would be taking a diagonal-like route back to the beginning. Does this shape look familiar to you? Right! It's a right triangle. And do the numbers 3, 4, and 5 sound familiar to you? Yup, it's a Pythagorean triplet. If the legs of a right triangle are 3 and 4, the hypotenuse is 5. Why am I saying this? Because, in the drawing you just did, the 4 miles west and 3 miles south were the legs, and the diagonal path back to the beginning is the hypotenuse. Get it now?
Happy to help! :)
Step-by-step explanation:
B The answer is B
10.9-> 11
Answer:
And rounded up we have that n=656
Step-by-step explanation:
In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 80% of confidence, our significance level would be given by 
and 
. And the critical value would be given by:
Solution to the problem
The margin of error for the proportion interval is given by this formula:
(a)
Since we don't have prior info for the proportion of interest we can use 
as estimator. And on this case we have that 
and we are interested in order to find the value of n, if we solve n from equation (a) we got:
(b)
And replacing into equation (b) the values from part a we got:
And rounded up we have that n=656
Answer:
Step-by-step explanation:
